(1 vs. 55) Results < UTfit

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Parameter	Input value	Full fit	SM Prediction
$\bar{\rho}$		$0.132 \pm 0.02$
$\bar{\eta}$		$0.358 \pm 0.012$
$\rho$		$0.135 \pm 0.021$
$\eta$		$0.367 \pm 0.013$
		$0.8095 \pm 0.0095$
$\lambda$	$0.2253 \pm 0.0011$	$0.22545 \pm 0.00065$
$\|V_{ub}\|$	$0.00376 \pm 0.0002$	$0.00364 \pm 0.00011$	$0.00355 \pm 0.00014$
$\|V_{cb}\|$	$0.04083 \pm 0.00045$	$0.04117 \pm 0.00043$	$0.04269 \pm 0.00099$
$\sin\theta_{12}$		$0.22545 \pm 0.00065$
$\sin\theta_{23}$		$0.04117 \pm 0.00043$
$\sin\theta_{13}$		$0.00364 \pm 0.00011$
$\delta$		$69.7 \pm 2.9$
$m_{b},{\rm {GeV}/c^{2}}$	$4.21 \pm 0.08$
$m_{c},{\rm {GeV}/c^{2}}$	$1.3 \pm 0.1$
$m_{t},{\rm {GeV}/c^{2}}$	$163.4 \pm 1.2$	$163.4 \pm 1.2$	$163.5 \pm 9.5$
$\Delta m_{s},{\rm ps^{-1}}$	$17.77 \pm 0.12$	$17.77 \pm 0.12$	$18.3 \pm 1.3$
$\Delta m_{d},{\rm ps^{-1}}$	$0.507 \pm 0.005$
$\Delta m_{K},10^{-15}{\rm ps^{-1}}$	$1.8 \pm 1.8$
$f_{B_{s}}$	$0.239 \pm 0.01$	$0.2359 \pm 0.0056$	$0.2349 \pm 0.0067$
$f_{B_{s}}/f_{B_{d}}$	$1.23 \pm 0.03$	$1.225 \pm 0.025$	$1.213 \pm 0.044$
$B_{B_{s}}/B_{B_{d}}$	$1.06 \pm 0.04$	$1.069 \pm 0.036$	$1.113 \pm 0.085$
$B_{B_{s}}$	$0.87 \pm 0.04$	$0.845 \pm 0.036$	$0.769 \pm 0.065$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$87.8 \pm 3.0$	$85.4 \pm 3.7$
$\beta, [^{\circ}]$		$22.42 \pm 0.74$	$25.2 \pm 1.6$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.705 \pm 0.018$	$0.771 \pm 0.036$
$\cos(2\beta)$	$0.87 \pm 0.13$	$0.71 \pm 0.018$	$0.639 \pm 0.043$
$2\beta+\gamma, [^{\circ}]$	$-90 \pm 56 \text{ and } 94 \pm 52$	$114.7 \pm 3.1$	$114.9 \pm 3.1$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$69.8 \pm 3.0$	$69.6 \pm 3.1$
$\|\varepsilon_{K}\|$	$0.00222994 \pm 1.04974 \times 10^{-5}$	$0.00222854 \pm 9.98004 \times 10^{-06}$	$0.00192 \pm 0.00018$
$B(B\rightarrow\tau\nu),10^{-4}$	$1.72 \pm 0.28$	$0.867 \pm 0.078$	$0.805 \pm 0.071$
$J_{cp}\times 10^{5}$		$3.09 \pm 0.11$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97425 \pm 0.00015 & 0.22549 \pm 0.00064 & (0.00364 \pm 0.00011)e^{i(-69.7 \pm 2.9)^\circ}\\ -(0.2253 \pm 0.00064)e^{i( 0.0348 \pm 0.0012)^\circ} & 0.97341 \pm 0.00015 & 0.04117 \pm 0.00043 \\ (0.00871 \pm 0.00019)e^{i(-22.46 \pm 0.73)^\circ} & -(0.04039 \pm 0.00043)e^{i( 1.089 \pm 0.038)^\circ} & 0.999145 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.132 \pm 0.02$ 95% prob:[0.092, 0.171] 99% prob:[0.074, 0.190]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.358 \pm 0.012$ 95% prob:[0.332, 0.383] 99% prob:[0.321, 0.396]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.135 \pm 0.021$ 95% prob:[0.095, 0.175] 99% prob:[0.076, 0.195]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.367 \pm 0.013$ 95% prob:[0.341, 0.393] 99% prob:[0.329, 0.406]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.8095 \pm 0.0095$ 95% prob:[0.791, 0.83] 99% prob:[0.782, 0.839]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|V_{ub}\|$

$0.00376 \pm 0.0002$ 95% prob:[0.00340, 0.00428] 99% prob:[0.00327, 0.00463]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{ub}\|$

$0.00364 \pm 0.00011$ 95% prob:[0.00342, 0.00386] 99% prob:[0.00332, 0.00399]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{ub}\|$

$0.00355 \pm 0.00014$ 95% prob:[0.00327, 0.00385] 99% prob:[0.00313, 0.00401]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|V_{ub}\|$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|V_{cb}\|$

$0.04083 \pm 0.00045$ 95% prob:[0.03995, 0.04177] 99% prob:[0.03955, 0.04217] U [0.04219, 0.04233]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{cb}\|$

$0.04117 \pm 0.00043$ 95% prob:[0.04037, 0.04209] 99% prob:[0.03995, 0.04247]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{cb}\|$

$0.04269 \pm 0.00099$ 95% prob:[0.04069, 0.0447] 99% prob:[0.03971, 0.04563]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|V_{cb}\|$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{12}$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{23}$

$0.04117 \pm 0.00043$ 95% prob:[0.04033, 0.04209] 99% prob:[0.03993, 0.04251]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{13}$

$0.00364 \pm 0.00011$ 95% prob:[0.00342,0.003867] 99% prob:[0.00332,0.00399]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\delta$

$69.7 \pm 2.9$ 95% prob:[63.9, 75.7] 99% prob:[61.1, 78.6]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,m_{t},{\rm {GeV}/c^{2}}$

Gaussian likelihood used $163.4 \pm 1.2$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.4 \pm 1.2$ 95% prob:[161, 165.7] 99% prob:[159.9, 166.9]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.5 \pm 9.5$ 95% prob:[144.7, 183.1] 99% prob:[137.6, 194.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,m_{t},{\rm {GeV}/c^{2}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\Delta m_{s},{\rm ps^{-1}}$

Gaussian likelihood used $17.77 \pm 0.12$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\Delta m_{s},{\rm ps^{-1}}$

$17.77 \pm 0.12$ 95% prob:[17.5, 18.0] 99% prob:[17.4, 18.1]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\Delta m_{s},{\rm ps^{-1}}$

$18.3 \pm 1.3$ 95% prob:[15.9, 20.9] 99% prob:[14.8, 22.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\Delta m_{s},{\rm ps^{-1}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,f_{B_{s}}$

Gaussian likelihood used $0.239 \pm 0.01$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}$

$0.2359 \pm 0.0056$ 95% prob:[0.2252, 0.2477] 99% prob:[0.22, 0.2537]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}$

$0.2349 \pm 0.0067$ 95% prob:[0.2221, 0.2491] 99% prob:[0.217, 0.2571]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,f_{B_{s}}/f_{B_{d}}$

Gaussian likelihood used $1.23 \pm 0.03$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}/f_{B_{d}}$

$1.225 \pm 0.025$ 95% prob:[1.175, 1.275] 99% prob:[1.151, 1.299]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}/f_{B_{d}}$

$1.213 \pm 0.044$ 95% prob:[1.13, 1.303] 99% prob:[1.083, 1.085] U [1.093, 1.352]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}/f_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B_{B_{s}}/B_{B_{d}}$

Gaussian likelihood used $1.06 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}/B_{B_{d}}$

$1.069 \pm 0.036$ 95% prob:[0.997, 1.141] 99% prob:[0.963, 1.179]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}/B_{B_{d}}$

$1.113 \pm 0.085$ 95% prob:[0.96, 1.279] 99% prob:[0.893, 1.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}/B_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B_{B_{s}}$

Gaussian likelihood used $0.87 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}$

$0.845 \pm 0.036$ 95% prob:[0.775, 0.919] 99% prob:[0.738, 0.954]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}$

$0.769 \pm 0.065$ 95% prob:[0.648, 0.915] 99% prob:[0.608, 0.999]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 95% prob:[81, 102.] U [161., 169] 99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\alpha, [^{\circ}]$

$87.8 \pm 3.0$ 95% prob:[82.1, 93.8] 99% prob:[79.2, 96.2]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\alpha, [^{\circ}]$

$85.4 \pm 3.7$ 95% prob:[78.3, 93.2] 99% prob:[74.5, 96.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\alpha, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\beta, [^{\circ}]$

$22.42 \pm 0.74$ 95% prob:[20.9, 23.9] 99% prob:[20.2, 24.7]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\beta, [^{\circ}]$

$25.2 \pm 1.6$ 95% prob:[22.3, 28.6] 99% prob:[21.3, 30.2]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\sin(2\beta)$

$0.705 \pm 0.018$ 95% prob:[0.669, 0.742] 99% prob:[0.651, 0.762]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\sin(2\beta)$

$0.771 \pm 0.036$ 95% prob:[0.706, 0.844] 99% prob:[0.68, 0.872] U [0.875, 0.878]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\sin(2\beta)$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\cos(2\beta)$

$0.87 \pm 0.13$ 95% prob:[0.44, 0.99] 99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\cos(2\beta)$

$0.71 \pm 0.018$ 95% prob:[0.672, 0.745] 99% prob:[0.649, 0.76]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\cos(2\beta)$

$0.639 \pm 0.043$ 95% prob:[0.544, 0.712] 99% prob:[0.507, 0.731]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\cos(2\beta)$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,2\beta+\gamma, [^{\circ}]$

$-90 \pm 56 \text{ and } 94 \pm 52$ 95% prob:[-166, 166.] 99% prob:[-179, 179]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,2\beta+\gamma, [^{\circ}]$

$114.7 \pm 3.1$ 95% prob:[108.3, 120.7] 99% prob:[105.6, 123.4]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,2\beta+\gamma, [^{\circ}]$

$114.9 \pm 3.1$ 95% prob:[108.6, 120.9] 99% prob:[105.8, 123.6]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,2\beta+\gamma, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\gamma, [^{\circ}]$

$69.8 \pm 3.0$ 95% prob:[63.9, 75.7] 99% prob:[61, 78.5]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\gamma, [^{\circ}]$

$69.6 \pm 3.1$ 95% prob:[63.4, 75.6] 99% prob:[60.5, 78.8]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\gamma, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|\varepsilon_{K}\|$

$0.00222994 \pm 1.04974\times 10^{-5}$ 95% prob:[0.00220745, 0.00224944] 99% prob:[0.00219845, 0.00225644]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|\varepsilon_{K}\|$

$0.00222854 \pm 9.98004\times 10^{-06}$ 95% prob:[0.00220858, 0.0022485] 99% prob:[0.0021986, 0.00225848]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|\varepsilon_{K}\|$

$0.00192 \pm 0.00018$ 95% prob:[0.00157, 0.00230] 99% prob:[0.00141, 0.00252]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|\varepsilon_{K}\|$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B(B\rightarrow\tau u),10^{-4}$

Gaussian likelihood used $1.72 \pm 0.28$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B(B\rightarrow\tau u),10^{-4}$

$0.867 \pm 0.078$ 95% prob:[0.721, 1.031] 99% prob:[0.661, 1.127]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B(B\rightarrow\tau u),10^{-4}$

$0.805 \pm 0.071$ 95% prob:[0.674, 0.958] 99% prob:[0.619, 1.051]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B(B\rightarrow\tau u),10^{-4}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,J_{cp}\times 10^{-5}$

$3.09 \pm 0.11$ 95% prob:[2.87, 3.30] 99% prob:[2.77, 3.42]
EPS - PDF - PNG - JPG - GIF

In principle, the presence of New Physics might affect the result of the UT analysis, changing the functional dependencies of the experimental quantities upon ρ and η. On the contrary, two constraints now available, are almost unchanged by the presence of NP: |Vub/Vcb| from semileptonic B decays and the UT angle γ from B → D(*)K decays. As usual from this fit one can gets predictions for each observable related to the Unitarity Triangle. This set of values is the minimal requirement that each model describing New Physics has to satisfy in order to be taken as a realistic description of physics beyond the Standard Model.

Parameter	Input value	Full fit
$\bar{\rho}$		$0.111 \pm 0.07$
$\bar{\eta}$		$0.381 \pm 0.03$
$\rho$		$0.114 \pm 0.071$
$\eta$		$0.391 \pm 0.031$
		$0.804 \pm 0.01$
$\lambda$		$0.22535 \pm 0.00065$
$\alpha, [^{\circ}]$		$83 \pm 10$
$\beta, [^{\circ}]$		$23.0 \pm 1.4$
$\sin(2\beta)$		$0.72 \pm 0.035$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$73 \pm 11$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97426 \pm 0.00015 & 0.22535 \pm 0.00065 & (0.00376 \pm 0.0002)e^{i(-73.8 \pm 9.4)^\circ}\\ -(0.2252 \pm 0.00065)e^{i(0.0365 \pm 0.0028)^\circ} & 0.97345 \pm 0.00015 & 0.04083 \pm 0.00045 \\ (0.00896 \text{ and } 0.01081 \pm 0.0006)e^{i(-22.9 \pm 1.4)^\circ} & -(0.03979 \pm 0.00052)e^{i(1.163 \pm 0.084)^\circ} & 0.99916 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.111 \pm 0.07$ 95% prob:[0.000, 0.230] 99% prob:[0.000, 0.298]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.381 \pm 0.03$ 95% prob:[0.311, 0.446] 99% prob:[0.264, 0.484]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.114 \pm 0.071$ 95% prob:[0.000, 0.236] 99% prob:[0.000, 0.305]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.391 \pm 0.031$ 95% prob:[0.320, 0.457] 99% prob:[0.275, 0.494]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.804 \pm 0.01$ 95% prob:[0.7850, 0.8250] 99% prob:[0.7760, 0.8360]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\lambda$

$0.22535 \pm 0.00065$ 95% prob:[0.22410, 0.22670] 99% prob:[0.22350, 0.22740]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\alpha, [^{\circ}]$

$83 \pm 10$ 95% prob:[63.9, 103.] 99% prob:[60.0, 115.]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\beta, [^{\circ}]$

$23.0 \pm 1.4$ 95% prob:[20.2, 26.5] 99% prob:[18.6, 29.0]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin(2\beta)$

$0.72 \pm 0.035$ 95% prob:[0.651, 0.802] 99% prob:[0.609, 0.851]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\gamma, [^{\circ}]$

$73 \pm 11$ 95% prob:[52.1, 94.3] 99% prob:[41.3, 104.]
EPS - PDF - PNG - JPG - GIF

It is possible to generalize the full UTfit beyond the Standard Model to all those NP models characterized by Minimal Flavour Violation, i.e. having quark mixing ruled only by the Standard Model CKM couplings (http://arxiv.org/abs/hep-ph/0007085). In fact, in this case no additional weak phases are generated and several observables entering into the Standard Model fit (the tree-level processes and the measurement of angles through the use of time dependent CP asymmetries) are not affected by the presence of New Physics. The only sizable effect we are sensitive to is a shift of the Inami-Lim function of the top contribution in meson mixing. This means that in general εK and Δmd cannot be used in a common SM and MFV framework. Also the ratio Δmd/Δms cannot be used in general, as Δms can get additional NP contributions at large tanβ. So, simply removing the information related to εK, Δmd and Δms from the full UTfit, one can obtain a more precise determination of the Universal Unitarity Triangle, which is a common starting point for the Standard Model and any MFV model.

Parameter	Input value	Full fit
$\bar{\rho}$		$0.143 \pm 0.03$
$\bar{\eta}$		$0.342 \pm 0.015$
$\rho$		$0.146 \pm 0.031$
$\eta$		$0.351 \pm 0.016$
		$0.807 \pm 0.01$
$\lambda$	$0.2253 \pm 0.0011$	$0.22545 \pm 0.00065$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$90.8 \pm 4.8$
$\beta, [^{\circ}]$		$21.73 \pm 0.74$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.688 \pm 0.018$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$67.3 \pm 4.8$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97425 \pm 0.00015 & 0.22545 \pm 0.00065 & (0.00352 \pm 0.00011)e^{i(-67.7 \pm 4.4)^\circ}\\ -(0.2253 \pm 0.00065)e^{i(0.033 \pm 0.0016)^\circ} & 0.97342 \pm 0.00015 & 0.04099 \pm 0.00046 \\ (0.00854 \pm 0.00031)e^{i(-21.66 \pm 0.73)^\circ} & -(0.04024 \pm 0.00045)e^{i(1.04 \pm 0.048)^\circ} & 0.999154 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.143 \pm 0.03$ 95% prob:[0.082, 0.204] 99% prob:[0.050, 0.238]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.342 \pm 0.015$ 95% prob:[0.310, 0.372] 99% prob:[0.293, 0.388]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.146 \pm 0.031$ 95% prob:[0.084, 0.209] 99% prob:[0.051, 0.244]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.351 \pm 0.016$ 95% prob:[0.319, 0.382] 99% prob:[0.301, 0.398]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.807 \pm 0.01$ 95% prob:[0.7870, 0.8280] 99% prob:[0.7780, 0.8390]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22545 \pm 0.00065$ 95% prob:[0.22410, 0.22670] 99% prob:[0.22360, 0.22750]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 95% prob:[81.0, 102.] U [161., 169.] 99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\alpha, [^{\circ}]$

$90.8 \pm 4.8$ 95% prob:[81.2, 100.] 99% prob:[76.4, 106.]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\beta, [^{\circ}]$

$21.73 \pm 0.74$ 95% prob:[20.2, 23.2] 99% prob:[19.6, 24.0]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\sin(2\beta)$

$0.688 \pm 0.018$ 95% prob:[0.651, 0.725] 99% prob:[0.633, 0.745]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\gamma, [^{\circ}]$

$67.3 \pm 4.8$ 95% prob:[57.5, 77.1] 99% prob:[52.0, 82.2]
EPS - PDF - PNG - JPG - GIF

The fit presented here is meant to constrain the NP contributions to |Δ F|=2 transitions by using the available experimental information on loop-mediated processes In general, NP models introduce a large number of new parameters: flavour changing couplings, short distance coefficients and matrix elements of new local operators. The specific list and the actual values of these parameters can only be determined within a given model. Nevertheless mixing processes are described by a single amplitude and can be parameterized, without loss of generality, in terms of two parameters, which quantify the difference of the complex amplitude with respect to the SM one. Thus, for instance, in the case of $B^0_q-\bar{B}^0_q$ mixing we define $C_{B_q} \, e^{2 i \phi_{B_q}} = \frac{\langle B^0_q|H_\mathrm{eff}^\mathrm{full}|\bar{B}^0_q\rangle} {\langle B^0_q|H_\mathrm{eff}^\mathrm{SM}|\bar{B}^0_q\rangle}\,, \qquad (q=d,s),$ where $H_\mathrm{eff}^\mathrm{SM}$ includes only the SM box diagrams, while $H_\mathrm{eff}^\mathrm{full}$ also includes the NP contributions. In the absence of NP effects, $C_{B_q}=1$ and $\phi_{B_q}=0$ by definition. In a similar way, one can write $C_{\epsilon_K} = \frac{\mathrm{Im}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{full}}|\bar{K}^0\rangle]} {\mathrm{Im}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{SM}}|\bar{K}^0\rangle]}\,,\qquad C_{\Delta m_K} = \frac{\mathrm{Re}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{full}}|\bar{K}^0\rangle]} {\mathrm{Re}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{SM}}|\bar{K}^0\rangle]}\,. \label{eq:ceps}$ Concerning $\Delta m_K$ , to be conservative, we add to the short-distance contribution a possible long-distance one that varies with a uniform distribution between zero and the experimental value of $\Delta m_K$ .

The experimental quantities determined from the $B^0_q-\bar{B}^0_q$ mixings are related to their SM counterparts and the NP parameters by the following relations:

$\Delta m_d^\mathrm{exp} = C_{B_d} \Delta m_d^\mathrm{SM} \,,\; \\ \sin 2 \beta^\mathrm{exp} = \sin (2 \beta^\mathrm{SM} + 2\phi_{B_d})\,,\; \\ \alpha^\mathrm{exp} = \alpha^\mathrm{SM} - \phi_{B_d}\,, \\ \Delta m_s^\mathrm{exp} = C_{B_s} \Delta m_s^\mathrm{SM} \,,\; \\ \phi_s^\mathrm{exp} = (\beta_s^\mathrm{SM} - \phi_{B_s})\,,\; \\ \Delta m_K^\mathrm{exp} = C_{\Delta m_K} \Delta m_K^\mathrm{SM} \,,\; \\ \epsilon_K^\mathrm{exp} = C_{\epsilon_K} \epsilon_K^\mathrm{SM} \,,\; \\$

in a self-explanatory notation.

All the measured observables can be written as a function of these NP parameters and the SM ones ρ and η, and additional parameters such as masses, form factors, and decay constants.

Click on the parameter name to jump to the corresponding plot

Parameter	Input value	Full fit
$\bar{\rho}$		$0.135 \pm 0.04$
$\bar{\eta}$		$0.374 \pm 0.026$
$\rho$		$0.138 \pm 0.041$
$\eta$		$0.384 \pm 0.027$
		$0.804 \pm 0.01$
$\lambda$	$0.2253 \pm 0.0011$	$0.22535 \pm 0.00065$
$C_{B_{d}}$		$0.95 \pm 0.14$
$\phi_{B_{d}}, [^{\circ}]$		$-3.1 \pm 1.7$
$C_{B_{s}}$		$0.95 \pm 0.095$
$\phi_{B_{s}}, [^{\circ}]$		$-68.2 \pm 7.6 \text{ and } -20.3 \pm 7.7$
$C_{\epsilon_{K}}$		$1.05 \pm 0.12$
$A_{SL_{d}}$	$-0.0005 \pm 0.0056$	$-0.0028 \pm 0.0024$
$A_{SL_{s}}$	$-0.0017 \pm 0.0091$	$-0.0044 \pm 0.0014$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97427 \pm 0.00015 & 0.22535 \pm 0.00065 & (0.00377 \pm 0.00021)e^{i(-70.0 \pm 5.6)^\circ}\\ -(0.22525 \pm 0.00065)e^{i(0.0358 \pm 0.0025)^\circ} & 0.97345 \pm 0.00015 & 0.04082 \pm 0.00045 \\ (0.00869 \pm 0.00039)e^{i(-23.3 \pm 1.3)^\circ} & -(0.04007 \pm 0.00044)e^{i(1.138 \pm 0.076)^\circ} & 0.99916 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.135 \pm 0.04$ 95% prob:[0.069, 0.223] 99% prob:[0.040, 0.262]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.374 \pm 0.026$ 95% prob:[0.322, 0.433] 99% prob:[0.297, 0.471]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.138 \pm 0.041$ 95% prob:[0.070, 0.228] 99% prob:[0.041, 0.269]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.384 \pm 0.027$ 95% prob:[0.330, 0.444] 99% prob:[0.305, 0.482]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.804 \pm 0.01$ 95% prob:[0.7840, 0.8240] 99% prob:[0.7750, 0.8350]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22535 \pm 0.00065$ 95% prob:[0.22410, 0.22670] 99% prob:[0.22350, 0.22750]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{d}}$

$0.95 \pm 0.14$ 95% prob:[0.70, 1.27] 99% prob:[0.59, 1.51]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{d}}, [^{\circ}]$

$-3.1 \pm 1.7$ 95% prob:[-7., 0.1] 99% prob:[-10, 2.1]
EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{d}} - C_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{d}} - A^{NP}_{d}/A^{SM}_{d}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{s}}$

$0.95 \pm 0.095$ 95% prob:[0.776, 1.162] 99% prob:[0.706, 1.295]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{s}}, [^{\circ}]$

$-68.2 \pm 7.6 \text{ and } -20.3 \pm 7.7$ 95% prob:[-81, -51] U [-38, -6.] 99% prob:[-85, -1.]
EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{s}} - C_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{s}} - A^{NP}_{s}/A^{SM}_{s}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{\epsilon_{K}}$

$1.05 \pm 0.12$ 95% prob:[0.82, 1.34] 99% prob:[-0.8, -0.8] U [0.70, 1.60]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{d}}$

Gaussian likelihood used $-0.0005 \pm 0.0056$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,A_{SL_{d}}$

$-0.0028 \pm 0.0024$ 95% prob:[-0.0077, 0.00129] 99% prob:[-0.0096, 0.00431]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{s}}$

Gaussian likelihood used $-0.0017 \pm 0.0091$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,A_{SL_{s}}$

$-0.0044 \pm 0.0014$ 95% prob:[-0.0072, -0.0015] 99% prob:[-0.0087, 0.00004]
EPS - PDF - PNG - JPG - GIF

In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model and some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using Dπ(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameters, Lattice QCD calculations play a central role.

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.

The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. The interest of this procedure is to quantify the agreement of all the measured quantities by the comparison between indirect parameter determinations and their direct experimental/theortical determinations. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.

For some of the quantities we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

The color code indicates the compatibility between direct and indirect determinations, given in terms of standard deviations, as a function of the measured value and its experimental uncertainty. The crosses indicate the direct world average measurement values.

Treatement of Lattice parameters in the fits.

In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints : $\Delta m_s, \Delta m_d, \epsilon_K, B \rightarrow \tau \nu,$ . Let's consider schematically the dependence of these observable in terms of the non perturbative QCD parameters :

$\Delta m_s \propto f^2_{Bs} {B_{Bs}} \\ \Delta m_d \propto f^2_{Bd} {B_{Bd}} = \frac{f^2_{Bs}}{f^2_{Bs}/f^2_{Bd}} \times \frac{B_{Bs}}{B_{Bs}/B_{Bd}} \\ Br(B \rightarrow \tau \nu) \propto f_{Bd}^2 = \frac{f_{Bs}^2}{f^2_{Bs}/f^2_{Bd}} \\ \epsilon_K \propto B_K \\$ .

We decide to express these observable in terms of five LQCD parameters

$f_{Bs}, \quad B_{Bs}, \quad \frac{f_{Bs}}{f_{Bd}} , \quad \frac{{B_{Bs}}}{{B_{Bd}}}, \quad B_K$

The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of $V_{ub}$ (exclusive) and $V_{cb}$ .

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Parameter	Input value	Full fit	SM Prediction
$\bar{\rho}$		$0.132 \pm 0.02$
$\bar{\eta}$		$0.358 \pm 0.012$
$\rho$		$0.135 \pm 0.021$
$\eta$		$0.367 \pm 0.013$
		$0.8095 \pm 0.0095$
$\lambda$	$0.2253 \pm 0.0011$	$0.22545 \pm 0.00065$
$\|V_{ub}\|$	$0.00376 \pm 0.0002$	$0.00364 \pm 0.00011$	$0.00355 \pm 0.00014$
$\|V_{cb}\|$	$0.04083 \pm 0.00045$	$0.04117 \pm 0.00043$	$0.04269 \pm 0.00099$
$\sin\theta_{12}$		$0.22545 \pm 0.00065$
$\sin\theta_{23}$		$0.04117 \pm 0.00043$
$\sin\theta_{13}$		$0.00364 \pm 0.00011$
$\delta$		$69.7 \pm 2.9$
$m_{b},{\rm {GeV}/c^{2}}$	$4.21 \pm 0.08$
$m_{c},{\rm {GeV}/c^{2}}$	$1.3 \pm 0.1$
$m_{t},{\rm {GeV}/c^{2}}$	$163.4 \pm 1.2$	$163.4 \pm 1.2$	$163.5 \pm 9.5$
$\Delta m_{s},{\rm ps^{-1}}$	$17.77 \pm 0.12$	$17.77 \pm 0.12$	$18.3 \pm 1.3$
$\Delta m_{d},{\rm ps^{-1}}$	$0.507 \pm 0.005$
$\Delta m_{K},10^{-15}{\rm ps^{-1}}$	$1.8 \pm 1.8$
$f_{B_{s}}$	$0.239 \pm 0.01$	$0.2359 \pm 0.0056$	$0.2349 \pm 0.0067$
$f_{B_{s}}/f_{B_{d}}$	$1.23 \pm 0.03$	$1.225 \pm 0.025$	$1.213 \pm 0.044$
$B_{B_{s}}/B_{B_{d}}$	$1.06 \pm 0.04$	$1.069 \pm 0.036$	$1.113 \pm 0.085$
$B_{B_{s}}$	$0.87 \pm 0.04$	$0.845 \pm 0.036$	$0.769 \pm 0.065$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$87.8 \pm 3.0$	$85.4 \pm 3.7$
$\beta, [^{\circ}]$		$22.42 \pm 0.74$	$25.2 \pm 1.6$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.705 \pm 0.018$	$0.771 \pm 0.036$
$\cos(2\beta)$	$0.87 \pm 0.13$	$0.71 \pm 0.018$	$0.639 \pm 0.043$
$2\beta+\gamma, [^{\circ}]$	$-90 \pm 56 \text{ and } 94 \pm 52$	$114.7 \pm 3.1$	$114.9 \pm 3.1$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$69.8 \pm 3.0$	$69.6 \pm 3.1$
$\|\varepsilon_{K}\|$	$0.00222994 \pm 1.04974 \times 10^{-5}$	$0.00222854 \pm 9.98004 \times 10^{-06}$	$0.00192 \pm 0.00018$
$B(B\rightarrow\tau\nu),10^{-4}$	$1.72 \pm 0.28$	$0.867 \pm 0.078$	$0.805 \pm 0.071$
$J_{cp}\times 10^{5}$		$3.09 \pm 0.11$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97425 \pm 0.00015 & 0.22549 \pm 0.00064 & (0.00364 \pm 0.00011)e^{i(-69.7 \pm 2.9)^\circ}\\ -(0.2253 \pm 0.00064)e^{i( 0.0348 \pm 0.0012)^\circ} & 0.97341 \pm 0.00015 & 0.04117 \pm 0.00043 \\ (0.00871 \pm 0.00019)e^{i(-22.46 \pm 0.73)^\circ} & -(0.04039 \pm 0.00043)e^{i( 1.089 \pm 0.038)^\circ} & 0.999145 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.132 \pm 0.02$ 95% prob:[0.092, 0.171] 99% prob:[0.074, 0.190]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.358 \pm 0.012$ 95% prob:[0.332, 0.383] 99% prob:[0.321, 0.396]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.135 \pm 0.021$ 95% prob:[0.095, 0.175] 99% prob:[0.076, 0.195]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.367 \pm 0.013$ 95% prob:[0.341, 0.393] 99% prob:[0.329, 0.406]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.8095 \pm 0.0095$ 95% prob:[0.791, 0.83] 99% prob:[0.782, 0.839]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|V_{ub}\|$

$0.00376 \pm 0.0002$ 95% prob:[0.00340, 0.00428] 99% prob:[0.00327, 0.00463]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{ub}\|$

$0.00364 \pm 0.00011$ 95% prob:[0.00342, 0.00386] 99% prob:[0.00332, 0.00399]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{ub}\|$

$0.00355 \pm 0.00014$ 95% prob:[0.00327, 0.00385] 99% prob:[0.00313, 0.00401]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|V_{ub}\|$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|V_{cb}\|$

$0.04083 \pm 0.00045$ 95% prob:[0.03995, 0.04177] 99% prob:[0.03955, 0.04217] U [0.04219, 0.04233]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{cb}\|$

$0.04117 \pm 0.00043$ 95% prob:[0.04037, 0.04209] 99% prob:[0.03995, 0.04247]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{cb}\|$

$0.04269 \pm 0.00099$ 95% prob:[0.04069, 0.0447] 99% prob:[0.03971, 0.04563]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|V_{cb}\|$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{12}$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{23}$

$0.04117 \pm 0.00043$ 95% prob:[0.04033, 0.04209] 99% prob:[0.03993, 0.04251]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{13}$

$0.00364 \pm 0.00011$ 95% prob:[0.00342,0.003867] 99% prob:[0.00332,0.00399]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\delta$

$69.7 \pm 2.9$ 95% prob:[63.9, 75.7] 99% prob:[61.1, 78.6]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,m_{t},{\rm {GeV}/c^{2}}$

Gaussian likelihood used $163.4 \pm 1.2$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.4 \pm 1.2$ 95% prob:[161, 165.7] 99% prob:[159.9, 166.9]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.5 \pm 9.5$ 95% prob:[144.7, 183.1] 99% prob:[137.6, 194.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,m_{t},{\rm {GeV}/c^{2}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\Delta m_{s},{\rm ps^{-1}}$

Gaussian likelihood used $17.77 \pm 0.12$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\Delta m_{s},{\rm ps^{-1}}$

$17.77 \pm 0.12$ 95% prob:[17.5, 18.0] 99% prob:[17.4, 18.1]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\Delta m_{s},{\rm ps^{-1}}$

$18.3 \pm 1.3$ 95% prob:[15.9, 20.9] 99% prob:[14.8, 22.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\Delta m_{s},{\rm ps^{-1}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,f_{B_{s}}$

Gaussian likelihood used $0.239 \pm 0.01$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}$

$0.2359 \pm 0.0056$ 95% prob:[0.2252, 0.2477] 99% prob:[0.22, 0.2537]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}$

$0.2349 \pm 0.0067$ 95% prob:[0.2221, 0.2491] 99% prob:[0.217, 0.2571]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,f_{B_{s}}/f_{B_{d}}$

Gaussian likelihood used $1.23 \pm 0.03$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}/f_{B_{d}}$

$1.225 \pm 0.025$ 95% prob:[1.175, 1.275] 99% prob:[1.151, 1.299]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}/f_{B_{d}}$

$1.213 \pm 0.044$ 95% prob:[1.13, 1.303] 99% prob:[1.083, 1.085] U [1.093, 1.352]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}/f_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B_{B_{s}}/B_{B_{d}}$

Gaussian likelihood used $1.06 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}/B_{B_{d}}$

$1.069 \pm 0.036$ 95% prob:[0.997, 1.141] 99% prob:[0.963, 1.179]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}/B_{B_{d}}$

$1.113 \pm 0.085$ 95% prob:[0.96, 1.279] 99% prob:[0.893, 1.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}/B_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B_{B_{s}}$

Gaussian likelihood used $0.87 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}$

$0.845 \pm 0.036$ 95% prob:[0.775, 0.919] 99% prob:[0.738, 0.954]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}$

$0.769 \pm 0.065$ 95% prob:[0.648, 0.915] 99% prob:[0.608, 0.999]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 95% prob:[81, 102.] U [161., 169] 99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\alpha, [^{\circ}]$

$87.8 \pm 3.0$ 95% prob:[82.1, 93.8] 99% prob:[79.2, 96.2]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\alpha, [^{\circ}]$

$85.4 \pm 3.7$ 95% prob:[78.3, 93.2] 99% prob:[74.5, 96.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\alpha, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\beta, [^{\circ}]$

$22.42 \pm 0.74$ 95% prob:[20.9, 23.9] 99% prob:[20.2, 24.7]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\beta, [^{\circ}]$

$25.2 \pm 1.6$ 95% prob:[22.3, 28.6] 99% prob:[21.3, 30.2]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\sin(2\beta)$

$0.705 \pm 0.018$ 95% prob:[0.669, 0.742] 99% prob:[0.651, 0.762]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\sin(2\beta)$

$0.771 \pm 0.036$ 95% prob:[0.706, 0.844] 99% prob:[0.68, 0.872] U [0.875, 0.878]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\sin(2\beta)$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\cos(2\beta)$

$0.87 \pm 0.13$ 95% prob:[0.44, 0.99] 99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\cos(2\beta)$

$0.71 \pm 0.018$ 95% prob:[0.672, 0.745] 99% prob:[0.649, 0.76]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\cos(2\beta)$

$0.639 \pm 0.043$ 95% prob:[0.544, 0.712] 99% prob:[0.507, 0.731]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\cos(2\beta)$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,2\beta+\gamma, [^{\circ}]$

$-90 \pm 56 \text{ and } 94 \pm 52$ 95% prob:[-166, 166.] 99% prob:[-179, 179]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,2\beta+\gamma, [^{\circ}]$

$114.7 \pm 3.1$ 95% prob:[108.3, 120.7] 99% prob:[105.6, 123.4]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,2\beta+\gamma, [^{\circ}]$

$114.9 \pm 3.1$ 95% prob:[108.6, 120.9] 99% prob:[105.8, 123.6]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,2\beta+\gamma, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\gamma, [^{\circ}]$

$69.8 \pm 3.0$ 95% prob:[63.9, 75.7] 99% prob:[61, 78.5]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\gamma, [^{\circ}]$

$69.6 \pm 3.1$ 95% prob:[63.4, 75.6] 99% prob:[60.5, 78.8]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\gamma, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|\varepsilon_{K}\|$

$0.00222994 \pm 1.04974\times 10^{-5}$ 95% prob:[0.00220745, 0.00224944] 99% prob:[0.00219845, 0.00225644]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|\varepsilon_{K}\|$

$0.00222854 \pm 9.98004\times 10^{-06}$ 95% prob:[0.00220858, 0.0022485] 99% prob:[0.0021986, 0.00225848]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|\varepsilon_{K}\|$

$0.00192 \pm 0.00018$ 95% prob:[0.00157, 0.00230] 99% prob:[0.00141, 0.00252]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|\varepsilon_{K}\|$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B(B\rightarrow\tau u),10^{-4}$

Gaussian likelihood used $1.72 \pm 0.28$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B(B\rightarrow\tau u),10^{-4}$

$0.867 \pm 0.078$ 95% prob:[0.721, 1.031] 99% prob:[0.661, 1.127]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B(B\rightarrow\tau u),10^{-4}$

$0.805 \pm 0.071$ 95% prob:[0.674, 0.958] 99% prob:[0.619, 1.051]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B(B\rightarrow\tau u),10^{-4}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,J_{cp}\times 10^{-5}$

$3.09 \pm 0.11$ 95% prob:[2.87, 3.30] 99% prob:[2.77, 3.42]
EPS - PDF - PNG - JPG - GIF

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

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%TWISTY{

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}% It is possible to generalize the full UTfit beyond the Standard Model to all those NP models characterized by Minimal Flavour Violation, i.e. having quark mixing ruled only by the Standard Model CKM couplings (http://arxiv.org/abs/hep-ph/0007085). In fact, in this case no additional weak phases are generated and several observables entering into the Standard Model fit (the tree-level processes and the measurement of angles through the use of time dependent CP asymmetries) are not affected by the presence of New Physics. The only sizable effect we are sensitive to is a shift of the Inami-Lim function of the top contribution in meson mixing. This means that in general εK and Δmd cannot be used in a common SM and MFV framework, but any New Physics contribution disappears in the case of Δmd/Δms. So, simply removing the information related to εK and Δmd from the full UTfit one can obtain a more precise determination of the Universal Unitarity Triangle, which is a common starting point for the Standard Model and any MFV model.

>
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}% It is possible to generalize the full UTfit beyond the Standard Model to all those NP models characterized by Minimal Flavour Violation, i.e. having quark mixing ruled only by the Standard Model CKM couplings (http://arxiv.org/abs/hep-ph/0007085). In fact, in this case no additional weak phases are generated and several observables entering into the Standard Model fit (the tree-level processes and the measurement of angles through the use of time dependent CP asymmetries) are not affected by the presence of New Physics. The only sizable effect we are sensitive to is a shift of the Inami-Lim function of the top contribution in meson mixing. This means that in general εK and Δmd cannot be used in a common SM and MFV framework. Also the ratio Δmd/Δms cannot be used in general, as Δms can get additional NP contributions at large tanβ. So, simply removing the information related to εK, Δmd and Δms from the full UTfit, one can obtain a more precise determination of the Universal Unitarity Triangle, which is a common starting point for the Standard Model and any MFV model.

Parameter	Input value	Full fit
$\bar{\rho}$		$0.143 \pm 0.03$
$\bar{\eta}$		$0.342 \pm 0.015$
$\rho$		$0.146 \pm 0.031$
$\eta$		$0.351 \pm 0.016$
		$0.807 \pm 0.01$
$\lambda$	$0.2253 \pm 0.0011$	$0.22545 \pm 0.00065$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$90.8 \pm 4.8$
$\beta, [^{\circ}]$		$21.73 \pm 0.74$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.688 \pm 0.018$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$67.3 \pm 4.8$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97425 \pm 0.00015 & 0.22545 \pm 0.00065 & (0.00352 \pm 0.00011)e^{i(-67.7 \pm 4.4)^\circ}\\ -(0.2253 \pm 0.00065)e^{i(0.033 \pm 0.0016)^\circ} & 0.97342 \pm 0.00015 & 0.04099 \pm 0.00046 \\ (0.00854 \pm 0.00031)e^{i(-21.66 \pm 0.73)^\circ} & -(0.04024 \pm 0.00045)e^{i(1.04 \pm 0.048)^\circ} & 0.999154 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.143 \pm 0.03$ 95% prob:[0.082, 0.204] 99% prob:[0.050, 0.238]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.342 \pm 0.015$ 95% prob:[0.310, 0.372] 99% prob:[0.293, 0.388]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.146 \pm 0.031$ 95% prob:[0.084, 0.209] 99% prob:[0.051, 0.244]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.351 \pm 0.016$ 95% prob:[0.319, 0.382] 99% prob:[0.301, 0.398]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.807 \pm 0.01$ 95% prob:[0.7870, 0.8280] 99% prob:[0.7780, 0.8390]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22545 \pm 0.00065$ 95% prob:[0.22410, 0.22670] 99% prob:[0.22360, 0.22750]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 95% prob:[81.0, 102.] U [161., 169.] 99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\alpha, [^{\circ}]$

$90.8 \pm 4.8$ 95% prob:[81.2, 100.] 99% prob:[76.4, 106.]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\beta, [^{\circ}]$

$21.73 \pm 0.74$ 95% prob:[20.2, 23.2] 99% prob:[19.6, 24.0]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\sin(2\beta)$

$0.688 \pm 0.018$ 95% prob:[0.651, 0.725] 99% prob:[0.633, 0.745]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\gamma, [^{\circ}]$

$67.3 \pm 4.8$ 95% prob:[57.5, 77.1] 99% prob:[52.0, 82.2]
EPS - PDF - PNG - JPG - GIF

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

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}% In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model and some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using Dπ(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameters, Lattice QCD calculations play a central role.

>
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}% In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model and some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using Dπ(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameters, Lattice QCD calculations play a central role.

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.

The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. The interest of this procedure is to quantify the agreement of all the measured quantities by the comparison between indirect parameter determinations and their direct experimental/theortical determinations. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.

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For some of the quantities we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

>
>

For some of the quantities we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

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The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of $V_{ub}$ (exclusive) and $V_{cb}$ .

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In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model and some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using Dπ(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameters, Lattice QCD calculations play a central role.

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.

The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. The interest of this procedure is to quantify the agreement of all the measured quantities by the comparison between indirect parameter determinations and their direct experimental/theortical determinations. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.

For some of the quantities we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

The color code indicates the compatibility between direct and indirect determinations, given in terms of standard deviations, as a function of the measured value and its experimental uncertainty. The crosses indicate the direct world average measurement values.

%TWISTY{ mode="div" showlink="Fit results: Summer 2010 (pre-ICHEP) "

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showlink="No-Lattice Fit" hidelink="No-Lattice Fit" showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" suffix="" remember="on" }% In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints : $\Delta m_s, \Delta m_d, \epsilon_K, B \rightarrow \tau \nu,$ . Let's consider schematically the dependence of these observable in terms of the non perturbative QCD parameters :

$\Delta m_s \propto f^2_{Bs} {B_{Bs}} \\ \Delta m_d \propto f^2_{Bd} {B_{Bd}} = \frac{f^2_{Bs}}{f^2_{Bs}/f^2_{Bd}} \times \frac{B_{Bs}}{B_{Bs}/B_{Bd}} \\ Br(B \rightarrow \tau \nu) \propto f_{Bd}^2 = \frac{f_{Bs}^2}{f^2_{Bs}/f^2_{Bd}} \\ \epsilon_K \propto B_K \\$ .

We decide to express these observable in terms of five LQCD parameters

$f_{Bs}, \quad B_{Bs}, \quad \frac{f_{Bs}}{f_{Bd}} , \quad \frac{{B_{Bs}}}{{B_{Bd}}}, \quad B_K$

The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of $V_{ub}$ (exclusive) and $V_{cs}$ . The "no-lattice" fit is performed removing from the fitting procedure the use of the hadronic parameters coming from lattice calculations, leaving them as free parameters of the fit. This approach allows for the possibility of making a full UT analysis without relying at all on theoretical calculations of hadronic matrix elements.

Parameter	Input value	Full fit
$\bar{\rho}$		$0.1141 \pm 0.0045 \text{ and } 0.151 \pm 0.0243$
$\bar{\eta}$		$0.3199 \pm 0.0024 \text{ and } 0.3358 \pm 0.0126$
		$0.805 \pm 0.012$
$\lambda$	$0.2253 \pm 0.0011$	$0.2254 \pm 0.0009$
$\xi$		$1.24 \pm 0.043$
$F_{B_{d}}*\sqrt{B_{d}}$		$0.2159 \pm 0.008$
$F_{B_{s}}*\sqrt{B_{s}}$		$0.2681 \pm 0.004$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$91.6 \pm 4.8$
$\beta, [^{\circ}]$		$20.45 \pm 0.03 \text{ and } 21.405 \pm 0.725$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.6605 \pm 0.0025 \text{ and } 0.682 \pm 0.016$
$\cos(2\beta)$	$0.87 \pm 0.13$	$0.737 \pm 0.018$
$2\beta+\gamma, [^{\circ}]$	$-90 \pm 56 \text{ and } 94 \pm 52$	$103.85 \pm 0.55 \text{ and } 110.8 \pm 4.3$
$\gamma, [^{\circ}]$	$-106 \pm 10 \text{ and } 74 \pm 11$	$67.0 \pm 4.8$

Full fit result for $\,\bar{\rho}$

$0.1141 \pm 0.0045 \text{ and } 0.151 \pm 0.0243$ 68% prob:[0.126, 0.175] U [0.109, 0.118] 95% prob:[0.085, 0.203] 99% prob:[0.053, 0.239]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.3199 \pm 0.0024 \text{ and } 0.3358 \pm 0.0126$ 68% prob:[0.323, 0.348] U [0.317, 0.322] 95% prob:[0.307, 0.367] 99% prob:[0.289, 0.382]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.805 \pm 0.012$ 68% prob:[0.794, 0.817] 95% prob:[0.784, 0.829] U [0.833, 0.836] 99% prob:[0.769, 0.772] U [0.776, 0.842]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 68% prob:[0.2242, 0.2265] 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.2254 \pm 0.0009$ 68% prob:[0.22450, 0.22630] 95% prob:[0.22370, 0.22730] 99% prob:[0.22290, 0.22780] U [0.22840, 0.22890]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\xi$

$1.24 \pm 0.043$ 68% prob:[1.197, 1.283] 95% prob:[1.147, 1.327] 99% prob:[1.097, 1.378]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,F_{B_{d}}*\sqrt{B_{d}}$

$0.2159 \pm 0.008$ 68% prob:[0.2079, 0.2240] 95% prob:[0.2006, 0.2353] 99% prob:[0.1929, 0.2452]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,F_{B_{s}}*\sqrt{B_{s}}$

$0.2681 \pm 0.004$ 68% prob:[0.2642, 0.2721] 95% prob:[0.2601, 0.2765] 99% prob:[0.2569, 0.2810] U [0.2840, 0.2860]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 68% prob:[85.3, 97.5] 95% prob:[81.0, 102.] U [161., 169.] 99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\alpha, [^{\circ}]$

$91.6 \pm 4.8$ 68% prob:[86.8, 96.4] 95% prob:[82.2, 101.] 99% prob:[77.2, 107.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\beta, [^{\circ}]$

$20.45 \pm 0.03 \text{ and } 21.405 \pm 0.725$ 68% prob:[20.6, 22.1] U [20.4, 20.4] 95% prob:[20.0, 22.9] 99% prob:[19.4, 23.7]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 68% prob:[0.628, 0.681] 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\sin(2\beta)$

$0.6605 \pm 0.0025 \text{ and } 0.682 \pm 0.016$ 68% prob:[0.666, 0.698] U [0.658, 0.663] 95% prob:[0.647, 0.719] 99% prob:[0.624, 0.735]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\cos(2\beta)$

$0.87 \pm 0.13$ 68% prob:[0.73, 0.99] 95% prob:[0.44, 0.99] 99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\cos(2\beta)$

$0.737 \pm 0.018$ 68% prob:[0.719, 0.755] 95% prob:[0.696, 0.765] 99% prob:[0.677, 0.781]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,2\beta+\gamma, [^{\circ}]$

$-90 \pm 56 \text{ and } 94 \pm 52$ 68% prob:[-146, -33.] U [41.6, 146.] 95% prob:[-166, 166.] 99% prob:[-179, 179.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,2\beta+\gamma, [^{\circ}]$

$103.85 \pm 0.55 \text{ and } 110.8 \pm 4.3$ 68% prob:[103.3, 104.4] U [106.5, 115.1] 95% prob:[99.70, 119.3] 99% prob:[91.40, 92.00] U [94.30, 94.60] U [95.60, 124.7]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 10 \text{ and } 74 \pm 11$ 68% prob:[-116, -96.] U [62.5, 84.7] 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\gamma, [^{\circ}]$

$67.0 \pm 4.8$ 68% prob:[62.2, 71.9] 95% prob:[56.9, 76.3] 99% prob:[51.2, 81.7]
EPS - PDF - PNG - JPG - GIF

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%TWISTY{ prefix=" " mode="div"

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Click on the parameter name to jump to the corresponding plot

Parameter	Input value	Full fit
$\bar{\rho}$		$0.135 \pm 0.04$
$\bar{\eta}$		$0.374 \pm 0.026$
$\rho$		$0.138 \pm 0.041$
$\eta$		$0.384 \pm 0.027$
		$0.804 \pm 0.01$
$\lambda$	$0.2253 \pm 0.0011$	$0.22535 \pm 0.00065$
$C_{B_{d}}$		$0.95 \pm 0.14$
$\phi_{B_{d}}, [^{\circ}]$		$-3.1 \pm 1.7$
$C_{B_{s}}$		$0.95 \pm 0.095$
$\phi_{B_{s}}, [^{\circ}]$		$-68.2 \pm 7.6 \text{ and } -20.3 \pm 7.7$
$C_{\epsilon_{K}}$		$1.05 \pm 0.12$
$A_{SL_{d}}$	$-0.0005 \pm 0.0056$	$-0.0028 \pm 0.0024$
$A_{SL_{s}}$	$-0.0017 \pm 0.0091$	$-0.0044 \pm 0.0014$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97427 \pm 0.00015 & 0.22535 \pm 0.00065 & (0.00377 \pm 0.00021)e^{i(-70.0 \pm 5.6)^\circ}\\ -(0.22525 \pm 0.00065)e^{i(0.0358 \pm 0.0025)^\circ} & 0.97345 \pm 0.00015 & 0.04082 \pm 0.00045 \\ (0.00869 \pm 0.00039)e^{i(-23.3 \pm 1.3)^\circ} & -(0.04007 \pm 0.00044)e^{i(1.138 \pm 0.076)^\circ} & 0.99916 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.135 \pm 0.04$ 95% prob:[0.069, 0.223] 99% prob:[0.040, 0.262]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.374 \pm 0.026$ 95% prob:[0.322, 0.433] 99% prob:[0.297, 0.471]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.138 \pm 0.041$ 95% prob:[0.070, 0.228] 99% prob:[0.041, 0.269]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.384 \pm 0.027$ 95% prob:[0.330, 0.444] 99% prob:[0.305, 0.482]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.804 \pm 0.01$ 95% prob:[0.7840, 0.8240] 99% prob:[0.7750, 0.8350]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22535 \pm 0.00065$ 95% prob:[0.22410, 0.22670] 99% prob:[0.22350, 0.22750]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{d}}$

$0.95 \pm 0.14$ 95% prob:[0.70, 1.27] 99% prob:[0.59, 1.51]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{d}}, [^{\circ}]$

$-3.1 \pm 1.7$ 95% prob:[-7., 0.1] 99% prob:[-10, 2.1]
EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{d}} - C_{B_{d}}$


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2D for $\,\Phi_{B_{d}} - A^{NP}_{d}/A^{SM}_{d}$


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Full fit result for $\,C_{B_{s}}$

$0.95 \pm 0.095$ 95% prob:[0.776, 1.162] 99% prob:[0.706, 1.295]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{s}}, [^{\circ}]$

$-68.2 \pm 7.6 \text{ and } -20.3 \pm 7.7$ 95% prob:[-81, -51] U [-38, -6.] 99% prob:[-85, -1.]
EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{s}} - C_{B_{s}}$


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2D for $\,\Phi_{B_{s}} - A^{NP}_{s}/A^{SM}_{s}$


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Full fit result for $\,C_{\epsilon_{K}}$

$1.05 \pm 0.12$ 95% prob:[0.82, 1.34] 99% prob:[-0.8, -0.8] U [0.70, 1.60]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{d}}$

Gaussian likelihood used $-0.0005 \pm 0.0056$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,A_{SL_{d}}$

$-0.0028 \pm 0.0024$ 95% prob:[-0.0077, 0.00129] 99% prob:[-0.0096, 0.00431]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{s}}$

Gaussian likelihood used $-0.0017 \pm 0.0091$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,A_{SL_{s}}$

$-0.0044 \pm 0.0014$ 95% prob:[-0.0072, -0.0015] 99% prob:[-0.0087, 0.00004]
EPS - PDF - PNG - JPG - GIF

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

Added:

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In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model and some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using Dπ(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameters, Lattice QCD calculations play a central role.

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.

The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. The interest of this procedure is to quantify the agreement of all the measured quantities by the comparison between indirect parameter determinations and their direct experimental/theortical determinations. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.

For some of the quantities we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

The color code indicates the compatibility between direct and indirect determinations, given in terms of standard deviations, as a function of the measured value and its experimental uncertainty. The crosses indicate the direct world average measurement values.

Treatement of Lattice parameters in the fits.

In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints : $\Delta m_s, \Delta m_d, \epsilon_K, B \rightarrow \tau \nu,$ . Let's consider schematically the dependence of these observable in terms of the non perturbative QCD parameters :

$\Delta m_s \propto f^2_{Bs} {B_{Bs}} \\ \Delta m_d \propto f^2_{Bd} {B_{Bd}} = \frac{f^2_{Bs}}{f^2_{Bs}/f^2_{Bd}} \times \frac{B_{Bs}}{B_{Bs}/B_{Bd}} \\ Br(B \rightarrow \tau \nu) \propto f_{Bd}^2 = \frac{f_{Bs}^2}{f^2_{Bs}/f^2_{Bd}} \\ \epsilon_K \propto B_K \\$ .

We decide to express these observable in terms of five LQCD parameters

$f_{Bs}, \quad B_{Bs}, \quad \frac{f_{Bs}}{f_{Bd}} , \quad \frac{{B_{Bs}}}{{B_{Bd}}}, \quad B_K$

The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of $V_{ub}$ (exclusive) and $V_{cb}$ .

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Parameter	Input value	Full fit	SM Prediction
$\bar{\rho}$		$0.132 \pm 0.02$
$\bar{\eta}$		$0.358 \pm 0.012$
$\rho$		$0.135 \pm 0.021$
$\eta$		$0.367 \pm 0.013$
		$0.8095 \pm 0.0095$
$\lambda$	$0.2253 \pm 0.0011$	$0.22545 \pm 0.00065$
$\|V_{ub}\|$	$0.00376 \pm 0.0002$	$0.00364 \pm 0.00011$	$0.00355 \pm 0.00014$
$\|V_{cb}\|$	$0.04083 \pm 0.00045$	$0.04117 \pm 0.00043$	$0.04269 \pm 0.00099$
$\sin\theta_{12}$		$0.22545 \pm 0.00065$
$\sin\theta_{23}$		$0.04117 \pm 0.00043$
$\sin\theta_{13}$		$0.00364 \pm 0.00011$
$\delta$		$69.7 \pm 2.9$
$m_{b},{\rm {GeV}/c^{2}}$	$4.21 \pm 0.08$
$m_{c},{\rm {GeV}/c^{2}}$	$1.3 \pm 0.1$
$m_{t},{\rm {GeV}/c^{2}}$	$163.4 \pm 1.2$	$163.4 \pm 1.2$	$163.5 \pm 9.5$
$\Delta m_{s},{\rm ps^{-1}}$	$17.77 \pm 0.12$	$17.77 \pm 0.12$	$18.3 \pm 1.3$
$\Delta m_{d},{\rm ps^{-1}}$	$0.507 \pm 0.005$
$\Delta m_{K},10^{-15}{\rm ps^{-1}}$	$1.8 \pm 1.8$
$f_{B_{s}}$	$0.239 \pm 0.01$	$0.2359 \pm 0.0056$	$0.2349 \pm 0.0067$
$f_{B_{s}}/f_{B_{d}}$	$1.23 \pm 0.03$	$1.225 \pm 0.025$	$1.213 \pm 0.044$
$B_{B_{s}}/B_{B_{d}}$	$1.06 \pm 0.04$	$1.069 \pm 0.036$	$1.113 \pm 0.085$
$B_{B_{s}}$	$0.87 \pm 0.04$	$0.845 \pm 0.036$	$0.769 \pm 0.065$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$87.8 \pm 3.0$	$85.4 \pm 3.7$
$\beta, [^{\circ}]$		$22.42 \pm 0.74$	$25.2 \pm 1.6$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.705 \pm 0.018$	$0.771 \pm 0.036$
$\cos(2\beta)$	$0.87 \pm 0.13$	$0.71 \pm 0.018$	$0.639 \pm 0.043$
$2\beta+\gamma, [^{\circ}]$	$-90 \pm 56 \text{ and } 94 \pm 52$	$114.7 \pm 3.1$	$114.9 \pm 3.1$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$69.8 \pm 3.0$	$69.6 \pm 3.1$
$\|\varepsilon_{K}\|$	$0.00222994 \pm 1.04974 \times 10^{-5}$	$0.00222854 \pm 9.98004 \times 10^{-06}$	$0.00192 \pm 0.00018$
$B(B\rightarrow\tau\nu),10^{-4}$	$1.72 \pm 0.28$	$0.867 \pm 0.078$	$0.805 \pm 0.071$
$J_{cp}\times 10^{5}$		$3.09 \pm 0.11$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97425 \pm 0.00015 & 0.22549 \pm 0.00064 & (0.00364 \pm 0.00011)e^{i(-69.7 \pm 2.9)^\circ}\\ -(0.2253 \pm 0.00064)e^{i( 0.0348 \pm 0.0012)^\circ} & 0.97341 \pm 0.00015 & 0.04117 \pm 0.00043 \\ (0.00871 \pm 0.00019)e^{i(-22.46 \pm 0.73)^\circ} & -(0.04039 \pm 0.00043)e^{i( 1.089 \pm 0.038)^\circ} & 0.999145 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.132 \pm 0.02$ 95% prob:[0.092, 0.171] 99% prob:[0.074, 0.190]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.358 \pm 0.012$ 95% prob:[0.332, 0.383] 99% prob:[0.321, 0.396]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.135 \pm 0.021$ 95% prob:[0.095, 0.175] 99% prob:[0.076, 0.195]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.367 \pm 0.013$ 95% prob:[0.341, 0.393] 99% prob:[0.329, 0.406]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.8095 \pm 0.0095$ 95% prob:[0.791, 0.83] 99% prob:[0.782, 0.839]
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Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|V_{ub}\|$

$0.00376 \pm 0.0002$ 95% prob:[0.00340, 0.00428] 99% prob:[0.00327, 0.00463]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{ub}\|$

$0.00364 \pm 0.00011$ 95% prob:[0.00342, 0.00386] 99% prob:[0.00332, 0.00399]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{ub}\|$

$0.00355 \pm 0.00014$ 95% prob:[0.00327, 0.00385] 99% prob:[0.00313, 0.00401]
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Compatibility Plot for $\,\|V_{ub}\|$


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Fit Input for $\,\|V_{cb}\|$

$0.04083 \pm 0.00045$ 95% prob:[0.03995, 0.04177] 99% prob:[0.03955, 0.04217] U [0.04219, 0.04233]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{cb}\|$

$0.04117 \pm 0.00043$ 95% prob:[0.04037, 0.04209] 99% prob:[0.03995, 0.04247]
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SM Fit prediction for $\,\|V_{cb}\|$

$0.04269 \pm 0.00099$ 95% prob:[0.04069, 0.0447] 99% prob:[0.03971, 0.04563]
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Compatibility Plot for $\,\|V_{cb}\|$


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Full fit result for $\,\sin\theta_{12}$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
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Full fit result for $\,\sin\theta_{23}$

$0.04117 \pm 0.00043$ 95% prob:[0.04033, 0.04209] 99% prob:[0.03993, 0.04251]
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Full fit result for $\,\sin\theta_{13}$

$0.00364 \pm 0.00011$ 95% prob:[0.00342,0.003867] 99% prob:[0.00332,0.00399]
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Full fit result for $\,\delta$

$69.7 \pm 2.9$ 95% prob:[63.9, 75.7] 99% prob:[61.1, 78.6]
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Fit Input for $\,m_{t},{\rm {GeV}/c^{2}}$

Gaussian likelihood used $163.4 \pm 1.2$
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Full Fit result for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.4 \pm 1.2$ 95% prob:[161, 165.7] 99% prob:[159.9, 166.9]
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SM Fit prediction for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.5 \pm 9.5$ 95% prob:[144.7, 183.1] 99% prob:[137.6, 194.2]
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Compatibility Plot for $\,m_{t},{\rm {GeV}/c^{2}}$


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Fit Input for $\,\Delta m_{s},{\rm ps^{-1}}$

Gaussian likelihood used $17.77 \pm 0.12$
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Full Fit result for $\,\Delta m_{s},{\rm ps^{-1}}$

$17.77 \pm 0.12$ 95% prob:[17.5, 18.0] 99% prob:[17.4, 18.1]
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SM Fit prediction for $\,\Delta m_{s},{\rm ps^{-1}}$

$18.3 \pm 1.3$ 95% prob:[15.9, 20.9] 99% prob:[14.8, 22.3]
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Compatibility Plot for $\,\Delta m_{s},{\rm ps^{-1}}$


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Fit Input for $\,f_{B_{s}}$

Gaussian likelihood used $0.239 \pm 0.01$
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Full Fit result for $\,f_{B_{s}}$

$0.2359 \pm 0.0056$ 95% prob:[0.2252, 0.2477] 99% prob:[0.22, 0.2537]
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SM Fit prediction for $\,f_{B_{s}}$

$0.2349 \pm 0.0067$ 95% prob:[0.2221, 0.2491] 99% prob:[0.217, 0.2571]
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Compatibility Plot for $\,f_{B_{s}}$


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Fit Input for $\,f_{B_{s}}/f_{B_{d}}$

Gaussian likelihood used $1.23 \pm 0.03$
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Full Fit result for $\,f_{B_{s}}/f_{B_{d}}$

$1.225 \pm 0.025$ 95% prob:[1.175, 1.275] 99% prob:[1.151, 1.299]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}/f_{B_{d}}$

$1.213 \pm 0.044$ 95% prob:[1.13, 1.303] 99% prob:[1.083, 1.085] U [1.093, 1.352]
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Compatibility Plot for $\,f_{B_{s}}/f_{B_{d}}$


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Fit Input for $\,B_{B_{s}}/B_{B_{d}}$

Gaussian likelihood used $1.06 \pm 0.04$
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Full Fit result for $\,B_{B_{s}}/B_{B_{d}}$

$1.069 \pm 0.036$ 95% prob:[0.997, 1.141] 99% prob:[0.963, 1.179]
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SM Fit prediction for $\,B_{B_{s}}/B_{B_{d}}$

$1.113 \pm 0.085$ 95% prob:[0.96, 1.279] 99% prob:[0.893, 1.3]
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Compatibility Plot for $\,B_{B_{s}}/B_{B_{d}}$


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Fit Input for $\,B_{B_{s}}$

Gaussian likelihood used $0.87 \pm 0.04$
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Full Fit result for $\,B_{B_{s}}$

$0.845 \pm 0.036$ 95% prob:[0.775, 0.919] 99% prob:[0.738, 0.954]
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SM Fit prediction for $\,B_{B_{s}}$

$0.769 \pm 0.065$ 95% prob:[0.648, 0.915] 99% prob:[0.608, 0.999]
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Compatibility Plot for $\,B_{B_{s}}$


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Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 95% prob:[81, 102.] U [161., 169] 99% prob:[76.8, 108.] U [157., 171.]
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Full Fit result for $\,\alpha, [^{\circ}]$

$87.8 \pm 3.0$ 95% prob:[82.1, 93.8] 99% prob:[79.2, 96.2]
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SM Fit prediction for $\,\alpha, [^{\circ}]$

$85.4 \pm 3.7$ 95% prob:[78.3, 93.2] 99% prob:[74.5, 96.2]
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Compatibility Plot for $\,\alpha, [^{\circ}]$


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Full Fit result for $\,\beta, [^{\circ}]$

$22.42 \pm 0.74$ 95% prob:[20.9, 23.9] 99% prob:[20.2, 24.7]
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SM Fit prediction for $\,\beta, [^{\circ}]$

$25.2 \pm 1.6$ 95% prob:[22.3, 28.6] 99% prob:[21.3, 30.2]
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Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
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Full Fit result for $\,\sin(2\beta)$

$0.705 \pm 0.018$ 95% prob:[0.669, 0.742] 99% prob:[0.651, 0.762]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\sin(2\beta)$

$0.771 \pm 0.036$ 95% prob:[0.706, 0.844] 99% prob:[0.68, 0.872] U [0.875, 0.878]
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Compatibility Plot for $\,\sin(2\beta)$


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Fit Input for $\,\cos(2\beta)$

$0.87 \pm 0.13$ 95% prob:[0.44, 0.99] 99% prob:[0.12, 0.99]
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Full Fit result for $\,\cos(2\beta)$

$0.71 \pm 0.018$ 95% prob:[0.672, 0.745] 99% prob:[0.649, 0.76]
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SM Fit prediction for $\,\cos(2\beta)$

$0.639 \pm 0.043$ 95% prob:[0.544, 0.712] 99% prob:[0.507, 0.731]
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Compatibility Plot for $\,\cos(2\beta)$


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Fit Input for $\,2\beta+\gamma, [^{\circ}]$

$-90 \pm 56 \text{ and } 94 \pm 52$ 95% prob:[-166, 166.] 99% prob:[-179, 179]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,2\beta+\gamma, [^{\circ}]$

$114.7 \pm 3.1$ 95% prob:[108.3, 120.7] 99% prob:[105.6, 123.4]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,2\beta+\gamma, [^{\circ}]$

$114.9 \pm 3.1$ 95% prob:[108.6, 120.9] 99% prob:[105.8, 123.6]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,2\beta+\gamma, [^{\circ}]$


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Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
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Full Fit result for $\,\gamma, [^{\circ}]$

$69.8 \pm 3.0$ 95% prob:[63.9, 75.7] 99% prob:[61, 78.5]
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SM Fit prediction for $\,\gamma, [^{\circ}]$

$69.6 \pm 3.1$ 95% prob:[63.4, 75.6] 99% prob:[60.5, 78.8]
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Compatibility Plot for $\,\gamma, [^{\circ}]$


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Fit Input for $\,\|\varepsilon_{K}\|$

$0.00222994 \pm 1.04974\times 10^{-5}$ 95% prob:[0.00220745, 0.00224944] 99% prob:[0.00219845, 0.00225644]
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Full Fit result for $\,\|\varepsilon_{K}\|$

$0.00222854 \pm 9.98004\times 10^{-06}$ 95% prob:[0.00220858, 0.0022485] 99% prob:[0.0021986, 0.00225848]
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SM Fit prediction for $\,\|\varepsilon_{K}\|$

$0.00192 \pm 0.00018$ 95% prob:[0.00157, 0.00230] 99% prob:[0.00141, 0.00252]
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Compatibility Plot for $\,\|\varepsilon_{K}\|$


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Fit Input for $\,B(B\rightarrow\tau u),10^{-4}$

Gaussian likelihood used $1.72 \pm 0.28$
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Full Fit result for $\,B(B\rightarrow\tau u),10^{-4}$

$0.867 \pm 0.078$ 95% prob:[0.721, 1.031] 99% prob:[0.661, 1.127]
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SM Fit prediction for $\,B(B\rightarrow\tau u),10^{-4}$

$0.805 \pm 0.071$ 95% prob:[0.674, 0.958] 99% prob:[0.619, 1.051]
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Compatibility Plot for $\,B(B\rightarrow\tau u),10^{-4}$


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Full fit result for $\,J_{cp}\times 10^{-5}$

$3.09 \pm 0.11$ 95% prob:[2.87, 3.30] 99% prob:[2.77, 3.42]
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remember="on" }% In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints : $\Delta m_s, \Delta m_d, \epsilon_K, B \rightarrow \tau \nu,$ . Let's consider schematically the dependence of these observable in terms of the non perturbative QCD parameters :

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\Delta m_s \propto f_{Bs} \sqrt{B_{Bs}} \ \Delta m_d \propto f_{Bd} \sqrt{B_{Bd}} = \frac{f_{Bs}}{\xi} \times \sqrt{B_{Bs}} \ Br(B \rightarrow \tau \nu) \propto f_{Bd}^2 = \frac{f_{Bs}^2}{\xi^2} \times \frac{{B_{Bs}}}{{B_{Bd}}} \

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\Delta m_s \propto f^2_{Bs} {B_{Bs}} \ \Delta m_d \propto f^2_{Bd} {B_{Bd}} = \frac{f^2_{Bs}}{f^2_{Bs}/f^2_{Bd}} \times \frac{B_{Bs}}{B_{Bs}/B_{Bd}} \ Br(B \rightarrow \tau \nu) \propto f_{Bd}^2 = \frac{f_{Bs}^2}{f^2_{Bs}/f^2_{Bd}} \

\epsilon_K \propto B_K \.

We decide to express these observable in terms of five LQCD parameters

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$f_{Bs}, \quad B_{Bs}, \quad \xi, \quad \frac{{B_{Bs}}}{{B_{Bd}}}, \quad B_K$

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$f_{Bs}, \quad B_{Bs}, \quad \frac{f_{Bs}}{f_{Bd}} , \quad \frac{{B_{Bs}}}{{B_{Bd}}}, \quad B_K$

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The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of $V_{ub}$ (exclusive) and $V_{cs}$ . The "no-lattice" fit is performed removing from the fitting procedure the use of the hadronic parameters coming from lattice calculations, leaving them as free parameters of the fit. This approach allows for the possibility of making a full UT analysis without relying at all on theoretical calculations of hadronic matrix elements and on the other hand to obtain the a-posteriori p.d.f. for a given hadronic quantity.

>
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The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of $V_{ub}$ (exclusive) and $V_{cs}$ . The "no-lattice" fit is performed removing from the fitting procedure the use of the hadronic parameters coming from lattice calculations, leaving them as free parameters of the fit. This approach allows for the possibility of making a full UT analysis without relying at all on theoretical calculations of hadronic matrix elements.

Parameter	Input value	Full fit
$\bar{\rho}$		$0.1141 \pm 0.0045 \text{ and } 0.151 \pm 0.0243$
$\bar{\eta}$		$0.3199 \pm 0.0024 \text{ and } 0.3358 \pm 0.0126$
		$0.805 \pm 0.012$
$\lambda$	$0.2253 \pm 0.0011$	$0.2254 \pm 0.0009$
$\xi$		$1.24 \pm 0.043$
$F_{B_{d}}*\sqrt{B_{d}}$		$0.2159 \pm 0.008$
$F_{B_{s}}*\sqrt{B_{s}}$		$0.2681 \pm 0.004$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$91.6 \pm 4.8$
$\beta, [^{\circ}]$		$20.45 \pm 0.03 \text{ and } 21.405 \pm 0.725$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.6605 \pm 0.0025 \text{ and } 0.682 \pm 0.016$
$\cos(2\beta)$	$0.87 \pm 0.13$	$0.737 \pm 0.018$
$2\beta+\gamma, [^{\circ}]$	$-90 \pm 56 \text{ and } 94 \pm 52$	$103.85 \pm 0.55 \text{ and } 110.8 \pm 4.3$
$\gamma, [^{\circ}]$	$-106 \pm 10 \text{ and } 74 \pm 11$	$67.0 \pm 4.8$

Full fit result for $\,\bar{\rho}$

$0.1141 \pm 0.0045 \text{ and } 0.151 \pm 0.0243$ 68% prob:[0.126, 0.175] U [0.109, 0.118] 95% prob:[0.085, 0.203] 99% prob:[0.053, 0.239]
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Full fit result for $\,\bar{\eta}$

$0.3199 \pm 0.0024 \text{ and } 0.3358 \pm 0.0126$ 68% prob:[0.323, 0.348] U [0.317, 0.322] 95% prob:[0.307, 0.367] 99% prob:[0.289, 0.382]
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Full fit result for $\,A$

$0.805 \pm 0.012$ 68% prob:[0.794, 0.817] 95% prob:[0.784, 0.829] U [0.833, 0.836] 99% prob:[0.769, 0.772] U [0.776, 0.842]
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Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 68% prob:[0.2242, 0.2265] 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
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Full Fit result for $\,\lambda$

$0.2254 \pm 0.0009$ 68% prob:[0.22450, 0.22630] 95% prob:[0.22370, 0.22730] 99% prob:[0.22290, 0.22780] U [0.22840, 0.22890]
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Full fit result for $\,\xi$

$1.24 \pm 0.043$ 68% prob:[1.197, 1.283] 95% prob:[1.147, 1.327] 99% prob:[1.097, 1.378]
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Full fit result for $\,F_{B_{d}}*\sqrt{B_{d}}$

$0.2159 \pm 0.008$ 68% prob:[0.2079, 0.2240] 95% prob:[0.2006, 0.2353] 99% prob:[0.1929, 0.2452]
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Full fit result for $\,F_{B_{s}}*\sqrt{B_{s}}$

$0.2681 \pm 0.004$ 68% prob:[0.2642, 0.2721] 95% prob:[0.2601, 0.2765] 99% prob:[0.2569, 0.2810] U [0.2840, 0.2860]
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Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 68% prob:[85.3, 97.5] 95% prob:[81.0, 102.] U [161., 169.] 99% prob:[76.8, 108.] U [157., 171.]
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Full Fit result for $\,\alpha, [^{\circ}]$

$91.6 \pm 4.8$ 68% prob:[86.8, 96.4] 95% prob:[82.2, 101.] 99% prob:[77.2, 107.]
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Full Fit result for $\,\beta, [^{\circ}]$

$20.45 \pm 0.03 \text{ and } 21.405 \pm 0.725$ 68% prob:[20.6, 22.1] U [20.4, 20.4] 95% prob:[20.0, 22.9] 99% prob:[19.4, 23.7]
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Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 68% prob:[0.628, 0.681] 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
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Full Fit result for $\,\sin(2\beta)$

$0.6605 \pm 0.0025 \text{ and } 0.682 \pm 0.016$ 68% prob:[0.666, 0.698] U [0.658, 0.663] 95% prob:[0.647, 0.719] 99% prob:[0.624, 0.735]
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Fit Input for $\,\cos(2\beta)$

$0.87 \pm 0.13$ 68% prob:[0.73, 0.99] 95% prob:[0.44, 0.99] 99% prob:[0.12, 0.99]
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Full Fit result for $\,\cos(2\beta)$

$0.737 \pm 0.018$ 68% prob:[0.719, 0.755] 95% prob:[0.696, 0.765] 99% prob:[0.677, 0.781]
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Fit Input for $\,2\beta+\gamma, [^{\circ}]$

$-90 \pm 56 \text{ and } 94 \pm 52$ 68% prob:[-146, -33.] U [41.6, 146.] 95% prob:[-166, 166.] 99% prob:[-179, 179.]
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Full Fit result for $\,2\beta+\gamma, [^{\circ}]$

$103.85 \pm 0.55 \text{ and } 110.8 \pm 4.3$ 68% prob:[103.3, 104.4] U [106.5, 115.1] 95% prob:[99.70, 119.3] 99% prob:[91.40, 92.00] U [94.30, 94.60] U [95.60, 124.7]
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Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 10 \text{ and } 74 \pm 11$ 68% prob:[-116, -96.] U [62.5, 84.7] 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
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Full Fit result for $\,\gamma, [^{\circ}]$

$67.0 \pm 4.8$ 68% prob:[62.2, 71.9] 95% prob:[56.9, 76.3] 99% prob:[51.2, 81.7]
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In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model an some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using D(*)π(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameter, Lattice QCD calculations play a central role

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In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model and some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using Dπ(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameters, Lattice QCD calculations play a central role.

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.

The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. The interest of this procedure is to quantify the agreement of all the measured quantities by the comparison between indirect parameter determinations and their direct experimental/theortical determinations. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.

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For some of the quantities we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

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For some of the quantity we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution 1. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

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Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

The color code indicates the compatibility between direct and indirect determinations, given in terms of standard deviations, as a function of the measured value and its experimental uncertainty. The crosses indicate the direct world average measurement values.

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}% In principle, the presence of New Physics might affect the result of the UT analysis, changing the functional dependences of the experimental quantities upon ρ and η. On the contrary, two constraints now available, are almost unchanged by the presence of NP: |Vub/Vcb| from semileptonic B decays and the UT angle γ from B → D(*)K decays. As usual from this fit one can gets predictions for each observable related to the Unitarity Triangle. This set of values is the minimal requirement that each model describing New Physics has to satisfy, in order to be taken as a realistic description of physics beyond the Standard Model.

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}% In principle, the presence of New Physics might affect the result of the UT analysis, changing the functional dependencies of the experimental quantities upon ρ and η. On the contrary, two constraints now available, are almost unchanged by the presence of NP: |Vub/Vcb| from semileptonic B decays and the UT angle γ from B → D(*)K decays. As usual from this fit one can gets predictions for each observable related to the Unitarity Triangle. This set of values is the minimal requirement that each model describing New Physics has to satisfy in order to be taken as a realistic description of physics beyond the Standard Model.

Parameter	Input value	Full fit
$\bar{\rho}$		$0.111 \pm 0.07$
$\bar{\eta}$		$0.381 \pm 0.03$
$\rho$		$0.114 \pm 0.071$
$\eta$		$0.391 \pm 0.031$
		$0.804 \pm 0.01$
$\lambda$		$0.22535 \pm 0.00065$
$\alpha, [^{\circ}]$		$83 \pm 10$
$\beta, [^{\circ}]$		$23.0 \pm 1.4$
$\sin(2\beta)$		$0.72 \pm 0.035$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$73 \pm 11$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97426 \pm 0.00015 & 0.22535 \pm 0.00065 & (0.00376 \pm 0.0002)e^{i(-73.8 \pm 9.4)^\circ}\\ -(0.2252 \pm 0.00065)e^{i(0.0365 \pm 0.0028)^\circ} & 0.97345 \pm 0.00015 & 0.04083 \pm 0.00045 \\ (0.00896 \text{ and } 0.01081 \pm 0.0006)e^{i(-22.9 \pm 1.4)^\circ} & -(0.03979 \pm 0.00052)e^{i(1.163 \pm 0.084)^\circ} & 0.99916 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.111 \pm 0.07$ 95% prob:[0.000, 0.230] 99% prob:[0.000, 0.298]
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Full fit result for $\,\bar{\eta}$

$0.381 \pm 0.03$ 95% prob:[0.311, 0.446] 99% prob:[0.264, 0.484]
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Full fit result for $\,\bar{\rho} - \bar{\eta}$


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Full fit result for $\,\rho$

$0.114 \pm 0.071$ 95% prob:[0.000, 0.236] 99% prob:[0.000, 0.305]
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Full fit result for $\,\eta$

$0.391 \pm 0.031$ 95% prob:[0.320, 0.457] 99% prob:[0.275, 0.494]
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Full fit result for $\,A$

$0.804 \pm 0.01$ 95% prob:[0.7850, 0.8250] 99% prob:[0.7760, 0.8360]
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Full fit result for $\,\lambda$

$0.22535 \pm 0.00065$ 95% prob:[0.22410, 0.22670] 99% prob:[0.22350, 0.22740]
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Full fit result for $\,\alpha, [^{\circ}]$

$83 \pm 10$ 95% prob:[63.9, 103.] 99% prob:[60.0, 115.]
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Full fit result for $\,\beta, [^{\circ}]$

$23.0 \pm 1.4$ 95% prob:[20.2, 26.5] 99% prob:[18.6, 29.0]
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Full fit result for $\,\sin(2\beta)$

$0.72 \pm 0.035$ 95% prob:[0.651, 0.802] 99% prob:[0.609, 0.851]
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Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
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Full Fit result for $\,\gamma, [^{\circ}]$

$73 \pm 11$ 95% prob:[52.1, 94.3] 99% prob:[41.3, 104.]
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woops, ordering error: got an ENDTWISTY before seeing a TWISTY

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}% In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints : $\Delta m_s, \Delta m_d, \epsilon_K, B \rightarrow \tau \nu,$ . Let's consider schematically the dependence of these observable in terms of the non perturbative QCD parameters :

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}% In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints : $\Delta m_s, \Delta m_d, \epsilon_K, B \rightarrow \tau \nu,$ . Let's consider schematically the dependence of these observable in terms of the non perturbative QCD parameters :

\Delta m_s \propto f_{Bs} \sqrt{B_{Bs}} \ \Delta m_d \propto f_{Bd} \sqrt{B_{Bd}} = \frac{f_{Bs}}{\xi} \times \sqrt{B_{Bs}} \

Line: 107 to 93

$f_{Bs}, \quad B_{Bs}, \quad \xi, \quad \frac{{B_{Bs}}}{{B_{Bd}}}, \quad B_K$

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The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of $V_{ub}$ (exclusive) and $V_{cs}$ . The "no-lattice" fit is performed removing from the fitting procedure the use of the hadronic parameters coming from lattice calculations, letting them as free parameters of the fit. This approach allows for the possibility of making a full UT analysis without relying at all on theoretical calculations of hadronic matrix elements and on the other hands to obtain the a-posteriori p.d.f. for a given hadronic quantity.

>
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The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of $V_{ub}$ (exclusive) and $V_{cs}$ . The "no-lattice" fit is performed removing from the fitting procedure the use of the hadronic parameters coming from lattice calculations, leaving them as free parameters of the fit. This approach allows for the possibility of making a full UT analysis without relying at all on theoretical calculations of hadronic matrix elements and on the other hand to obtain the a-posteriori p.d.f. for a given hadronic quantity.

Parameter	Input value	Full fit
$\bar{\rho}$		$0.1141 \pm 0.0045 \text{ and } 0.151 \pm 0.0243$
$\bar{\eta}$		$0.3199 \pm 0.0024 \text{ and } 0.3358 \pm 0.0126$
		$0.805 \pm 0.012$
$\lambda$	$0.2253 \pm 0.0011$	$0.2254 \pm 0.0009$
$\xi$		$1.24 \pm 0.043$
$F_{B_{d}}*\sqrt{B_{d}}$		$0.2159 \pm 0.008$
$F_{B_{s}}*\sqrt{B_{s}}$		$0.2681 \pm 0.004$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$91.6 \pm 4.8$
$\beta, [^{\circ}]$		$20.45 \pm 0.03 \text{ and } 21.405 \pm 0.725$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.6605 \pm 0.0025 \text{ and } 0.682 \pm 0.016$
$\cos(2\beta)$	$0.87 \pm 0.13$	$0.737 \pm 0.018$
$2\beta+\gamma, [^{\circ}]$	$-90 \pm 56 \text{ and } 94 \pm 52$	$103.85 \pm 0.55 \text{ and } 110.8 \pm 4.3$
$\gamma, [^{\circ}]$	$-106 \pm 10 \text{ and } 74 \pm 11$	$67.0 \pm 4.8$

Full fit result for $\,\bar{\rho}$

$0.1141 \pm 0.0045 \text{ and } 0.151 \pm 0.0243$ 68% prob:[0.126, 0.175] U [0.109, 0.118] 95% prob:[0.085, 0.203] 99% prob:[0.053, 0.239]
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Full fit result for $\,\bar{\eta}$

$0.3199 \pm 0.0024 \text{ and } 0.3358 \pm 0.0126$ 68% prob:[0.323, 0.348] U [0.317, 0.322] 95% prob:[0.307, 0.367] 99% prob:[0.289, 0.382]
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Full fit result for $\,A$

$0.805 \pm 0.012$ 68% prob:[0.794, 0.817] 95% prob:[0.784, 0.829] U [0.833, 0.836] 99% prob:[0.769, 0.772] U [0.776, 0.842]
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Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 68% prob:[0.2242, 0.2265] 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
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Full Fit result for $\,\lambda$

$0.2254 \pm 0.0009$ 68% prob:[0.22450, 0.22630] 95% prob:[0.22370, 0.22730] 99% prob:[0.22290, 0.22780] U [0.22840, 0.22890]
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Full fit result for $\,\xi$

$1.24 \pm 0.043$ 68% prob:[1.197, 1.283] 95% prob:[1.147, 1.327] 99% prob:[1.097, 1.378]
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Full fit result for $\,F_{B_{d}}*\sqrt{B_{d}}$

$0.2159 \pm 0.008$ 68% prob:[0.2079, 0.2240] 95% prob:[0.2006, 0.2353] 99% prob:[0.1929, 0.2452]
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Full fit result for $\,F_{B_{s}}*\sqrt{B_{s}}$

$0.2681 \pm 0.004$ 68% prob:[0.2642, 0.2721] 95% prob:[0.2601, 0.2765] 99% prob:[0.2569, 0.2810] U [0.2840, 0.2860]
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Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 68% prob:[85.3, 97.5] 95% prob:[81.0, 102.] U [161., 169.] 99% prob:[76.8, 108.] U [157., 171.]
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Full Fit result for $\,\alpha, [^{\circ}]$

$91.6 \pm 4.8$ 68% prob:[86.8, 96.4] 95% prob:[82.2, 101.] 99% prob:[77.2, 107.]
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Full Fit result for $\,\beta, [^{\circ}]$

$20.45 \pm 0.03 \text{ and } 21.405 \pm 0.725$ 68% prob:[20.6, 22.1] U [20.4, 20.4] 95% prob:[20.0, 22.9] 99% prob:[19.4, 23.7]
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Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 68% prob:[0.628, 0.681] 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
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Full Fit result for $\,\sin(2\beta)$

$0.6605 \pm 0.0025 \text{ and } 0.682 \pm 0.016$ 68% prob:[0.666, 0.698] U [0.658, 0.663] 95% prob:[0.647, 0.719] 99% prob:[0.624, 0.735]
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Fit Input for $\,\cos(2\beta)$

$0.87 \pm 0.13$ 68% prob:[0.73, 0.99] 95% prob:[0.44, 0.99] 99% prob:[0.12, 0.99]
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Full Fit result for $\,\cos(2\beta)$

$0.737 \pm 0.018$ 68% prob:[0.719, 0.755] 95% prob:[0.696, 0.765] 99% prob:[0.677, 0.781]
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Fit Input for $\,2\beta+\gamma, [^{\circ}]$

$-90 \pm 56 \text{ and } 94 \pm 52$ 68% prob:[-146, -33.] U [41.6, 146.] 95% prob:[-166, 166.] 99% prob:[-179, 179.]
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Full Fit result for $\,2\beta+\gamma, [^{\circ}]$

$103.85 \pm 0.55 \text{ and } 110.8 \pm 4.3$ 68% prob:[103.3, 104.4] U [106.5, 115.1] 95% prob:[99.70, 119.3] 99% prob:[91.40, 92.00] U [94.30, 94.60] U [95.60, 124.7]
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Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 10 \text{ and } 74 \pm 11$ 68% prob:[-116, -96.] U [62.5, 84.7] 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
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Full Fit result for $\,\gamma, [^{\circ}]$

$67.0 \pm 4.8$ 68% prob:[62.2, 71.9] 95% prob:[56.9, 76.3] 99% prob:[51.2, 81.7]
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woops, ordering error: got an ENDTWISTY before seeing a TWISTY

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}% It is possible to generalize the full UTfit beyond the Standard Model to all those NP models characterized by Minimal Flavour Violation, i.e. having quark miking ruled only by the Standard Model CKM couplings (http://arxiv.org/abs/hep-ph/0007085). In fact, in this case no additional weak phases are generated and several observables entering into the Standard Model fit (the tree-level processes and the measurement of angles through the use of time dependent CP asymmetries) are not affected by the presence of New Physics. The only sizable effect we are sensitive to is a shift of the Inami-Lim function of the top contribution in meson mixing. This means that in general εK and Δmd cannot be used in a common SM and MFV framework, but any New Physics contribution disappear in the case of Δmd/Δms. So, simply removing the information related to εK and Δmd from the full UTfit one can obtain a more precise determination of the Universal Unitarity Triangle, which is a common starting point for the Standard Model and any MFV model.

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}% It is possible to generalize the full UTfit beyond the Standard Model to all those NP models characterized by Minimal Flavour Violation, i.e. having quark mixing ruled only by the Standard Model CKM couplings (http://arxiv.org/abs/hep-ph/0007085). In fact, in this case no additional weak phases are generated and several observables entering into the Standard Model fit (the tree-level processes and the measurement of angles through the use of time dependent CP asymmetries) are not affected by the presence of New Physics. The only sizable effect we are sensitive to is a shift of the Inami-Lim function of the top contribution in meson mixing. This means that in general εK and Δmd cannot be used in a common SM and MFV framework, but any New Physics contribution disappears in the case of Δmd/Δms. So, simply removing the information related to εK and Δmd from the full UTfit one can obtain a more precise determination of the Universal Unitarity Triangle, which is a common starting point for the Standard Model and any MFV model.

Parameter	Input value	Full fit
$\bar{\rho}$		$0.143 \pm 0.03$
$\bar{\eta}$		$0.342 \pm 0.015$
$\rho$		$0.146 \pm 0.031$
$\eta$		$0.351 \pm 0.016$
		$0.807 \pm 0.01$
$\lambda$	$0.2253 \pm 0.0011$	$0.22545 \pm 0.00065$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$90.8 \pm 4.8$
$\beta, [^{\circ}]$		$21.73 \pm 0.74$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.688 \pm 0.018$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$67.3 \pm 4.8$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97425 \pm 0.00015 & 0.22545 \pm 0.00065 & (0.00352 \pm 0.00011)e^{i(-67.7 \pm 4.4)^\circ}\\ -(0.2253 \pm 0.00065)e^{i(0.033 \pm 0.0016)^\circ} & 0.97342 \pm 0.00015 & 0.04099 \pm 0.00046 \\ (0.00854 \pm 0.00031)e^{i(-21.66 \pm 0.73)^\circ} & -(0.04024 \pm 0.00045)e^{i(1.04 \pm 0.048)^\circ} & 0.999154 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.143 \pm 0.03$ 95% prob:[0.082, 0.204] 99% prob:[0.050, 0.238]
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Full fit result for $\,\bar{\eta}$

$0.342 \pm 0.015$ 95% prob:[0.310, 0.372] 99% prob:[0.293, 0.388]
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Full fit result for $\,\bar{\rho} - \bar{\eta}$


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Full fit result for $\,\rho$

$0.146 \pm 0.031$ 95% prob:[0.084, 0.209] 99% prob:[0.051, 0.244]
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Full fit result for $\,\eta$

$0.351 \pm 0.016$ 95% prob:[0.319, 0.382] 99% prob:[0.301, 0.398]
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Full fit result for $\,A$

$0.807 \pm 0.01$ 95% prob:[0.7870, 0.8280] 99% prob:[0.7780, 0.8390]
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Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
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Full Fit result for $\,\lambda$

$0.22545 \pm 0.00065$ 95% prob:[0.22410, 0.22670] 99% prob:[0.22360, 0.22750]
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Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 95% prob:[81.0, 102.] U [161., 169.] 99% prob:[76.8, 108.] U [157., 171.]
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Full Fit result for $\,\alpha, [^{\circ}]$

$90.8 \pm 4.8$ 95% prob:[81.2, 100.] 99% prob:[76.4, 106.]
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Full fit result for $\,\beta, [^{\circ}]$

$21.73 \pm 0.74$ 95% prob:[20.2, 23.2] 99% prob:[19.6, 24.0]
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Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
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Full Fit result for $\,\sin(2\beta)$

$0.688 \pm 0.018$ 95% prob:[0.651, 0.725] 99% prob:[0.633, 0.745]
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Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
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Full Fit result for $\,\gamma, [^{\circ}]$

$67.3 \pm 4.8$ 95% prob:[57.5, 77.1] 99% prob:[52.0, 82.2]
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woops, ordering error: got an ENDTWISTY before seeing a TWISTY

Line: 140 to 119

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}% The fit presented here is meant to constrain the NP contributions to |Δ F|=2 transitions by using the available experimental information on loop-mediated processes In general, NP models introduce a large number of new parameters: flavour changing couplings, short distance coefficients and matrix elements of new local operators. The specific list and the actual values of these parameters can only be determined within a given model. Nevertheless mixing processes are described by a single amplitude and can be parameterized, without loss of generality, in terms of two parameters, which quantify the difference of the complex amplitude with respect to the SM one. Thus, for instance, in the case of $B^0_q-\bar{B}^0_q$ mixing we define $C_{B_q} \, e^{2 i \phi_{B_q}} = \frac{\langle B^0_q|H_\mathrm{eff}^\mathrm{full}|\bar{B}^0_q\rangle} {\langle B^0_q|H_\mathrm{eff}^\mathrm{SM}|\bar{B}^0_q\rangle}\,, \qquad (q=d,s)$ where $H_\mathrm{eff}^\mathrm{SM}$ includes only the SM box diagrams, while $H_\mathrm{eff}^\mathrm{full}$ includes also the NP contributions. In the absence of NP effects, $C_{B_q}=1$ and $\phi_{B_q}=0$ by definition. In a similar way, one can write

>
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}% The fit presented here is meant to constrain the NP contributions to |Δ F|=2 transitions by using the available experimental information on loop-mediated processes In general, NP models introduce a large number of new parameters: flavour changing couplings, short distance coefficients and matrix elements of new local operators. The specific list and the actual values of these parameters can only be determined within a given model. Nevertheless mixing processes are described by a single amplitude and can be parameterized, without loss of generality, in terms of two parameters, which quantify the difference of the complex amplitude with respect to the SM one. Thus, for instance, in the case of $B^0_q-\bar{B}^0_q$ mixing we define $C_{B_q} \, e^{2 i \phi_{B_q}} = \frac{\langle B^0_q|H_\mathrm{eff}^\mathrm{full}|\bar{B}^0_q\rangle} {\langle B^0_q|H_\mathrm{eff}^\mathrm{SM}|\bar{B}^0_q\rangle}\,, \qquad (q=d,s),$ where $H_\mathrm{eff}^\mathrm{SM}$ includes only the SM box diagrams, while $H_\mathrm{eff}^\mathrm{full}$ also includes the NP contributions. In the absence of NP effects, $C_{B_q}=1$ and $\phi_{B_q}=0$ by definition. In a similar way, one can write

C_{\epsilon_K} = \frac{\mathrm{Im}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{full}}|\bar{K}^0\rangle]} {\mathrm{Im}[\langle

Line: 166 to 130

{\mathrm{Re}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{SM}}|\bar{K}^0\rangle]}\,. \label{eq:ceps}

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Concerning $\Delta m_K$ , to be conservative, we add to the short-distance contribution a possible long-distance one that varies with a uniform distribution between zero and the experimental value of $\Delta m_K$

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Concerning $\Delta m_K$ , to be conservative, we add to the short-distance contribution a possible long-distance one that varies with a uniform distribution between zero and the experimental value of $\Delta m_K$ .

The experimental quantities determined from the $B^0_q-\bar{B}^0_q$ mixings are related to their SM counterparts and the NP parameters by the following relations:

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\Delta m_d^\mathrm{exp} = C_{B_d} \Delta m_d^\mathrm{SM} \,,\; \\sin 2 \beta^\mathrm{exp} = \sin (2 \beta^\mathrm{SM} + 2\phi_{B_d})\,,\; \\ \alpha^\mathrm{exp} = \alpha^\mathrm{SM} - \phi_{B_d}\,, \

Line: 182 to 142

\phi_s^\mathrm{exp} = (\beta_s^\mathrm{SM} - \phi_{B_s})\,,\; \\Delta m_K^\mathrm{exp} = C_{\Delta m_K} \Delta m_K^\mathrm{SM} \,,\; \\epsilon_K^\mathrm{exp} = C_{\epsilon_K} \epsilon_K^\mathrm{SM} \,,\; \

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in a self-explanatory notation.

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All the measured observables can be written as a function of these NP parameters and the SM ones ρ and η, and additional parameters such as masses, form factors, and decay constants.

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All the measured observables can be written as a function of these NP parameters and the SM ones ρ and η, and additional parameters such as masses, form factors, and decay constants.

Click on the parameter name to jump to the corresponding plot

Parameter	Input value	Full fit
$\bar{\rho}$		$0.135 \pm 0.04$
$\bar{\eta}$		$0.374 \pm 0.026$
$\rho$		$0.138 \pm 0.041$
$\eta$		$0.384 \pm 0.027$
		$0.804 \pm 0.01$
$\lambda$	$0.2253 \pm 0.0011$	$0.22535 \pm 0.00065$
$C_{B_{d}}$		$0.95 \pm 0.14$
$\phi_{B_{d}}, [^{\circ}]$		$-3.1 \pm 1.7$
$C_{B_{s}}$		$0.95 \pm 0.095$
$\phi_{B_{s}}, [^{\circ}]$		$-68.2 \pm 7.6 \text{ and } -20.3 \pm 7.7$
$C_{\epsilon_{K}}$		$1.05 \pm 0.12$
$A_{SL_{d}}$	$-0.0005 \pm 0.0056$	$-0.0028 \pm 0.0024$
$A_{SL_{s}}$	$-0.0017 \pm 0.0091$	$-0.0044 \pm 0.0014$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97427 \pm 0.00015 & 0.22535 \pm 0.00065 & (0.00377 \pm 0.00021)e^{i(-70.0 \pm 5.6)^\circ}\\ -(0.22525 \pm 0.00065)e^{i(0.0358 \pm 0.0025)^\circ} & 0.97345 \pm 0.00015 & 0.04082 \pm 0.00045 \\ (0.00869 \pm 0.00039)e^{i(-23.3 \pm 1.3)^\circ} & -(0.04007 \pm 0.00044)e^{i(1.138 \pm 0.076)^\circ} & 0.99916 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.135 \pm 0.04$ 95% prob:[0.069, 0.223] 99% prob:[0.040, 0.262]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.374 \pm 0.026$ 95% prob:[0.322, 0.433] 99% prob:[0.297, 0.471]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.138 \pm 0.041$ 95% prob:[0.070, 0.228] 99% prob:[0.041, 0.269]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.384 \pm 0.027$ 95% prob:[0.330, 0.444] 99% prob:[0.305, 0.482]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.804 \pm 0.01$ 95% prob:[0.7840, 0.8240] 99% prob:[0.7750, 0.8350]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22535 \pm 0.00065$ 95% prob:[0.22410, 0.22670] 99% prob:[0.22350, 0.22750]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{d}}$

$0.95 \pm 0.14$ 95% prob:[0.70, 1.27] 99% prob:[0.59, 1.51]
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Full fit result for $\,\phi_{B_{d}}, [^{\circ}]$

$-3.1 \pm 1.7$ 95% prob:[-7., 0.1] 99% prob:[-10, 2.1]
EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{d}} - C_{B_{d}}$


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2D for $\,\Phi_{B_{d}} - A^{NP}_{d}/A^{SM}_{d}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{s}}$

$0.95 \pm 0.095$ 95% prob:[0.776, 1.162] 99% prob:[0.706, 1.295]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{s}}, [^{\circ}]$

$-68.2 \pm 7.6 \text{ and } -20.3 \pm 7.7$ 95% prob:[-81, -51] U [-38, -6.] 99% prob:[-85, -1.]
EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{s}} - C_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{s}} - A^{NP}_{s}/A^{SM}_{s}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{\epsilon_{K}}$

$1.05 \pm 0.12$ 95% prob:[0.82, 1.34] 99% prob:[-0.8, -0.8] U [0.70, 1.60]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{d}}$

Gaussian likelihood used $-0.0005 \pm 0.0056$
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Full Fit result for $\,A_{SL_{d}}$

$-0.0028 \pm 0.0024$ 95% prob:[-0.0077, 0.00129] 99% prob:[-0.0096, 0.00431]
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Fit Input for $\,A_{SL_{s}}$

Gaussian likelihood used $-0.0017 \pm 0.0091$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,A_{SL_{s}}$

$-0.0044 \pm 0.0014$ 95% prob:[-0.0072, -0.0015] 99% prob:[-0.0087, 0.00004]
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Revision 27

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In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model an some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities

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in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D()K() modes), 2β + γ (using D(*)π(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameter, LQCD calculations play a central role

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in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D K, DK*, D*K modes), 2β + γ (using D(*)π(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameter, Lattice QCD calculations play a central role

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.

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As usual from this fit one can gets predictions for each observable related to the Unitarity Triangle. This set of values is the minimal requirement that each model describing New Physics has to satisfy, in order to be taken as a realistic description of physics beyond the Standard Model.

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Parameter	Input value	Full fit
$\bar{\rho}$		$0.111 \pm 0.07$
$\bar{\eta}$		$0.381 \pm 0.03$
$\rho$		$0.114 \pm 0.071$
$\eta$		$0.391 \pm 0.031$
		$0.804 \pm 0.01$
$\lambda$		$0.22535 \pm 0.00065$
$\alpha, [^{\circ}]$		$83 \pm 10$
$\beta, [^{\circ}]$		$23.0 \pm 1.4$
$\sin(2\beta)$		$0.72 \pm 0.035$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$73 \pm 11$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97426 \pm 0.00015 & 0.22535 \pm 0.00065 & (0.00376 \pm 0.0002)e^{i(-73.8 \pm 9.4)^\circ}\\ -(0.2252 \pm 0.00065)e^{i(0.0365 \pm 0.0028)^\circ} & 0.97345 \pm 0.00015 & 0.04083 \pm 0.00045 \\ (0.00896 \text{ and } 0.01081 \pm 0.0006)e^{i(-22.9 \pm 1.4)^\circ} & -(0.03979 \pm 0.00052)e^{i(1.163 \pm 0.084)^\circ} & 0.99916 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.111 \pm 0.07$ 95% prob:[0.000, 0.230] 99% prob:[0.000, 0.298]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.381 \pm 0.03$ 95% prob:[0.311, 0.446] 99% prob:[0.264, 0.484]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.114 \pm 0.071$ 95% prob:[0.000, 0.236] 99% prob:[0.000, 0.305]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.391 \pm 0.031$ 95% prob:[0.320, 0.457] 99% prob:[0.275, 0.494]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.804 \pm 0.01$ 95% prob:[0.7850, 0.8250] 99% prob:[0.7760, 0.8360]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\lambda$

$0.22535 \pm 0.00065$ 95% prob:[0.22410, 0.22670] 99% prob:[0.22350, 0.22740]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\alpha, [^{\circ}]$

$83 \pm 10$ 95% prob:[63.9, 103.] 99% prob:[60.0, 115.]
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Full fit result for $\,\beta, [^{\circ}]$

$23.0 \pm 1.4$ 95% prob:[20.2, 26.5] 99% prob:[18.6, 29.0]
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Full fit result for $\,\sin(2\beta)$

$0.72 \pm 0.035$ 95% prob:[0.651, 0.802] 99% prob:[0.609, 0.851]
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Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\gamma, [^{\circ}]$

$73 \pm 11$ 95% prob:[52.1, 94.3] 99% prob:[41.3, 104.]
EPS - PDF - PNG - JPG - GIF

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

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$V_{ub}$ (exclusive) and $V_{cs}$ . The "no-lattice" fit is performed removing from the fitting procedure the use of the hadronic parameters coming from lattice calculations, letting them as free parameters of the fit. This approach allows for the possibility of making a full UT analysis without relying at all on theoretical calculations of hadronic matrix elements and on the other hands to obtain the a-posteriori p.d.f. for a given hadronic quantity.

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Parameter	Input value	Full fit
$\bar{\rho}$		$0.1141 \pm 0.0045 \text{ and } 0.151 \pm 0.0243$
$\bar{\eta}$		$0.3199 \pm 0.0024 \text{ and } 0.3358 \pm 0.0126$
		$0.805 \pm 0.012$
$\lambda$	$0.2253 \pm 0.0011$	$0.2254 \pm 0.0009$
$\xi$		$1.24 \pm 0.043$
$F_{B_{d}}*\sqrt{B_{d}}$		$0.2159 \pm 0.008$
$F_{B_{s}}*\sqrt{B_{s}}$		$0.2681 \pm 0.004$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$91.6 \pm 4.8$
$\beta, [^{\circ}]$		$20.45 \pm 0.03 \text{ and } 21.405 \pm 0.725$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.6605 \pm 0.0025 \text{ and } 0.682 \pm 0.016$
$\cos(2\beta)$	$0.87 \pm 0.13$	$0.737 \pm 0.018$
$2\beta+\gamma, [^{\circ}]$	$-90 \pm 56 \text{ and } 94 \pm 52$	$103.85 \pm 0.55 \text{ and } 110.8 \pm 4.3$
$\gamma, [^{\circ}]$	$-106 \pm 10 \text{ and } 74 \pm 11$	$67.0 \pm 4.8$

Full fit result for $\,\bar{\rho}$

$0.1141 \pm 0.0045 \text{ and } 0.151 \pm 0.0243$ 68% prob:[0.126, 0.175] U [0.109, 0.118] 95% prob:[0.085, 0.203] 99% prob:[0.053, 0.239]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.3199 \pm 0.0024 \text{ and } 0.3358 \pm 0.0126$ 68% prob:[0.323, 0.348] U [0.317, 0.322] 95% prob:[0.307, 0.367] 99% prob:[0.289, 0.382]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.805 \pm 0.012$ 68% prob:[0.794, 0.817] 95% prob:[0.784, 0.829] U [0.833, 0.836] 99% prob:[0.769, 0.772] U [0.776, 0.842]
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Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 68% prob:[0.2242, 0.2265] 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.2254 \pm 0.0009$ 68% prob:[0.22450, 0.22630] 95% prob:[0.22370, 0.22730] 99% prob:[0.22290, 0.22780] U [0.22840, 0.22890]
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Full fit result for $\,\xi$

$1.24 \pm 0.043$ 68% prob:[1.197, 1.283] 95% prob:[1.147, 1.327] 99% prob:[1.097, 1.378]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,F_{B_{d}}*\sqrt{B_{d}}$

$0.2159 \pm 0.008$ 68% prob:[0.2079, 0.2240] 95% prob:[0.2006, 0.2353] 99% prob:[0.1929, 0.2452]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,F_{B_{s}}*\sqrt{B_{s}}$

$0.2681 \pm 0.004$ 68% prob:[0.2642, 0.2721] 95% prob:[0.2601, 0.2765] 99% prob:[0.2569, 0.2810] U [0.2840, 0.2860]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 68% prob:[85.3, 97.5] 95% prob:[81.0, 102.] U [161., 169.] 99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\alpha, [^{\circ}]$

$91.6 \pm 4.8$ 68% prob:[86.8, 96.4] 95% prob:[82.2, 101.] 99% prob:[77.2, 107.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\beta, [^{\circ}]$

$20.45 \pm 0.03 \text{ and } 21.405 \pm 0.725$ 68% prob:[20.6, 22.1] U [20.4, 20.4] 95% prob:[20.0, 22.9] 99% prob:[19.4, 23.7]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 68% prob:[0.628, 0.681] 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\sin(2\beta)$

$0.6605 \pm 0.0025 \text{ and } 0.682 \pm 0.016$ 68% prob:[0.666, 0.698] U [0.658, 0.663] 95% prob:[0.647, 0.719] 99% prob:[0.624, 0.735]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\cos(2\beta)$

$0.87 \pm 0.13$ 68% prob:[0.73, 0.99] 95% prob:[0.44, 0.99] 99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\cos(2\beta)$

$0.737 \pm 0.018$ 68% prob:[0.719, 0.755] 95% prob:[0.696, 0.765] 99% prob:[0.677, 0.781]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,2\beta+\gamma, [^{\circ}]$

$-90 \pm 56 \text{ and } 94 \pm 52$ 68% prob:[-146, -33.] U [41.6, 146.] 95% prob:[-166, 166.] 99% prob:[-179, 179.]
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Full Fit result for $\,2\beta+\gamma, [^{\circ}]$

$103.85 \pm 0.55 \text{ and } 110.8 \pm 4.3$ 68% prob:[103.3, 104.4] U [106.5, 115.1] 95% prob:[99.70, 119.3] 99% prob:[91.40, 92.00] U [94.30, 94.60] U [95.60, 124.7]
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Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 10 \text{ and } 74 \pm 11$ 68% prob:[-116, -96.] U [62.5, 84.7] 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
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Full Fit result for $\,\gamma, [^{\circ}]$

$67.0 \pm 4.8$ 68% prob:[62.2, 71.9] 95% prob:[56.9, 76.3] 99% prob:[51.2, 81.7]
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woops, ordering error: got an ENDTWISTY before seeing a TWISTY

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It is possible to generalize the full UTfit beyond the Standard Model to all those NP models characterized by Minimal Flavour Violation, i.e. having quark miking ruled only by the Standard Model CKM couplings. In fact, in this case no additional weak phases are generated and several observables entering into the Standard Model fit (the tree-level processes and the measurement of angles through the use of time dependent CP asymmetries) are not affected by the presence of New Physics. The only sizable effect we are sensitive to is a shift of the Inami-Lim function of the top contribution in meson mixing. This means that in general εK and Δmd cannot be used in a common SM and MFV framework, but any New Physics contribution disappear in the case of Δmd/Δms. So, simply removing the information related to εK and Δmd from the full UTfit one can obtain a more precise determination of the Universal Unitarity Triangle, which is a common starting point for the Standard Model and any MFV model.

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It is possible to generalize the full UTfit beyond the Standard Model to all those NP models characterized by Minimal Flavour Violation, i.e. having quark miking ruled only by the Standard Model CKM couplings (http://arxiv.org/abs/hep-ph/0007085). In fact, in this case no additional weak phases are generated and several observables entering into the Standard Model fit (the tree-level processes and the measurement of angles through the use of time dependent CP asymmetries) are not affected by the presence of New Physics. The only sizable effect we are sensitive to is a shift of the Inami-Lim function of the top contribution in meson mixing. This means that in general εK and Δmd cannot be used in a common SM and MFV framework, but any New Physics contribution disappear in the case of Δmd/Δms. So, simply removing the information related to εK and Δmd from the full UTfit one can obtain a more precise determination of the Universal Unitarity Triangle, which is a common starting point for the Standard Model and any MFV model.

Parameter	Input value	Full fit
$\bar{\rho}$		$0.143 \pm 0.03$
$\bar{\eta}$		$0.342 \pm 0.015$
$\rho$		$0.146 \pm 0.031$
$\eta$		$0.351 \pm 0.016$
		$0.807 \pm 0.01$
$\lambda$	$0.2253 \pm 0.0011$	$0.22545 \pm 0.00065$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$90.8 \pm 4.8$
$\beta, [^{\circ}]$		$21.73 \pm 0.74$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.688 \pm 0.018$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$67.3 \pm 4.8$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97425 \pm 0.00015 & 0.22545 \pm 0.00065 & (0.00352 \pm 0.00011)e^{i(-67.7 \pm 4.4)^\circ}\\ -(0.2253 \pm 0.00065)e^{i(0.033 \pm 0.0016)^\circ} & 0.97342 \pm 0.00015 & 0.04099 \pm 0.00046 \\ (0.00854 \pm 0.00031)e^{i(-21.66 \pm 0.73)^\circ} & -(0.04024 \pm 0.00045)e^{i(1.04 \pm 0.048)^\circ} & 0.999154 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.143 \pm 0.03$ 95% prob:[0.082, 0.204] 99% prob:[0.050, 0.238]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.342 \pm 0.015$ 95% prob:[0.310, 0.372] 99% prob:[0.293, 0.388]
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Full fit result for $\,\bar{\rho} - \bar{\eta}$


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Full fit result for $\,\rho$

$0.146 \pm 0.031$ 95% prob:[0.084, 0.209] 99% prob:[0.051, 0.244]
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Full fit result for $\,\eta$

$0.351 \pm 0.016$ 95% prob:[0.319, 0.382] 99% prob:[0.301, 0.398]
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Full fit result for $\,A$

$0.807 \pm 0.01$ 95% prob:[0.7870, 0.8280] 99% prob:[0.7780, 0.8390]
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Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22545 \pm 0.00065$ 95% prob:[0.22410, 0.22670] 99% prob:[0.22360, 0.22750]
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Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 95% prob:[81.0, 102.] U [161., 169.] 99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\alpha, [^{\circ}]$

$90.8 \pm 4.8$ 95% prob:[81.2, 100.] 99% prob:[76.4, 106.]
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Full fit result for $\,\beta, [^{\circ}]$

$21.73 \pm 0.74$ 95% prob:[20.2, 23.2] 99% prob:[19.6, 24.0]
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Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
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Full Fit result for $\,\sin(2\beta)$

$0.688 \pm 0.018$ 95% prob:[0.651, 0.725] 99% prob:[0.633, 0.745]
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Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\gamma, [^{\circ}]$

$67.3 \pm 4.8$ 95% prob:[57.5, 77.1] 99% prob:[52.0, 82.2]
EPS - PDF - PNG - JPG - GIF

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

Revision 25

Changes from r23 to r25

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The fit presented here is meant to constrain the NP contributions to DF|=2 transitions by using the available experimental information on

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The fit presented here is meant to constrain the NP contributions to |Δ F|=2 transitions by using the available experimental information on

loop-mediated processes In general, NP models introduce a large number of new parameters: flavour changing couplings, short distance coefficients and matrix elements of new local operators. The specific list and the actual values of these parameters can only be determined

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within a given model. Nevertheless, mixing processes, are described by a single amplitude and can be parameterized, without loss of generality,

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within a given model. Nevertheless mixing processes are described by a single amplitude and can be parameterized, without loss of generality,

in terms of two parameters, which quantify the difference of the complex amplitude with respect to the SM one. Thus, for instance, in the case of $B^0_q-\bar{B}^0_q$ mixing we define

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where $H_\mathrm{eff}^\mathrm{SM}$ includes only the SM box diagrams, while $H_\mathrm{eff}^\mathrm{full}$ includes also the NP

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contributions. In the absence of NP effects, $C_{B_q}=1$ and $\phi_{B_q}=0$ by definition. The experimental quantities determined from the $B^0_q-\bar{B}^0_q$ mixings are related to their SM counterparts and the NP parameters by the following relations:

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contributions. In the absence of NP effects, $C_{B_q}=1$ and $\phi_{B_q}=0$ by definition. In a similar way, one can write $C_{\epsilon_K} = \frac{\mathrm{Im}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{full}}|\bar{K}^0\rangle]} {\mathrm{Im}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{SM}}|\bar{K}^0\rangle]}\,,\qquad C_{\Delta m_K} = \frac{\mathrm{Re}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{full}}|\bar{K}^0\rangle]} {\mathrm{Re}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{SM}}|\bar{K}^0\rangle]}\,. \label{eq:ceps}$ Concerning $\Delta m_K$ , to be conservative, we add to the short-distance contribution a possible long-distance one that varies with a uniform distribution between zero and the experimental value of $\Delta m_K$

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The experimental quantities determined from the $B^0_q-\bar{B}^0_q$ mixings are related to their SM counterparts and the NP parameters by the following relations:

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\Delta m_d^\mathrm{exp} = C_{B_d} \Delta m_d^\mathrm{SM} \,,\; \sin 2 \beta^\mathrm{exp} = \sin (2 \beta^\mathrm{SM} + 2\phi_{B_d})\,,\; \alpha^\mathrm{exp} = \alpha^\mathrm{SM} - \phi_{B_d}\,,

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\Delta m_d^\mathrm{exp} = C_{B_d} \Delta m_d^\mathrm{SM} \,,\; \\sin 2 \beta^\mathrm{exp} = \sin (2 \beta^\mathrm{SM} + 2\phi_{B_d})\,,\; \\ \alpha^\mathrm{exp} = \alpha^\mathrm{SM} - \phi_{B_d}\,, \\Delta m_s^\mathrm{exp} = C_{B_s} \Delta m_s^\mathrm{SM} \,,\; \\phi_s^\mathrm{exp} = (\beta_s^\mathrm{SM} - \phi_{B_s})\,,\; \\Delta m_K^\mathrm{exp} = C_{\Delta m_K} \Delta m_K^\mathrm{SM} \,,\; \\epsilon_K^\mathrm{exp} = C_{\epsilon_K} \epsilon_K^\mathrm{SM} \,,\; \

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in a self-explanatory notation.

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All the measured observables can be written as a function of these NP parameters and the SM ones ρ and η, and additional parameters such as masses, form factors, and decay constants.

Click on the parameter name to jump to the corresponding plot

Parameter	Input value	Full fit
$\bar{\rho}$		$0.135 \pm 0.04$
$\bar{\eta}$		$0.374 \pm 0.026$
$\rho$		$0.138 \pm 0.041$
$\eta$		$0.384 \pm 0.027$
		$0.804 \pm 0.01$
$\lambda$	$0.2253 \pm 0.0011$	$0.22535 \pm 0.00065$
$C_{B_{d}}$		$0.95 \pm 0.14$
$\phi_{B_{d}}, [^{\circ}]$		$-3.1 \pm 1.7$
$C_{B_{s}}$		$0.95 \pm 0.095$
$\phi_{B_{s}}, [^{\circ}]$		$-68.2 \pm 7.6 \text{ and } -20.3 \pm 7.7$
$C_{\epsilon_{K}}$		$1.05 \pm 0.12$
$A_{SL_{d}}$	$-0.0005 \pm 0.0056$	$-0.0028 \pm 0.0024$
$A_{SL_{s}}$	$-0.0017 \pm 0.0091$	$-0.0044 \pm 0.0014$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97427 \pm 0.00015 & 0.22535 \pm 0.00065 & (0.00377 \pm 0.00021)e^{i(-70.0 \pm 5.6)^\circ}\\ -(0.22525 \pm 0.00065)e^{i(0.0358 \pm 0.0025)^\circ} & 0.97345 \pm 0.00015 & 0.04082 \pm 0.00045 \\ (0.00869 \pm 0.00039)e^{i(-23.3 \pm 1.3)^\circ} & -(0.04007 \pm 0.00044)e^{i(1.138 \pm 0.076)^\circ} & 0.99916 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.135 \pm 0.04$ 95% prob:[0.069, 0.223] 99% prob:[0.040, 0.262]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.374 \pm 0.026$ 95% prob:[0.322, 0.433] 99% prob:[0.297, 0.471]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.138 \pm 0.041$ 95% prob:[0.070, 0.228] 99% prob:[0.041, 0.269]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.384 \pm 0.027$ 95% prob:[0.330, 0.444] 99% prob:[0.305, 0.482]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.804 \pm 0.01$ 95% prob:[0.7840, 0.8240] 99% prob:[0.7750, 0.8350]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22535 \pm 0.00065$ 95% prob:[0.22410, 0.22670] 99% prob:[0.22350, 0.22750]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{d}}$

$0.95 \pm 0.14$ 95% prob:[0.70, 1.27] 99% prob:[0.59, 1.51]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{d}}, [^{\circ}]$

$-3.1 \pm 1.7$ 95% prob:[-7., 0.1] 99% prob:[-10, 2.1]
EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{d}} - C_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{d}} - A^{NP}_{d}/A^{SM}_{d}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{s}}$

$0.95 \pm 0.095$ 95% prob:[0.776, 1.162] 99% prob:[0.706, 1.295]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{s}}, [^{\circ}]$

$-68.2 \pm 7.6 \text{ and } -20.3 \pm 7.7$ 95% prob:[-81, -51] U [-38, -6.] 99% prob:[-85, -1.]
EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{s}} - C_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{s}} - A^{NP}_{s}/A^{SM}_{s}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{\epsilon_{K}}$

$1.05 \pm 0.12$ 95% prob:[0.82, 1.34] 99% prob:[-0.8, -0.8] U [0.70, 1.60]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{d}}$

Gaussian likelihood used $-0.0005 \pm 0.0056$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,A_{SL_{d}}$

$-0.0028 \pm 0.0024$ 95% prob:[-0.0077, 0.00129] 99% prob:[-0.0096, 0.00431]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{s}}$

Gaussian likelihood used $-0.0017 \pm 0.0091$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,A_{SL_{s}}$

$-0.0044 \pm 0.0014$ 95% prob:[-0.0072, -0.0015] 99% prob:[-0.0087, 0.00004]
EPS - PDF - PNG - JPG - GIF

Revision 23

Changes from r21 to r23

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%TWISTY{ prefix="" mode="div"

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suffix="" remember="on" }%

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In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model an some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters.

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All the analyses presented here rely on the several measurements: |Vub| / |Vcb|, Dmd, Dms, and the measurements of CP-violating quantities

>
>

All the analyses presented here rely on the several measurements: |Vub/Vcb|, Δmd, Δms, and the measurements of CP-violating quantities

in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D()K() modes), 2β + γ (using D(*)π(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameter, LQCD calculations play a central role

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For some of the quantity we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

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Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution 1. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, ¯x2 ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of ¯x2 (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

>
>

Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution 1. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, x2(meas.) ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of x2(meas.) (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

The color code indicates the compatibility between direct and indirect determinations, given in terms of standard deviations, as a function of the measured value and its experimental uncertainty. The crosses indicate the direct world average measurement values.

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

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}% Click on the parameter name to jump to the corresponding plot

Parameter	Input value	Full fit	SM Prediction
$\bar{\rho}$		$0.132 \pm 0.02$
$\bar{\eta}$		$0.358 \pm 0.012$
$\rho$		$0.135 \pm 0.021$
$\eta$		$0.367 \pm 0.013$
		$0.8095 \pm 0.0095$
$\lambda$	$0.2253 \pm 0.0011$	$0.22545 \pm 0.00065$
$\|V_{ub}\|$	$0.00376 \pm 0.0002$	$0.00364 \pm 0.00011$	$0.00355 \pm 0.00014$
$\|V_{cb}\|$	$0.04083 \pm 0.00045$	$0.04117 \pm 0.00043$	$0.04269 \pm 0.00099$
$\sin\theta_{12}$		$0.22545 \pm 0.00065$
$\sin\theta_{23}$		$0.04117 \pm 0.00043$
$\sin\theta_{13}$		$0.00364 \pm 0.00011$
$\delta$		$69.7 \pm 2.9$
$m_{b},{\rm {GeV}/c^{2}}$	$4.21 \pm 0.08$
$m_{c},{\rm {GeV}/c^{2}}$	$1.3 \pm 0.1$
$m_{t},{\rm {GeV}/c^{2}}$	$163.4 \pm 1.2$	$163.4 \pm 1.2$	$163.5 \pm 9.5$
$\Delta m_{s},{\rm ps^{-1}}$	$17.77 \pm 0.12$	$17.77 \pm 0.12$	$18.3 \pm 1.3$
$\Delta m_{d},{\rm ps^{-1}}$	$0.507 \pm 0.005$
$\Delta m_{K},10^{-15}{\rm ps^{-1}}$	$1.8 \pm 1.8$
$f_{B_{s}}$	$0.239 \pm 0.01$	$0.2359 \pm 0.0056$	$0.2349 \pm 0.0067$
$f_{B_{s}}/f_{B_{d}}$	$1.23 \pm 0.03$	$1.225 \pm 0.025$	$1.213 \pm 0.044$
$B_{B_{s}}/B_{B_{d}}$	$1.06 \pm 0.04$	$1.069 \pm 0.036$	$1.113 \pm 0.085$
$B_{B_{s}}$	$0.87 \pm 0.04$	$0.845 \pm 0.036$	$0.769 \pm 0.065$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$87.8 \pm 3.0$	$85.4 \pm 3.7$
$\beta, [^{\circ}]$		$22.42 \pm 0.74$	$25.2 \pm 1.6$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.705 \pm 0.018$	$0.771 \pm 0.036$
$\cos(2\beta)$	$0.87 \pm 0.13$	$0.71 \pm 0.018$	$0.639 \pm 0.043$
$2\beta+\gamma, [^{\circ}]$	$-90 \pm 56 \text{ and } 94 \pm 52$	$114.7 \pm 3.1$	$114.9 \pm 3.1$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$69.8 \pm 3.0$	$69.6 \pm 3.1$
$\|\varepsilon_{K}\|$	$0.00222994 \pm 1.04974 \times 10^{-5}$	$0.00222854 \pm 9.98004 \times 10^{-06}$	$0.00192 \pm 0.00018$
$B(B\rightarrow\tau\nu),10^{-4}$	$1.72 \pm 0.28$	$0.867 \pm 0.078$	$0.805 \pm 0.071$
$J_{cp}\times 10^{5}$		$3.09 \pm 0.11$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97425 \pm 0.00015 & 0.22549 \pm 0.00064 & (0.00364 \pm 0.00011)e^{i(-69.7 \pm 2.9)^\circ}\\ -(0.2253 \pm 0.00064)e^{i( 0.0348 \pm 0.0012)^\circ} & 0.97341 \pm 0.00015 & 0.04117 \pm 0.00043 \\ (0.00871 \pm 0.00019)e^{i(-22.46 \pm 0.73)^\circ} & -(0.04039 \pm 0.00043)e^{i( 1.089 \pm 0.038)^\circ} & 0.999145 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.132 \pm 0.02$ 95% prob:[0.092, 0.171] 99% prob:[0.074, 0.190]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.358 \pm 0.012$ 95% prob:[0.332, 0.383] 99% prob:[0.321, 0.396]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.135 \pm 0.021$ 95% prob:[0.095, 0.175] 99% prob:[0.076, 0.195]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.367 \pm 0.013$ 95% prob:[0.341, 0.393] 99% prob:[0.329, 0.406]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.8095 \pm 0.0095$ 95% prob:[0.791, 0.83] 99% prob:[0.782, 0.839]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|V_{ub}\|$

$0.00376 \pm 0.0002$ 95% prob:[0.00340, 0.00428] 99% prob:[0.00327, 0.00463]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{ub}\|$

$0.00364 \pm 0.00011$ 95% prob:[0.00342, 0.00386] 99% prob:[0.00332, 0.00399]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{ub}\|$

$0.00355 \pm 0.00014$ 95% prob:[0.00327, 0.00385] 99% prob:[0.00313, 0.00401]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|V_{ub}\|$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|V_{cb}\|$

$0.04083 \pm 0.00045$ 95% prob:[0.03995, 0.04177] 99% prob:[0.03955, 0.04217] U [0.04219, 0.04233]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{cb}\|$

$0.04117 \pm 0.00043$ 95% prob:[0.04037, 0.04209] 99% prob:[0.03995, 0.04247]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{cb}\|$

$0.04269 \pm 0.00099$ 95% prob:[0.04069, 0.0447] 99% prob:[0.03971, 0.04563]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|V_{cb}\|$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{12}$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{23}$

$0.04117 \pm 0.00043$ 95% prob:[0.04033, 0.04209] 99% prob:[0.03993, 0.04251]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{13}$

$0.00364 \pm 0.00011$ 95% prob:[0.00342,0.003867] 99% prob:[0.00332,0.00399]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\delta$

$69.7 \pm 2.9$ 95% prob:[63.9, 75.7] 99% prob:[61.1, 78.6]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,m_{t},{\rm {GeV}/c^{2}}$

Gaussian likelihood used $163.4 \pm 1.2$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.4 \pm 1.2$ 95% prob:[161, 165.7] 99% prob:[159.9, 166.9]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.5 \pm 9.5$ 95% prob:[144.7, 183.1] 99% prob:[137.6, 194.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,m_{t},{\rm {GeV}/c^{2}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\Delta m_{s},{\rm ps^{-1}}$

Gaussian likelihood used $17.77 \pm 0.12$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\Delta m_{s},{\rm ps^{-1}}$

$17.77 \pm 0.12$ 95% prob:[17.5, 18.0] 99% prob:[17.4, 18.1]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\Delta m_{s},{\rm ps^{-1}}$

$18.3 \pm 1.3$ 95% prob:[15.9, 20.9] 99% prob:[14.8, 22.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\Delta m_{s},{\rm ps^{-1}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,f_{B_{s}}$

Gaussian likelihood used $0.239 \pm 0.01$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}$

$0.2359 \pm 0.0056$ 95% prob:[0.2252, 0.2477] 99% prob:[0.22, 0.2537]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}$

$0.2349 \pm 0.0067$ 95% prob:[0.2221, 0.2491] 99% prob:[0.217, 0.2571]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,f_{B_{s}}/f_{B_{d}}$

Gaussian likelihood used $1.23 \pm 0.03$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}/f_{B_{d}}$

$1.225 \pm 0.025$ 95% prob:[1.175, 1.275] 99% prob:[1.151, 1.299]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}/f_{B_{d}}$

$1.213 \pm 0.044$ 95% prob:[1.13, 1.303] 99% prob:[1.083, 1.085] U [1.093, 1.352]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}/f_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B_{B_{s}}/B_{B_{d}}$

Gaussian likelihood used $1.06 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}/B_{B_{d}}$

$1.069 \pm 0.036$ 95% prob:[0.997, 1.141] 99% prob:[0.963, 1.179]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}/B_{B_{d}}$

$1.113 \pm 0.085$ 95% prob:[0.96, 1.279] 99% prob:[0.893, 1.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}/B_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B_{B_{s}}$

Gaussian likelihood used $0.87 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}$

$0.845 \pm 0.036$ 95% prob:[0.775, 0.919] 99% prob:[0.738, 0.954]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}$

$0.769 \pm 0.065$ 95% prob:[0.648, 0.915] 99% prob:[0.608, 0.999]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 95% prob:[81, 102.] U [161., 169] 99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\alpha, [^{\circ}]$

$87.8 \pm 3.0$ 95% prob:[82.1, 93.8] 99% prob:[79.2, 96.2]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\alpha, [^{\circ}]$

$85.4 \pm 3.7$ 95% prob:[78.3, 93.2] 99% prob:[74.5, 96.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\alpha, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\beta, [^{\circ}]$

$22.42 \pm 0.74$ 95% prob:[20.9, 23.9] 99% prob:[20.2, 24.7]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\beta, [^{\circ}]$

$25.2 \pm 1.6$ 95% prob:[22.3, 28.6] 99% prob:[21.3, 30.2]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\sin(2\beta)$

$0.705 \pm 0.018$ 95% prob:[0.669, 0.742] 99% prob:[0.651, 0.762]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\sin(2\beta)$

$0.771 \pm 0.036$ 95% prob:[0.706, 0.844] 99% prob:[0.68, 0.872] U [0.875, 0.878]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\sin(2\beta)$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\cos(2\beta)$

$0.87 \pm 0.13$ 95% prob:[0.44, 0.99] 99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\cos(2\beta)$

$0.71 \pm 0.018$ 95% prob:[0.672, 0.745] 99% prob:[0.649, 0.76]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\cos(2\beta)$

$0.639 \pm 0.043$ 95% prob:[0.544, 0.712] 99% prob:[0.507, 0.731]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\cos(2\beta)$


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Fit Input for $\,2\beta+\gamma, [^{\circ}]$

$-90 \pm 56 \text{ and } 94 \pm 52$ 95% prob:[-166, 166.] 99% prob:[-179, 179]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,2\beta+\gamma, [^{\circ}]$

$114.7 \pm 3.1$ 95% prob:[108.3, 120.7] 99% prob:[105.6, 123.4]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,2\beta+\gamma, [^{\circ}]$

$114.9 \pm 3.1$ 95% prob:[108.6, 120.9] 99% prob:[105.8, 123.6]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,2\beta+\gamma, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\gamma, [^{\circ}]$

$69.8 \pm 3.0$ 95% prob:[63.9, 75.7] 99% prob:[61, 78.5]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\gamma, [^{\circ}]$

$69.6 \pm 3.1$ 95% prob:[63.4, 75.6] 99% prob:[60.5, 78.8]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\gamma, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|\varepsilon_{K}\|$

$0.00222994 \pm 1.04974\times 10^{-5}$ 95% prob:[0.00220745, 0.00224944] 99% prob:[0.00219845, 0.00225644]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|\varepsilon_{K}\|$

$0.00222854 \pm 9.98004\times 10^{-06}$ 95% prob:[0.00220858, 0.0022485] 99% prob:[0.0021986, 0.00225848]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|\varepsilon_{K}\|$

$0.00192 \pm 0.00018$ 95% prob:[0.00157, 0.00230] 99% prob:[0.00141, 0.00252]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|\varepsilon_{K}\|$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B(B\rightarrow\tau u),10^{-4}$

Gaussian likelihood used $1.72 \pm 0.28$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B(B\rightarrow\tau u),10^{-4}$

$0.867 \pm 0.078$ 95% prob:[0.721, 1.031] 99% prob:[0.661, 1.127]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B(B\rightarrow\tau u),10^{-4}$

$0.805 \pm 0.071$ 95% prob:[0.674, 0.958] 99% prob:[0.619, 1.051]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B(B\rightarrow\tau u),10^{-4}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,J_{cp}\times 10^{-5}$

$3.09 \pm 0.11$ 95% prob:[2.87, 3.30] 99% prob:[2.77, 3.42]
EPS - PDF - PNG - JPG - GIF

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

Deleted:

<
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Constraints, Parameters	Gaussian Error	Flat Error	Comments
$\lambda$		-	-
$\left \| V_{cb} \right \|~[10^{-3}]$		-	Average of exclusive
$\left \| V_{cb} \right \|~[10^{-3}]$		-	Average of inclusive
$\left \| V_{ub} \right \|~[10^{-4}] \mathrm{(excl.)}$		-	HFAG BR + Lattice QCD
$\left \| V_{ub} \right \|~[10^{-4}] \mathrm{(incl.)}$			HFAG average
		-	-
		-	-
$\Delta m_d~[ps^{-1}]$		-	WA (CDF/CLEO/LEP/BaBar/Belle)
$\Delta m_s~[ps^{-1}]$		-	CDF Likelihood is used
		-	(CDF/D0)
$f_{B_s}\sqrt{B_{B_s}}~[MeV]$		-	Lattice QCD
$\xi$		-	Lattice QCD
$\|\varepsilon_K\|~[10^{-3}]$		-	-
		-	Lattice QCD
	-	-	-
$\Delta m_K~[10^{-2}~ps^{-1}]$	-	-	-
$M_{K^0}~[GeV/c^2]$	-	-	-

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

%TWISTY{

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The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of $V_{ub}$ (exclusive) and $V_{cs}$ .

Added:

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The "no-lattice" fit is performed removing from the fitting procedure the use of the hadronic parameters coming from lattice calculations, letting them as free parameters of the fit. This approach allows for the possibility of making a full UT analysis without relying at all on theoretical calculations of hadronic matrix elements and on the other hands to obtain the a-posteriori p.d.f. for a given hadronic quantity.

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

Line: 150 to 140

hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" suffix="" remember="on"

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}% Click on the parameter name to jump to the corresponding plot

>
>

}% The fit presented here is meant to constrain the NP contributions to DF|=2 transitions by using the available experimental information on loop-mediated processes In general, NP models introduce a large number of new parameters: flavour changing couplings, short distance coefficients and matrix elements of new local operators. The specific list and the actual values of these parameters can only be determined within a given model. Nevertheless, mixing processes, are described by a single amplitude and can be parameterized, without loss of generality, in terms of two parameters, which quantify the difference of the complex amplitude with respect to the SM one. Thus, for instance, in the case of $B^0_q-\bar{B}^0_q$ mixing we define $C_{B_q} \, e^{2 i \phi_{B_q}} = \frac{\langle B^0_q|H_\mathrm{eff}^\mathrm{full}|\bar{B}^0_q\rangle} {\langle B^0_q|H_\mathrm{eff}^\mathrm{SM}|\bar{B}^0_q\rangle}\,, \qquad (q=d,s)$ where $H_\mathrm{eff}^\mathrm{SM}$ includes only the SM box diagrams, while $H_\mathrm{eff}^\mathrm{full}$ includes also the NP contributions. In the absence of NP effects, $C_{B_q}=1$ and $\phi_{B_q}=0$ by definition. The experimental quantities determined from the $B^0_q-\bar{B}^0_q$ mixings are related to their SM counterparts and the NP parameters by the following relations:

$\Delta m_d^\mathrm{exp} = C_{B_d} \Delta m_d^\mathrm{SM} \,,\; \sin 2 \beta^\mathrm{exp} = \sin (2 \beta^\mathrm{SM} + 2\phi_{B_d})\,,\; \alpha^\mathrm{exp} = \alpha^\mathrm{SM} - \phi_{B_d}\,,$

in a self-explanatory notation.

Click on the parameter name to jump to the corresponding plot

Parameter	Input value	Full fit
$\bar{\rho}$		$0.135 \pm 0.04$
$\bar{\eta}$		$0.374 \pm 0.026$
$\rho$		$0.138 \pm 0.041$
$\eta$		$0.384 \pm 0.027$
		$0.804 \pm 0.01$
$\lambda$	$0.2253 \pm 0.0011$	$0.22535 \pm 0.00065$
$C_{B_{d}}$		$0.95 \pm 0.14$
$\phi_{B_{d}}, [^{\circ}]$		$-3.1 \pm 1.7$
$C_{B_{s}}$		$0.95 \pm 0.095$
$\phi_{B_{s}}, [^{\circ}]$		$-68.2 \pm 7.6 \text{ and } -20.3 \pm 7.7$
$C_{\epsilon_{K}}$		$1.05 \pm 0.12$
$A_{SL_{d}}$	$-0.0005 \pm 0.0056$	$-0.0028 \pm 0.0024$
$A_{SL_{s}}$	$-0.0017 \pm 0.0091$	$-0.0044 \pm 0.0014$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97427 \pm 0.00015 & 0.22535 \pm 0.00065 & (0.00377 \pm 0.00021)e^{i(-70.0 \pm 5.6)^\circ}\\ -(0.22525 \pm 0.00065)e^{i(0.0358 \pm 0.0025)^\circ} & 0.97345 \pm 0.00015 & 0.04082 \pm 0.00045 \\ (0.00869 \pm 0.00039)e^{i(-23.3 \pm 1.3)^\circ} & -(0.04007 \pm 0.00044)e^{i(1.138 \pm 0.076)^\circ} & 0.99916 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.135 \pm 0.04$ 95% prob:[0.069, 0.223] 99% prob:[0.040, 0.262]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.374 \pm 0.026$ 95% prob:[0.322, 0.433] 99% prob:[0.297, 0.471]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.138 \pm 0.041$ 95% prob:[0.070, 0.228] 99% prob:[0.041, 0.269]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.384 \pm 0.027$ 95% prob:[0.330, 0.444] 99% prob:[0.305, 0.482]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.804 \pm 0.01$ 95% prob:[0.7840, 0.8240] 99% prob:[0.7750, 0.8350]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22535 \pm 0.00065$ 95% prob:[0.22410, 0.22670] 99% prob:[0.22350, 0.22750]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{d}}$

$0.95 \pm 0.14$ 95% prob:[0.70, 1.27] 99% prob:[0.59, 1.51]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{d}}, [^{\circ}]$

$-3.1 \pm 1.7$ 95% prob:[-7., 0.1] 99% prob:[-10, 2.1]
EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{d}} - C_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{d}} - A^{NP}_{d}/A^{SM}_{d}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{s}}$

$0.95 \pm 0.095$ 95% prob:[0.776, 1.162] 99% prob:[0.706, 1.295]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{s}}, [^{\circ}]$

$-68.2 \pm 7.6 \text{ and } -20.3 \pm 7.7$ 95% prob:[-81, -51] U [-38, -6.] 99% prob:[-85, -1.]
EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{s}} - C_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{s}} - A^{NP}_{s}/A^{SM}_{s}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{\epsilon_{K}}$

$1.05 \pm 0.12$ 95% prob:[0.82, 1.34] 99% prob:[-0.8, -0.8] U [0.70, 1.60]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{d}}$

Gaussian likelihood used $-0.0005 \pm 0.0056$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,A_{SL_{d}}$

$-0.0028 \pm 0.0024$ 95% prob:[-0.0077, 0.00129] 99% prob:[-0.0096, 0.00431]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{s}}$

Gaussian likelihood used $-0.0017 \pm 0.0091$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,A_{SL_{s}}$

$-0.0044 \pm 0.0014$ 95% prob:[-0.0072, -0.0015] 99% prob:[-0.0087, 0.00004]
EPS - PDF - PNG - JPG - GIF

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

Revision 21

Changes from r19 to r21

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In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model an some New Physics Models using all the available experimental and theoretical inputs which are available.

>
>

In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model an some New Physics Models using all the available experimental and theoretical inputs which are available.

Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub| / |Vcb|, Dmd, Dms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D()K() modes), 2β + γ (using D(*)π(ρ)

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The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.

The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. The interest of this procedure is to quantify the agreement of all the measured quantities by the comparison between indirect parameter determinations and their direct experimental/theortical determinations. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.

Changed:

<
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For some of the quantity we present the so called compatibility plots. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

>
>

For some of the quantity we present the so called COMPATIBILITY PLOTS. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution 1. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, ¯x2 ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of ¯x2 (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

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showlink="New Physics Fit" hidelink="New Physics Fit" showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" suffix="" remember="on" }% Under construction

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woops, ordering error: got an ENDTWISTY before seeing a TWISTY

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It is possible to generalize the full UTfit beyond the Standard Model to all those NP models characterized by Minimal Flavour Violation, i.e. having quark miking ruled only by the Standard Model CKM couplings. In fact, in this case no additional weak phases are generated and several observables entering into the Standard Model fit (the tree-level processes and the measurement of angles through the use of time dependent CP asymmetries) are not affected by the presence of New Physics. The only sizable effect we are sensitive to is a shift of the Inami-Lim function of the top contribution in meson mixing. This means that in general εK and Δmd cannot be used in a common SM and MFV framework, but any New Physics contribution disappear in the case of Δmd/Δms. So, simply removing the information related to εK and Δmd from the full UTfit one can obtain a more precise determination of the Universal Unitarity Triangle, which is a common starting point for the Standard Model and any MFV model.

Click on the parameter name to jump to the corresponding plot

Parameter	Input value	Full fit
$\bar{\rho}$		$0.135 \pm 0.04$
$\bar{\eta}$		$0.374 \pm 0.026$
$\rho$		$0.138 \pm 0.041$
$\eta$		$0.384 \pm 0.027$
		$0.804 \pm 0.01$
$\lambda$	$0.2253 \pm 0.0011$	$0.22535 \pm 0.00065$
$C_{B_{d}}$		$0.95 \pm 0.14$
$\phi_{B_{d}}, [^{\circ}]$		$-3.1 \pm 1.7$
$C_{B_{s}}$		$0.95 \pm 0.095$
$\phi_{B_{s}}, [^{\circ}]$		$-68.2 \pm 7.6 \text{ and } -20.3 \pm 7.7$
$C_{\epsilon_{K}}$		$1.05 \pm 0.12$
$A_{SL_{d}}$	$-0.0005 \pm 0.0056$	$-0.0028 \pm 0.0024$
$A_{SL_{s}}$	$-0.0017 \pm 0.0091$	$-0.0044 \pm 0.0014$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97427 \pm 0.00015 & 0.22535 \pm 0.00065 & (0.00377 \pm 0.00021)e^{i(-70.0 \pm 5.6)^\circ}\\ -(0.22525 \pm 0.00065)e^{i(0.0358 \pm 0.0025)^\circ} & 0.97345 \pm 0.00015 & 0.04082 \pm 0.00045 \\ (0.00869 \pm 0.00039)e^{i(-23.3 \pm 1.3)^\circ} & -(0.04007 \pm 0.00044)e^{i(1.138 \pm 0.076)^\circ} & 0.99916 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.135 \pm 0.04$ 95% prob:[0.069, 0.223] 99% prob:[0.040, 0.262]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.374 \pm 0.026$ 95% prob:[0.322, 0.433] 99% prob:[0.297, 0.471]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.138 \pm 0.041$ 95% prob:[0.070, 0.228] 99% prob:[0.041, 0.269]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.384 \pm 0.027$ 95% prob:[0.330, 0.444] 99% prob:[0.305, 0.482]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.804 \pm 0.01$ 95% prob:[0.7840, 0.8240] 99% prob:[0.7750, 0.8350]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22535 \pm 0.00065$ 95% prob:[0.22410, 0.22670] 99% prob:[0.22350, 0.22750]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{d}}$

$0.95 \pm 0.14$ 95% prob:[0.70, 1.27] 99% prob:[0.59, 1.51]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{d}}, [^{\circ}]$

$-3.1 \pm 1.7$ 95% prob:[-7., 0.1] 99% prob:[-10, 2.1]
EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{d}} - C_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{d}} - A^{NP}_{d}/A^{SM}_{d}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{B_{s}}$

$0.95 \pm 0.095$ 95% prob:[0.776, 1.162] 99% prob:[0.706, 1.295]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\phi_{B_{s}}, [^{\circ}]$

$-68.2 \pm 7.6 \text{ and } -20.3 \pm 7.7$ 95% prob:[-81, -51] U [-38, -6.] 99% prob:[-85, -1.]
EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{s}} - C_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

2D for $\,\Phi_{B_{s}} - A^{NP}_{s}/A^{SM}_{s}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,C_{\epsilon_{K}}$

$1.05 \pm 0.12$ 95% prob:[0.82, 1.34] 99% prob:[-0.8, -0.8] U [0.70, 1.60]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{d}}$

Gaussian likelihood used $-0.0005 \pm 0.0056$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,A_{SL_{d}}$

$-0.0028 \pm 0.0024$ 95% prob:[-0.0077, 0.00129] 99% prob:[-0.0096, 0.00431]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,A_{SL_{s}}$

Gaussian likelihood used $-0.0017 \pm 0.0091$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,A_{SL_{s}}$

$-0.0044 \pm 0.0014$ 95% prob:[-0.0072, -0.0015] 99% prob:[-0.0087, 0.00004]
EPS - PDF - PNG - JPG - GIF

Revision 19

Changes from r17 to r19

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> >	showlink="Tree level Fit" hidelink="Tree Level Fit" showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" suffix="" remember="on" }% In principle, the presence of New Physics might affect the result of the UT analysis, changing the functional dependences of the experimental quantities upon ρ and η. On the contrary, two constraints now available, are almost unchanged by the presence of NP: \|Vub/Vcb\| from semileptonic B decays and the UT angle γ from B → D(*)K decays. As usual from this fit one can gets predictions for each observable related to the Unitarity Triangle. This set of values is the minimal requirement that each model describing New Physics has to satisfy, in order to be taken as a realistic description of physics beyond the Standard Model. woops, ordering error: got an ENDTWISTY before seeing a TWISTY %TWISTY{ prefix=" " mode="div"
	showlink="No-Lattice Fit" hidelink="No-Lattice Fit" showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png"
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	remember="on" }% In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints :
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< <	\Deltam_s, Dms, eK, Vub (exclusive), B-->tau nu,
> >	$\Delta m_s, \Delta m_d, \epsilon_K, B \rightarrow \tau \nu,$ . Let's consider schematically the dependence of these observable in terms of the non perturbative QCD parameters : $\Delta m_s \propto f_{Bs} \sqrt{B_{Bs}} \\ \Delta m_d \propto f_{Bd} \sqrt{B_{Bd}} = \frac{f_{Bs}}{\xi} \times \sqrt{B_{Bs}} \\ Br(B \rightarrow \tau \nu) \propto f_{Bd}^2 = \frac{f_{Bs}^2}{\xi^2} \times \frac{{B_{Bs}}}{{B_{Bd}}} \\ \epsilon_K \propto B_K \\$ . We decide to express these observable in terms of five LQCD parameters $f_{Bs}, \quad B_{Bs}, \quad \xi, \quad \frac{{B_{Bs}}}{{B_{Bd}}}, \quad B_K$ The reason of this choice is to maxime the parameters on the Bs sector and parameters which are mostly uncorrelated. To this set of five parameters we should add the non perturbative parameters entering in the expression of $V_{ub}$ (exclusive) and $V_{cs}$ .

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	woops, ordering error: got an ENDTWISTY before seeing a TWISTY

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In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model an some New Physics Models using all the available experimental and theoretical inputs which are available. \The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in the given model. The agreement of all the measured quantities is quantified by the comparison between indirect parameter determinations and their direct experimental measurements. The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.

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showlink="Introduction" hidelink="Introduction" showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" suffix="" remember="on" }% In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model an some New Physics Models using all the available experimental and theoretical inputs which are available. Inputs to this analysis consist of a large body of both experimental measurements and theoretically determined parameters. All the analyses presented here rely on the several measurements: |Vub| / |Vcb|, Dmd, Dms, and the measurements of CP-violating quantities in the kaon (εK) and in the B sectors with the measurements of α (using ππ, ρρ and πρ modes), γ (using D()K() modes), 2β + γ (using D(*)π(ρ) modes), and sin2β and cos 2β from B0 → J/ψKS and B0 → J/ψK* respectively. Among the theoretical parameter, LQCD calculations play a central role

The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in a given model.

The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. The interest of this procedure is to quantify the agreement of all the measured quantities by the comparison between indirect parameter determinations and their direct experimental/theortical determinations. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

For some of the quantity we present the so called compatibility plots. In Unitarity Triangle fits based on a χ2 minimization, a conventional evaluation of compatibility stems automatically from the value of the χ2 at its minimum. The compatibility between constraints in the Bayesian approach is simply done by comparing two different p.d.f.’s.

Let us consider, for instance, two p.d.f.’s for a given quantity obtained from the Unitarity Triangle fit, f(x1), and from a direct measurement, f(x2): their compatibility is evaluated by constructing the p.d.f. of the difference variable, x2 − x1, and by estimating the distance of the most probable value from zero in units of standard deviations. The latter is done by integrating this p.d.f. between zero and the most probable value and converting it into the equivalent number of standard deviations for a Gaussian distribution 1. The advantage of this approach is that no approximation is made on the shape of p.d.f.’s. In the following analysis, f(x1) is the p.d.f. predicted by the Unitarity Triangle fit while the p.d.f of the measured quantity, f(x2), is taken Gaussian for simplicity. The number of standard deviations between the measured value, ¯x2 ± σ(x2), and the predicted value (distributed according to f(x1)) is plotted as a function of ¯x2 (x-axis) and σ(x2) (y-axis). The compatibility between x1 and x2 can be then directly estimated on the plot, for any central value and error of the measurement of x2.

The color code indicates the compatibility between direct and indirect determinations, given in terms of standard deviations, as a function of the measured value and its experimental uncertainty. The crosses indicate the direct world average measurement values.

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}% Click on the parameter name to jump to the corresponding plot

Parameter	Input value	Full fit	SM Prediction
$\bar{\rho}$		$0.132 \pm 0.02$
$\bar{\eta}$		$0.358 \pm 0.012$
$\rho$		$0.135 \pm 0.021$
$\eta$		$0.367 \pm 0.013$
		$0.8095 \pm 0.0095$
$\lambda$	$0.2253 \pm 0.0011$	$0.22545 \pm 0.00065$
$\|V_{ub}\|$	$0.00376 \pm 0.0002$	$0.00364 \pm 0.00011$	$0.00355 \pm 0.00014$
$\|V_{cb}\|$	$0.04083 \pm 0.00045$	$0.04117 \pm 0.00043$	$0.04269 \pm 0.00099$
$\sin\theta_{12}$		$0.22545 \pm 0.00065$
$\sin\theta_{23}$		$0.04117 \pm 0.00043$
$\sin\theta_{13}$		$0.00364 \pm 0.00011$
$\delta$		$69.7 \pm 2.9$
$m_{b},{\rm {GeV}/c^{2}}$	$4.21 \pm 0.08$
$m_{c},{\rm {GeV}/c^{2}}$	$1.3 \pm 0.1$
$m_{t},{\rm {GeV}/c^{2}}$	$163.4 \pm 1.2$	$163.4 \pm 1.2$	$163.5 \pm 9.5$
$\Delta m_{s},{\rm ps^{-1}}$	$17.77 \pm 0.12$	$17.77 \pm 0.12$	$18.3 \pm 1.3$
$\Delta m_{d},{\rm ps^{-1}}$	$0.507 \pm 0.005$
$\Delta m_{K},10^{-15}{\rm ps^{-1}}$	$1.8 \pm 1.8$
$f_{B_{s}}$	$0.239 \pm 0.01$	$0.2359 \pm 0.0056$	$0.2349 \pm 0.0067$
$f_{B_{s}}/f_{B_{d}}$	$1.23 \pm 0.03$	$1.225 \pm 0.025$	$1.213 \pm 0.044$
$B_{B_{s}}/B_{B_{d}}$	$1.06 \pm 0.04$	$1.069 \pm 0.036$	$1.113 \pm 0.085$
$B_{B_{s}}$	$0.87 \pm 0.04$	$0.845 \pm 0.036$	$0.769 \pm 0.065$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$87.8 \pm 3.0$	$85.4 \pm 3.7$
$\beta, [^{\circ}]$		$22.42 \pm 0.74$	$25.2 \pm 1.6$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.705 \pm 0.018$	$0.771 \pm 0.036$
$\cos(2\beta)$	$0.87 \pm 0.13$	$0.71 \pm 0.018$	$0.639 \pm 0.043$
$2\beta+\gamma, [^{\circ}]$	$-90 \pm 56 \text{ and } 94 \pm 52$	$114.7 \pm 3.1$	$114.9 \pm 3.1$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$69.8 \pm 3.0$	$69.6 \pm 3.1$
$\|\varepsilon_{K}\|$	$0.00222994 \pm 1.04974 \times 10^{-5}$	$0.00222854 \pm 9.98004 \times 10^{-06}$	$0.00192 \pm 0.00018$
$B(B\rightarrow\tau\nu),10^{-4}$	$1.72 \pm 0.28$	$0.867 \pm 0.078$	$0.805 \pm 0.071$
$J_{cp}\times 10^{5}$		$3.09 \pm 0.11$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97425 \pm 0.00015 & 0.22549 \pm 0.00064 & (0.00364 \pm 0.00011)e^{i(-69.7 \pm 2.9)^\circ}\\ -(0.2253 \pm 0.00064)e^{i( 0.0348 \pm 0.0012)^\circ} & 0.97341 \pm 0.00015 & 0.04117 \pm 0.00043 \\ (0.00871 \pm 0.00019)e^{i(-22.46 \pm 0.73)^\circ} & -(0.04039 \pm 0.00043)e^{i( 1.089 \pm 0.038)^\circ} & 0.999145 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.132 \pm 0.02$ 95% prob:[0.092, 0.171] 99% prob:[0.074, 0.190]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.358 \pm 0.012$ 95% prob:[0.332, 0.383] 99% prob:[0.321, 0.396]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.135 \pm 0.021$ 95% prob:[0.095, 0.175] 99% prob:[0.076, 0.195]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.367 \pm 0.013$ 95% prob:[0.341, 0.393] 99% prob:[0.329, 0.406]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.8095 \pm 0.0095$ 95% prob:[0.791, 0.83] 99% prob:[0.782, 0.839]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|V_{ub}\|$

$0.00376 \pm 0.0002$ 95% prob:[0.00340, 0.00428] 99% prob:[0.00327, 0.00463]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{ub}\|$

$0.00364 \pm 0.00011$ 95% prob:[0.00342, 0.00386] 99% prob:[0.00332, 0.00399]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{ub}\|$

$0.00355 \pm 0.00014$ 95% prob:[0.00327, 0.00385] 99% prob:[0.00313, 0.00401]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|V_{ub}\|$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|V_{cb}\|$

$0.04083 \pm 0.00045$ 95% prob:[0.03995, 0.04177] 99% prob:[0.03955, 0.04217] U [0.04219, 0.04233]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{cb}\|$

$0.04117 \pm 0.00043$ 95% prob:[0.04037, 0.04209] 99% prob:[0.03995, 0.04247]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{cb}\|$

$0.04269 \pm 0.00099$ 95% prob:[0.04069, 0.0447] 99% prob:[0.03971, 0.04563]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|V_{cb}\|$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{12}$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{23}$

$0.04117 \pm 0.00043$ 95% prob:[0.04033, 0.04209] 99% prob:[0.03993, 0.04251]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{13}$

$0.00364 \pm 0.00011$ 95% prob:[0.00342,0.003867] 99% prob:[0.00332,0.00399]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\delta$

$69.7 \pm 2.9$ 95% prob:[63.9, 75.7] 99% prob:[61.1, 78.6]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,m_{t},{\rm {GeV}/c^{2}}$

Gaussian likelihood used $163.4 \pm 1.2$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.4 \pm 1.2$ 95% prob:[161, 165.7] 99% prob:[159.9, 166.9]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.5 \pm 9.5$ 95% prob:[144.7, 183.1] 99% prob:[137.6, 194.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,m_{t},{\rm {GeV}/c^{2}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\Delta m_{s},{\rm ps^{-1}}$

Gaussian likelihood used $17.77 \pm 0.12$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\Delta m_{s},{\rm ps^{-1}}$

$17.77 \pm 0.12$ 95% prob:[17.5, 18.0] 99% prob:[17.4, 18.1]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\Delta m_{s},{\rm ps^{-1}}$

$18.3 \pm 1.3$ 95% prob:[15.9, 20.9] 99% prob:[14.8, 22.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\Delta m_{s},{\rm ps^{-1}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,f_{B_{s}}$

Gaussian likelihood used $0.239 \pm 0.01$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}$

$0.2359 \pm 0.0056$ 95% prob:[0.2252, 0.2477] 99% prob:[0.22, 0.2537]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}$

$0.2349 \pm 0.0067$ 95% prob:[0.2221, 0.2491] 99% prob:[0.217, 0.2571]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,f_{B_{s}}/f_{B_{d}}$

Gaussian likelihood used $1.23 \pm 0.03$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}/f_{B_{d}}$

$1.225 \pm 0.025$ 95% prob:[1.175, 1.275] 99% prob:[1.151, 1.299]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}/f_{B_{d}}$

$1.213 \pm 0.044$ 95% prob:[1.13, 1.303] 99% prob:[1.083, 1.085] U [1.093, 1.352]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}/f_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B_{B_{s}}/B_{B_{d}}$

Gaussian likelihood used $1.06 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}/B_{B_{d}}$

$1.069 \pm 0.036$ 95% prob:[0.997, 1.141] 99% prob:[0.963, 1.179]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}/B_{B_{d}}$

$1.113 \pm 0.085$ 95% prob:[0.96, 1.279] 99% prob:[0.893, 1.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}/B_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B_{B_{s}}$

Gaussian likelihood used $0.87 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}$

$0.845 \pm 0.036$ 95% prob:[0.775, 0.919] 99% prob:[0.738, 0.954]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}$

$0.769 \pm 0.065$ 95% prob:[0.648, 0.915] 99% prob:[0.608, 0.999]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 95% prob:[81, 102.] U [161., 169] 99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\alpha, [^{\circ}]$

$87.8 \pm 3.0$ 95% prob:[82.1, 93.8] 99% prob:[79.2, 96.2]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\alpha, [^{\circ}]$

$85.4 \pm 3.7$ 95% prob:[78.3, 93.2] 99% prob:[74.5, 96.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\alpha, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\beta, [^{\circ}]$

$22.42 \pm 0.74$ 95% prob:[20.9, 23.9] 99% prob:[20.2, 24.7]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\beta, [^{\circ}]$

$25.2 \pm 1.6$ 95% prob:[22.3, 28.6] 99% prob:[21.3, 30.2]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\sin(2\beta)$

$0.705 \pm 0.018$ 95% prob:[0.669, 0.742] 99% prob:[0.651, 0.762]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\sin(2\beta)$

$0.771 \pm 0.036$ 95% prob:[0.706, 0.844] 99% prob:[0.68, 0.872] U [0.875, 0.878]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\sin(2\beta)$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\cos(2\beta)$

$0.87 \pm 0.13$ 95% prob:[0.44, 0.99] 99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\cos(2\beta)$

$0.71 \pm 0.018$ 95% prob:[0.672, 0.745] 99% prob:[0.649, 0.76]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\cos(2\beta)$

$0.639 \pm 0.043$ 95% prob:[0.544, 0.712] 99% prob:[0.507, 0.731]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\cos(2\beta)$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,2\beta+\gamma, [^{\circ}]$

$-90 \pm 56 \text{ and } 94 \pm 52$ 95% prob:[-166, 166.] 99% prob:[-179, 179]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,2\beta+\gamma, [^{\circ}]$

$114.7 \pm 3.1$ 95% prob:[108.3, 120.7] 99% prob:[105.6, 123.4]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,2\beta+\gamma, [^{\circ}]$

$114.9 \pm 3.1$ 95% prob:[108.6, 120.9] 99% prob:[105.8, 123.6]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,2\beta+\gamma, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\gamma, [^{\circ}]$

$69.8 \pm 3.0$ 95% prob:[63.9, 75.7] 99% prob:[61, 78.5]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\gamma, [^{\circ}]$

$69.6 \pm 3.1$ 95% prob:[63.4, 75.6] 99% prob:[60.5, 78.8]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\gamma, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|\varepsilon_{K}\|$

$0.00222994 \pm 1.04974\times 10^{-5}$ 95% prob:[0.00220745, 0.00224944] 99% prob:[0.00219845, 0.00225644]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|\varepsilon_{K}\|$

$0.00222854 \pm 9.98004\times 10^{-06}$ 95% prob:[0.00220858, 0.0022485] 99% prob:[0.0021986, 0.00225848]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|\varepsilon_{K}\|$

$0.00192 \pm 0.00018$ 95% prob:[0.00157, 0.00230] 99% prob:[0.00141, 0.00252]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|\varepsilon_{K}\|$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B(B\rightarrow\tau u),10^{-4}$

Gaussian likelihood used $1.72 \pm 0.28$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B(B\rightarrow\tau u),10^{-4}$

$0.867 \pm 0.078$ 95% prob:[0.721, 1.031] 99% prob:[0.661, 1.127]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B(B\rightarrow\tau u),10^{-4}$

$0.805 \pm 0.071$ 95% prob:[0.674, 0.958] 99% prob:[0.619, 1.051]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B(B\rightarrow\tau u),10^{-4}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,J_{cp}\times 10^{-5}$

$3.09 \pm 0.11$ 95% prob:[2.87, 3.30] 99% prob:[2.77, 3.42]
EPS - PDF - PNG - JPG - GIF

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

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}% Under construction

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In the Unitarity Triangle fits the non perturbative QCD parameters enter in the expressions of several contraints : \Deltam_s, Dms, eK, Vub (exclusive), B-->tau nu,

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> >	In this page we present the results obtained for a set of interesting UT parameters in the framework of the Standard Model an some New Physics Models using all the available experimental and theoretical inputs which are available. \The results are presented in a summary table and in a series of probability density functions. The tables contain three entries per variable : the input ("direct") value, the output value and the prediction ("indirect determination") for this variable in the given model. The agreement of all the measured quantities is quantified by the comparison between indirect parameter determinations and their direct experimental measurements. The indirect determination of a particular quantity obtained performing the Unitarity Triangle fit in a given Model, including all the available constraints except from the direct measurement of the parameter of interest, gives a prediction of the quantity based on formulas which are valid in that given Model. Let's consider for example the Standard Model. The comparison between these predictions and a direct measurements can thus quantify the agreement of the single measurement with the overall fit and possibly reveal new physics phenomena.

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}% Click on the parameter name to jump to the corresponding plot

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}% Click on the parameter name to jump to the corresponding plot

Parameter	Input value	Full fit	SM Prediction
$\bar{\rho}$		$0.132 \pm 0.02$
$\bar{\eta}$		$0.358 \pm 0.012$
$\rho$		$0.135 \pm 0.021$
$\eta$		$0.367 \pm 0.013$
		$0.8095 \pm 0.0095$
$\lambda$	$0.2253 \pm 0.0011$	$0.22545 \pm 0.00065$
$\|V_{ub}\|$	$0.00376 \pm 0.0002$	$0.00364 \pm 0.00011$	$0.00355 \pm 0.00014$
$\|V_{cb}\|$	$0.04083 \pm 0.00045$	$0.04117 \pm 0.00043$	$0.04269 \pm 0.00099$
$\sin\theta_{12}$		$0.22545 \pm 0.00065$
$\sin\theta_{23}$		$0.04117 \pm 0.00043$
$\sin\theta_{13}$		$0.00364 \pm 0.00011$
$\delta$		$69.7 \pm 2.9$
$m_{b},{\rm {GeV}/c^{2}}$	$4.21 \pm 0.08$
$m_{c},{\rm {GeV}/c^{2}}$	$1.3 \pm 0.1$
$m_{t},{\rm {GeV}/c^{2}}$	$163.4 \pm 1.2$	$163.4 \pm 1.2$	$163.5 \pm 9.5$
$\Delta m_{s},{\rm ps^{-1}}$	$17.77 \pm 0.12$	$17.77 \pm 0.12$	$18.3 \pm 1.3$
$\Delta m_{d},{\rm ps^{-1}}$	$0.507 \pm 0.005$
$\Delta m_{K},10^{-15}{\rm ps^{-1}}$	$1.8 \pm 1.8$
$f_{B_{s}}$	$0.239 \pm 0.01$	$0.2359 \pm 0.0056$	$0.2349 \pm 0.0067$
$f_{B_{s}}/f_{B_{d}}$	$1.23 \pm 0.03$	$1.225 \pm 0.025$	$1.213 \pm 0.044$
$B_{B_{s}}/B_{B_{d}}$	$1.06 \pm 0.04$	$1.069 \pm 0.036$	$1.113 \pm 0.085$
$B_{B_{s}}$	$0.87 \pm 0.04$	$0.845 \pm 0.036$	$0.769 \pm 0.065$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$87.8 \pm 3.0$	$85.4 \pm 3.7$
$\beta, [^{\circ}]$		$22.42 \pm 0.74$	$25.2 \pm 1.6$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.705 \pm 0.018$	$0.771 \pm 0.036$
$\cos(2\beta)$	$0.87 \pm 0.13$	$0.71 \pm 0.018$	$0.639 \pm 0.043$
$2\beta+\gamma, [^{\circ}]$	$-90 \pm 56 \text{ and } 94 \pm 52$	$114.7 \pm 3.1$	$114.9 \pm 3.1$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$69.8 \pm 3.0$	$69.6 \pm 3.1$
$\|\varepsilon_{K}\|$	$0.00222994 \pm 1.04974 \times 10^{-5}$	$0.00222854 \pm 9.98004 \times 10^{-06}$	$0.00192 \pm 0.00018$
$B(B\rightarrow\tau\nu),10^{-4}$	$1.72 \pm 0.28$	$0.867 \pm 0.078$	$0.805 \pm 0.071$
$J_{cp}\times 10^{5}$		$3.09 \pm 0.11$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97425 \pm 0.00015 & 0.22549 \pm 0.00064 & (0.00364 \pm 0.00011)e^{i(-69.7 \pm 2.9)^\circ}\\ -(0.2253 \pm 0.00064)e^{i( 0.0348 \pm 0.0012)^\circ} & 0.97341 \pm 0.00015 & 0.04117 \pm 0.00043 \\ (0.00871 \pm 0.00019)e^{i(-22.46 \pm 0.73)^\circ} & -(0.04039 \pm 0.00043)e^{i( 1.089 \pm 0.038)^\circ} & 0.999145 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.132 \pm 0.02$ 95% prob:[0.092, 0.171] 99% prob:[0.074, 0.190]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.358 \pm 0.012$ 95% prob:[0.332, 0.383] 99% prob:[0.321, 0.396]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.135 \pm 0.021$ 95% prob:[0.095, 0.175] 99% prob:[0.076, 0.195]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.367 \pm 0.013$ 95% prob:[0.341, 0.393] 99% prob:[0.329, 0.406]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.8095 \pm 0.0095$ 95% prob:[0.791, 0.83] 99% prob:[0.782, 0.839]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|V_{ub}\|$

$0.00376 \pm 0.0002$ 95% prob:[0.00340, 0.00428] 99% prob:[0.00327, 0.00463]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{ub}\|$

$0.00364 \pm 0.00011$ 95% prob:[0.00342, 0.00386] 99% prob:[0.00332, 0.00399]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{ub}\|$

$0.00355 \pm 0.00014$ 95% prob:[0.00327, 0.00385] 99% prob:[0.00313, 0.00401]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|V_{ub}\|$


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Fit Input for $\,\|V_{cb}\|$

$0.04083 \pm 0.00045$ 95% prob:[0.03995, 0.04177] 99% prob:[0.03955, 0.04217] U [0.04219, 0.04233]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{cb}\|$

$0.04117 \pm 0.00043$ 95% prob:[0.04037, 0.04209] 99% prob:[0.03995, 0.04247]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{cb}\|$

$0.04269 \pm 0.00099$ 95% prob:[0.04069, 0.0447] 99% prob:[0.03971, 0.04563]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|V_{cb}\|$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{12}$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{23}$

$0.04117 \pm 0.00043$ 95% prob:[0.04033, 0.04209] 99% prob:[0.03993, 0.04251]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{13}$

$0.00364 \pm 0.00011$ 95% prob:[0.00342,0.003867] 99% prob:[0.00332,0.00399]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\delta$

$69.7 \pm 2.9$ 95% prob:[63.9, 75.7] 99% prob:[61.1, 78.6]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,m_{t},{\rm {GeV}/c^{2}}$

Gaussian likelihood used $163.4 \pm 1.2$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.4 \pm 1.2$ 95% prob:[161, 165.7] 99% prob:[159.9, 166.9]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.5 \pm 9.5$ 95% prob:[144.7, 183.1] 99% prob:[137.6, 194.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,m_{t},{\rm {GeV}/c^{2}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\Delta m_{s},{\rm ps^{-1}}$

Gaussian likelihood used $17.77 \pm 0.12$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\Delta m_{s},{\rm ps^{-1}}$

$17.77 \pm 0.12$ 95% prob:[17.5, 18.0] 99% prob:[17.4, 18.1]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\Delta m_{s},{\rm ps^{-1}}$

$18.3 \pm 1.3$ 95% prob:[15.9, 20.9] 99% prob:[14.8, 22.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\Delta m_{s},{\rm ps^{-1}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,f_{B_{s}}$

Gaussian likelihood used $0.239 \pm 0.01$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}$

$0.2359 \pm 0.0056$ 95% prob:[0.2252, 0.2477] 99% prob:[0.22, 0.2537]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}$

$0.2349 \pm 0.0067$ 95% prob:[0.2221, 0.2491] 99% prob:[0.217, 0.2571]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,f_{B_{s}}/f_{B_{d}}$

Gaussian likelihood used $1.23 \pm 0.03$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}/f_{B_{d}}$

$1.225 \pm 0.025$ 95% prob:[1.175, 1.275] 99% prob:[1.151, 1.299]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}/f_{B_{d}}$

$1.213 \pm 0.044$ 95% prob:[1.13, 1.303] 99% prob:[1.083, 1.085] U [1.093, 1.352]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}/f_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B_{B_{s}}/B_{B_{d}}$

Gaussian likelihood used $1.06 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}/B_{B_{d}}$

$1.069 \pm 0.036$ 95% prob:[0.997, 1.141] 99% prob:[0.963, 1.179]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}/B_{B_{d}}$

$1.113 \pm 0.085$ 95% prob:[0.96, 1.279] 99% prob:[0.893, 1.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}/B_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B_{B_{s}}$

Gaussian likelihood used $0.87 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}$

$0.845 \pm 0.036$ 95% prob:[0.775, 0.919] 99% prob:[0.738, 0.954]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}$

$0.769 \pm 0.065$ 95% prob:[0.648, 0.915] 99% prob:[0.608, 0.999]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 95% prob:[81, 102.] U [161., 169] 99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\alpha, [^{\circ}]$

$87.8 \pm 3.0$ 95% prob:[82.1, 93.8] 99% prob:[79.2, 96.2]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\alpha, [^{\circ}]$

$85.4 \pm 3.7$ 95% prob:[78.3, 93.2] 99% prob:[74.5, 96.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\alpha, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\beta, [^{\circ}]$

$22.42 \pm 0.74$ 95% prob:[20.9, 23.9] 99% prob:[20.2, 24.7]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\beta, [^{\circ}]$

$25.2 \pm 1.6$ 95% prob:[22.3, 28.6] 99% prob:[21.3, 30.2]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\sin(2\beta)$

$0.705 \pm 0.018$ 95% prob:[0.669, 0.742] 99% prob:[0.651, 0.762]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\sin(2\beta)$

$0.771 \pm 0.036$ 95% prob:[0.706, 0.844] 99% prob:[0.68, 0.872] U [0.875, 0.878]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\sin(2\beta)$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\cos(2\beta)$

$0.87 \pm 0.13$ 95% prob:[0.44, 0.99] 99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\cos(2\beta)$

$0.71 \pm 0.018$ 95% prob:[0.672, 0.745] 99% prob:[0.649, 0.76]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\cos(2\beta)$

$0.639 \pm 0.043$ 95% prob:[0.544, 0.712] 99% prob:[0.507, 0.731]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\cos(2\beta)$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,2\beta+\gamma, [^{\circ}]$

$-90 \pm 56 \text{ and } 94 \pm 52$ 95% prob:[-166, 166.] 99% prob:[-179, 179]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,2\beta+\gamma, [^{\circ}]$

$114.7 \pm 3.1$ 95% prob:[108.3, 120.7] 99% prob:[105.6, 123.4]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,2\beta+\gamma, [^{\circ}]$

$114.9 \pm 3.1$ 95% prob:[108.6, 120.9] 99% prob:[105.8, 123.6]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,2\beta+\gamma, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\gamma, [^{\circ}]$

$69.8 \pm 3.0$ 95% prob:[63.9, 75.7] 99% prob:[61, 78.5]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\gamma, [^{\circ}]$

$69.6 \pm 3.1$ 95% prob:[63.4, 75.6] 99% prob:[60.5, 78.8]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\gamma, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|\varepsilon_{K}\|$

$0.00222994 \pm 1.04974\times 10^{-5}$ 95% prob:[0.00220745, 0.00224944] 99% prob:[0.00219845, 0.00225644]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|\varepsilon_{K}\|$

$0.00222854 \pm 9.98004\times 10^{-06}$ 95% prob:[0.00220858, 0.0022485] 99% prob:[0.0021986, 0.00225848]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|\varepsilon_{K}\|$

$0.00192 \pm 0.00018$ 95% prob:[0.00157, 0.00230] 99% prob:[0.00141, 0.00252]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|\varepsilon_{K}\|$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B(B\rightarrow\tau u),10^{-4}$

Gaussian likelihood used $1.72 \pm 0.28$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B(B\rightarrow\tau u),10^{-4}$

$0.867 \pm 0.078$ 95% prob:[0.721, 1.031] 99% prob:[0.661, 1.127]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B(B\rightarrow\tau u),10^{-4}$

$0.805 \pm 0.071$ 95% prob:[0.674, 0.958] 99% prob:[0.619, 1.051]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B(B\rightarrow\tau u),10^{-4}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,J_{cp}\times 10^{-5}$

$3.09 \pm 0.11$ 95% prob:[2.87, 3.30] 99% prob:[2.77, 3.42]
EPS - PDF - PNG - JPG - GIF

woops, ordering error: got an ENDTWISTY before seeing a TWISTY

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Parameter	Input value	Full fit	SM Prediction
$\bar{\rho}$		$0.132 \pm 0.02$
$\bar{\eta}$		$0.358 \pm 0.012$
$\rho$		$0.135 \pm 0.021$
$\eta$		$0.367 \pm 0.013$
		$0.8095 \pm 0.0095$
$\lambda$	$0.2253 \pm 0.0011$	$0.22545 \pm 0.00065$
$\|V_{ub}\|$	$0.00376 \pm 0.0002$	$0.00364 \pm 0.00011$	$0.00355 \pm 0.00014$
$\|V_{cb}\|$	$0.04083 \pm 0.00045$	$0.04117 \pm 0.00043$	$0.04269 \pm 0.00099$
$\sin\theta_{12}$		$0.22545 \pm 0.00065$
$\sin\theta_{23}$		$0.04117 \pm 0.00043$
$\sin\theta_{13}$		$0.00364 \pm 0.00011$
$\delta$		$69.7 \pm 2.9$
$m_{b},{\rm {GeV}/c^{2}}$	$4.21 \pm 0.08$
$m_{c},{\rm {GeV}/c^{2}}$	$1.3 \pm 0.1$
$m_{t},{\rm {GeV}/c^{2}}$	$163.4 \pm 1.2$	$163.4 \pm 1.2$	$163.5 \pm 9.5$
$\Delta m_{s},{\rm ps^{-1}}$	$17.77 \pm 0.12$	$17.77 \pm 0.12$	$18.3 \pm 1.3$
$\Delta m_{d},{\rm ps^{-1}}$	$0.507 \pm 0.005$
$\Delta m_{K},10^{-15}{\rm ps^{-1}}$	$1.8 \pm 1.8$
$f_{B_{s}}$	$0.239 \pm 0.01$	$0.2359 \pm 0.0056$	$0.2349 \pm 0.0067$
$f_{B_{s}}/f_{B_{d}}$	$1.23 \pm 0.03$	$1.225 \pm 0.025$	$1.213 \pm 0.044$
$B_{B_{s}}/B_{B_{d}}$	$1.06 \pm 0.04$	$1.069 \pm 0.036$	$1.113 \pm 0.085$
$B_{B_{s}}$	$0.87 \pm 0.04$	$0.845 \pm 0.036$	$0.769 \pm 0.065$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$87.8 \pm 3.0$	$85.4 \pm 3.7$
$\beta, [^{\circ}]$		$22.42 \pm 0.74$	$25.2 \pm 1.6$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.705 \pm 0.018$	$0.771 \pm 0.036$
$\cos(2\beta)$	$0.87 \pm 0.13$	$0.71 \pm 0.018$	$0.639 \pm 0.043$
$2\beta+\gamma, [^{\circ}]$	$-90 \pm 56 \text{ and } 94 \pm 52$	$114.7 \pm 3.1$	$114.9 \pm 3.1$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$69.8 \pm 3.0$	$69.6 \pm 3.1$
$\|\varepsilon_{K}\|$	$0.00222994 \pm 1.04974 \times 10^{-5}$	$0.00222854 \pm 9.98004 \times 10^{-06}$	$0.00192 \pm 0.00018$
$B(B\rightarrow\tau\nu),10^{-4}$	$1.72 \pm 0.28$	$0.867 \pm 0.078$	$0.805 \pm 0.071$
$J_{cp}\times 10^{5}$		$3.09 \pm 0.11$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97425 \pm 0.00015 & 0.22549 \pm 0.00064 & (0.00364 \pm 0.00011)e^{i(-69.7 \pm 2.9)^\circ}\\ -(0.2253 \pm 0.00064)e^{i( 0.0348 \pm 0.0012)^\circ} & 0.97341 \pm 0.00015 & 0.04117 \pm 0.00043 \\ (0.00871 \pm 0.00019)e^{i(-22.46 \pm 0.73)^\circ} & -(0.04039 \pm 0.00043)e^{i( 1.089 \pm 0.038)^\circ} & 0.999145 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.132 \pm 0.02$ 95% prob:[0.092, 0.171] 99% prob:[0.074, 0.190]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.358 \pm 0.012$ 95% prob:[0.332, 0.383] 99% prob:[0.321, 0.396]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.135 \pm 0.021$ 95% prob:[0.095, 0.175] 99% prob:[0.076, 0.195]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.367 \pm 0.013$ 95% prob:[0.341, 0.393] 99% prob:[0.329, 0.406]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.8095 \pm 0.0095$ 95% prob:[0.791, 0.83] 99% prob:[0.782, 0.839]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|V_{ub}\|$

$0.00376 \pm 0.0002$ 95% prob:[0.00340, 0.00428] 99% prob:[0.00327, 0.00463]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{ub}\|$

$0.00364 \pm 0.00011$ 95% prob:[0.00342, 0.00386] 99% prob:[0.00332, 0.00399]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{ub}\|$

$0.00355 \pm 0.00014$ 95% prob:[0.00327, 0.00385] 99% prob:[0.00313, 0.00401]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|V_{ub}\|$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|V_{cb}\|$

$0.04083 \pm 0.00045$ 95% prob:[0.03995, 0.04177] 99% prob:[0.03955, 0.04217] U [0.04219, 0.04233]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{cb}\|$

$0.04117 \pm 0.00043$ 95% prob:[0.04037, 0.04209] 99% prob:[0.03995, 0.04247]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{cb}\|$

$0.04269 \pm 0.00099$ 95% prob:[0.04069, 0.0447] 99% prob:[0.03971, 0.04563]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|V_{cb}\|$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{12}$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{23}$

$0.04117 \pm 0.00043$ 95% prob:[0.04033, 0.04209] 99% prob:[0.03993, 0.04251]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{13}$

$0.00364 \pm 0.00011$ 95% prob:[0.00342,0.003867] 99% prob:[0.00332,0.00399]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\delta$

$69.7 \pm 2.9$ 95% prob:[63.9, 75.7] 99% prob:[61.1, 78.6]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,m_{t},{\rm {GeV}/c^{2}}$

Gaussian likelihood used $163.4 \pm 1.2$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.4 \pm 1.2$ 95% prob:[161, 165.7] 99% prob:[159.9, 166.9]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.5 \pm 9.5$ 95% prob:[144.7, 183.1] 99% prob:[137.6, 194.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,m_{t},{\rm {GeV}/c^{2}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\Delta m_{s},{\rm ps^{-1}}$

Gaussian likelihood used $17.77 \pm 0.12$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\Delta m_{s},{\rm ps^{-1}}$

$17.77 \pm 0.12$ 95% prob:[17.5, 18.0] 99% prob:[17.4, 18.1]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\Delta m_{s},{\rm ps^{-1}}$

$18.3 \pm 1.3$ 95% prob:[15.9, 20.9] 99% prob:[14.8, 22.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\Delta m_{s},{\rm ps^{-1}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,f_{B_{s}}$

Gaussian likelihood used $0.239 \pm 0.01$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}$

$0.2359 \pm 0.0056$ 95% prob:[0.2252, 0.2477] 99% prob:[0.22, 0.2537]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}$

$0.2349 \pm 0.0067$ 95% prob:[0.2221, 0.2491] 99% prob:[0.217, 0.2571]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,f_{B_{s}}/f_{B_{d}}$

Gaussian likelihood used $1.23 \pm 0.03$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}/f_{B_{d}}$

$1.225 \pm 0.025$ 95% prob:[1.175, 1.275] 99% prob:[1.151, 1.299]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}/f_{B_{d}}$

$1.213 \pm 0.044$ 95% prob:[1.13, 1.303] 99% prob:[1.083, 1.085] U [1.093, 1.352]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}/f_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B_{B_{s}}/B_{B_{d}}$

Gaussian likelihood used $1.06 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}/B_{B_{d}}$

$1.069 \pm 0.036$ 95% prob:[0.997, 1.141] 99% prob:[0.963, 1.179]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}/B_{B_{d}}$

$1.113 \pm 0.085$ 95% prob:[0.96, 1.279] 99% prob:[0.893, 1.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}/B_{B_{d}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B_{B_{s}}$

Gaussian likelihood used $0.87 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}$

$0.845 \pm 0.036$ 95% prob:[0.775, 0.919] 99% prob:[0.738, 0.954]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}$

$0.769 \pm 0.065$ 95% prob:[0.648, 0.915] 99% prob:[0.608, 0.999]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 95% prob:[81, 102.] U [161., 169] 99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\alpha, [^{\circ}]$

$87.8 \pm 3.0$ 95% prob:[82.1, 93.8] 99% prob:[79.2, 96.2]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\alpha, [^{\circ}]$

$85.4 \pm 3.7$ 95% prob:[78.3, 93.2] 99% prob:[74.5, 96.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\alpha, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\beta, [^{\circ}]$

$22.42 \pm 0.74$ 95% prob:[20.9, 23.9] 99% prob:[20.2, 24.7]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\beta, [^{\circ}]$

$25.2 \pm 1.6$ 95% prob:[22.3, 28.6] 99% prob:[21.3, 30.2]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\sin(2\beta)$

$0.705 \pm 0.018$ 95% prob:[0.669, 0.742] 99% prob:[0.651, 0.762]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\sin(2\beta)$

$0.771 \pm 0.036$ 95% prob:[0.706, 0.844] 99% prob:[0.68, 0.872] U [0.875, 0.878]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\sin(2\beta)$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\cos(2\beta)$

$0.87 \pm 0.13$ 95% prob:[0.44, 0.99] 99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\cos(2\beta)$

$0.71 \pm 0.018$ 95% prob:[0.672, 0.745] 99% prob:[0.649, 0.76]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\cos(2\beta)$

$0.639 \pm 0.043$ 95% prob:[0.544, 0.712] 99% prob:[0.507, 0.731]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\cos(2\beta)$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,2\beta+\gamma, [^{\circ}]$

$-90 \pm 56 \text{ and } 94 \pm 52$ 95% prob:[-166, 166.] 99% prob:[-179, 179]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,2\beta+\gamma, [^{\circ}]$

$114.7 \pm 3.1$ 95% prob:[108.3, 120.7] 99% prob:[105.6, 123.4]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,2\beta+\gamma, [^{\circ}]$

$114.9 \pm 3.1$ 95% prob:[108.6, 120.9] 99% prob:[105.8, 123.6]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,2\beta+\gamma, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\gamma, [^{\circ}]$

$69.8 \pm 3.0$ 95% prob:[63.9, 75.7] 99% prob:[61, 78.5]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\gamma, [^{\circ}]$

$69.6 \pm 3.1$ 95% prob:[63.4, 75.6] 99% prob:[60.5, 78.8]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\gamma, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|\varepsilon_{K}\|$

$0.00222994 \pm 1.04974\times 10^{-5}$ 95% prob:[0.00220745, 0.00224944] 99% prob:[0.00219845, 0.00225644]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|\varepsilon_{K}\|$

$0.00222854 \pm 9.98004\times 10^{-06}$ 95% prob:[0.00220858, 0.0022485] 99% prob:[0.0021986, 0.00225848]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|\varepsilon_{K}\|$

$0.00192 \pm 0.00018$ 95% prob:[0.00157, 0.00230] 99% prob:[0.00141, 0.00252]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|\varepsilon_{K}\|$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,B(B\rightarrow\tau u),10^{-4}$

Gaussian likelihood used $1.72 \pm 0.28$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B(B\rightarrow\tau u),10^{-4}$

$0.867 \pm 0.078$ 95% prob:[0.721, 1.031] 99% prob:[0.661, 1.127]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B(B\rightarrow\tau u),10^{-4}$

$0.805 \pm 0.071$ 95% prob:[0.674, 0.958] 99% prob:[0.619, 1.051]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B(B\rightarrow\tau u),10^{-4}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,J_{cp}\times 10^{-5}$

$3.09 \pm 0.11$ 95% prob:[2.87, 3.30] 99% prob:[2.77, 3.42]
EPS - PDF - PNG - JPG - GIF

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Click on the parameter name to jump to the corresponding plot

Parameter	Input value	Full fit	SM Prediction
$\bar{\rho}$		$0.132 \pm 0.02$
$\bar{\eta}$		$0.358 \pm 0.012$
$\rho$		$0.135 \pm 0.021$
$\eta$		$0.367 \pm 0.013$
		$0.8095 \pm 0.0095$
$\lambda$	$0.2253 \pm 0.0011$	$0.22545 \pm 0.00065$
$\|V_{ub}\|$	$0.00376 \pm 0.0002$	$0.00364 \pm 0.00011$	$0.00355 \pm 0.00014$
$\|V_{cb}\|$	$0.04083 \pm 0.00045$	$0.04117 \pm 0.00043$	$0.04269 \pm 0.00099$
$\sin\theta_{12}$		$0.22545 \pm 0.00065$
$\sin\theta_{23}$		$0.04117 \pm 0.00043$
$\sin\theta_{13}$		$0.00364 \pm 0.00011$
$\delta$		$69.7 \pm 2.9$
$m_{b},{\rm {GeV}/c^{2}}$	$4.21 \pm 0.08$
$m_{c},{\rm {GeV}/c^{2}}$	$1.3 \pm 0.1$
$m_{t},{\rm {GeV}/c^{2}}$	$163.4 \pm 1.2$	$163.4 \pm 1.2$	$163.5 \pm 9.5$
$\Delta m_{s},{\rm ps^{-1}}$	$17.77 \pm 0.12$	$17.77 \pm 0.12$	$18.3 \pm 1.3$
$\Delta m_{d},{\rm ps^{-1}}$	$0.507 \pm 0.005$
$\Delta m_{K},10^{-15}{\rm ps^{-1}}$	$1.8 \pm 1.8$
$f_{B_{s}}$	$0.239 \pm 0.01$	$0.2359 \pm 0.0056$	$0.2349 \pm 0.0067$
$f_{B_{s}}/f_{B_{d}}$	$1.23 \pm 0.03$	$1.225 \pm 0.025$	$1.213 \pm 0.044$
$B_{B_{s}}/B_{B_{d}}$	$1.06 \pm 0.04$	$1.069 \pm 0.036$	$1.113 \pm 0.085$
$B_{B_{s}}$	$0.87 \pm 0.04$	$0.845 \pm 0.036$	$0.769 \pm 0.065$
$\alpha, [^{\circ}]$	$91.4 \pm 6.1$	$87.8 \pm 3.0$	$85.4 \pm 3.7$
$\beta, [^{\circ}]$		$22.42 \pm 0.74$	$25.2 \pm 1.6$
$\sin(2\beta)$	$0.654 \pm 0.026$	$0.705 \pm 0.018$	$0.771 \pm 0.036$
$\cos(2\beta)$	$0.87 \pm 0.13$	$0.71 \pm 0.018$	$0.639 \pm 0.043$
$2\beta+\gamma, [^{\circ}]$	$-90 \pm 56 \text{ and } 94 \pm 52$	$114.7 \pm 3.1$	$114.9 \pm 3.1$
$\gamma, [^{\circ}]$	$-106 \pm 11 \text{ and } 74 \pm 11$	$69.8 \pm 3.0$	$69.6 \pm 3.1$
$\|\varepsilon_{K}\|$	$0.00222994 \pm 1.04974 \times 10^{-5}$	$0.00222854 \pm 9.98004 \times 10^{-06}$	$0.00192 \pm 0.00018$
$B(B\rightarrow\tau\nu),10^{-4}$	$1.72 \pm 0.28$	$0.867 \pm 0.078$	$0.805 \pm 0.071$
$J_{cp}\times 10^{5}$		$3.09 \pm 0.11$

The fit results for all the nine CKM elements are

${\small V_{CKM}=\left(\begin{array}{ccc} 0.97425 \pm 0.00015 & 0.22549 \pm 0.00064 & (0.00364 \pm 0.00011)e^{i(-69.7 \pm 2.9)^\circ}\\ -(0.2253 \pm 0.00064)e^{i( 0.0348 \pm 0.0012)^\circ} & 0.97341 \pm 0.00015 & 0.04117 \pm 0.00043 \\ (0.00871 \pm 0.00019)e^{i(-22.46 \pm 0.73)^\circ} & -(0.04039 \pm 0.00043)e^{i( 1.089 \pm 0.038)^\circ} & 0.999145 \pm 1.8\times 10^{-5}\end{array}\right)}$

Full fit result for $\,\bar{\rho}$

$0.132 \pm 0.02$ 95% prob:[0.092, 0.171] 99% prob:[0.074, 0.190]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\eta}$

$0.358 \pm 0.012$ 95% prob:[0.332, 0.383] 99% prob:[0.321, 0.396]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\bar{\rho} - \bar{\eta}$


EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\rho$

$0.135 \pm 0.021$ 95% prob:[0.095, 0.175] 99% prob:[0.076, 0.195]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\eta$

$0.367 \pm 0.013$ 95% prob:[0.341, 0.393] 99% prob:[0.329, 0.406]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,A$

$0.8095 \pm 0.0095$ 95% prob:[0.791, 0.83] 99% prob:[0.782, 0.839]
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Fit Input for $\,\lambda$

$0.2253 \pm 0.0011$ 95% prob:[0.2231, 0.2275] 99% prob:[0.2218, 0.2285]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\lambda$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\|V_{ub}\|$

$0.00376 \pm 0.0002$ 95% prob:[0.00340, 0.00428] 99% prob:[0.00327, 0.00463]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{ub}\|$

$0.00364 \pm 0.00011$ 95% prob:[0.00342, 0.00386] 99% prob:[0.00332, 0.00399]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{ub}\|$

$0.00355 \pm 0.00014$ 95% prob:[0.00327, 0.00385] 99% prob:[0.00313, 0.00401]
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Compatibility Plot for $\,\|V_{ub}\|$


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Fit Input for $\,\|V_{cb}\|$

$0.04083 \pm 0.00045$ 95% prob:[0.03995, 0.04177] 99% prob:[0.03955, 0.04217] U [0.04219, 0.04233]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|V_{cb}\|$

$0.04117 \pm 0.00043$ 95% prob:[0.04037, 0.04209] 99% prob:[0.03995, 0.04247]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|V_{cb}\|$

$0.04269 \pm 0.00099$ 95% prob:[0.04069, 0.0447] 99% prob:[0.03971, 0.04563]
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Compatibility Plot for $\,\|V_{cb}\|$


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Full fit result for $\,\sin\theta_{12}$

$0.22545 \pm 0.00065$ 95% prob:[0.2242, 0.2268] 99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{23}$

$0.04117 \pm 0.00043$ 95% prob:[0.04033, 0.04209] 99% prob:[0.03993, 0.04251]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\sin\theta_{13}$

$0.00364 \pm 0.00011$ 95% prob:[0.00342,0.003867] 99% prob:[0.00332,0.00399]
EPS - PDF - PNG - JPG - GIF

Full fit result for $\,\delta$

$69.7 \pm 2.9$ 95% prob:[63.9, 75.7] 99% prob:[61.1, 78.6]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,m_{t},{\rm {GeV}/c^{2}}$

Gaussian likelihood used $163.4 \pm 1.2$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.4 \pm 1.2$ 95% prob:[161, 165.7] 99% prob:[159.9, 166.9]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,m_{t},{\rm {GeV}/c^{2}}$

$163.5 \pm 9.5$ 95% prob:[144.7, 183.1] 99% prob:[137.6, 194.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,m_{t},{\rm {GeV}/c^{2}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\Delta m_{s},{\rm ps^{-1}}$

Gaussian likelihood used $17.77 \pm 0.12$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\Delta m_{s},{\rm ps^{-1}}$

$17.77 \pm 0.12$ 95% prob:[17.5, 18.0] 99% prob:[17.4, 18.1]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\Delta m_{s},{\rm ps^{-1}}$

$18.3 \pm 1.3$ 95% prob:[15.9, 20.9] 99% prob:[14.8, 22.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\Delta m_{s},{\rm ps^{-1}}$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,f_{B_{s}}$

Gaussian likelihood used $0.239 \pm 0.01$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}$

$0.2359 \pm 0.0056$ 95% prob:[0.2252, 0.2477] 99% prob:[0.22, 0.2537]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}$

$0.2349 \pm 0.0067$ 95% prob:[0.2221, 0.2491] 99% prob:[0.217, 0.2571]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}$


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Fit Input for $\,f_{B_{s}}/f_{B_{d}}$

Gaussian likelihood used $1.23 \pm 0.03$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,f_{B_{s}}/f_{B_{d}}$

$1.225 \pm 0.025$ 95% prob:[1.175, 1.275] 99% prob:[1.151, 1.299]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,f_{B_{s}}/f_{B_{d}}$

$1.213 \pm 0.044$ 95% prob:[1.13, 1.303] 99% prob:[1.083, 1.085] U [1.093, 1.352]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,f_{B_{s}}/f_{B_{d}}$


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Fit Input for $\,B_{B_{s}}/B_{B_{d}}$

Gaussian likelihood used $1.06 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}/B_{B_{d}}$

$1.069 \pm 0.036$ 95% prob:[0.997, 1.141] 99% prob:[0.963, 1.179]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}/B_{B_{d}}$

$1.113 \pm 0.085$ 95% prob:[0.96, 1.279] 99% prob:[0.893, 1.3]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}/B_{B_{d}}$


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Fit Input for $\,B_{B_{s}}$

Gaussian likelihood used $0.87 \pm 0.04$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B_{B_{s}}$

$0.845 \pm 0.036$ 95% prob:[0.775, 0.919] 99% prob:[0.738, 0.954]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B_{B_{s}}$

$0.769 \pm 0.065$ 95% prob:[0.648, 0.915] 99% prob:[0.608, 0.999]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B_{B_{s}}$


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Fit Input for $\,\alpha, [^{\circ}]$

$91.4 \pm 6.1$ 95% prob:[81, 102.] U [161., 169] 99% prob:[76.8, 108.] U [157., 171.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\alpha, [^{\circ}]$

$87.8 \pm 3.0$ 95% prob:[82.1, 93.8] 99% prob:[79.2, 96.2]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\alpha, [^{\circ}]$

$85.4 \pm 3.7$ 95% prob:[78.3, 93.2] 99% prob:[74.5, 96.2]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\alpha, [^{\circ}]$


EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\beta, [^{\circ}]$

$22.42 \pm 0.74$ 95% prob:[20.9, 23.9] 99% prob:[20.2, 24.7]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\beta, [^{\circ}]$

$25.2 \pm 1.6$ 95% prob:[22.3, 28.6] 99% prob:[21.3, 30.2]
EPS - PDF - PNG - JPG - GIF

Fit Input for $\,\sin(2\beta)$

$0.654 \pm 0.026$ 95% prob:[0.601, 0.708] 99% prob:[0.574, 0.735]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\sin(2\beta)$

$0.705 \pm 0.018$ 95% prob:[0.669, 0.742] 99% prob:[0.651, 0.762]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\sin(2\beta)$

$0.771 \pm 0.036$ 95% prob:[0.706, 0.844] 99% prob:[0.68, 0.872] U [0.875, 0.878]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\sin(2\beta)$


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Fit Input for $\,\cos(2\beta)$

$0.87 \pm 0.13$ 95% prob:[0.44, 0.99] 99% prob:[0.12, 0.99]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\cos(2\beta)$

$0.71 \pm 0.018$ 95% prob:[0.672, 0.745] 99% prob:[0.649, 0.76]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\cos(2\beta)$

$0.639 \pm 0.043$ 95% prob:[0.544, 0.712] 99% prob:[0.507, 0.731]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\cos(2\beta)$


EPS - PDF - PNG - JPG - GIF

Fit Input for $\,2\beta+\gamma, [^{\circ}]$

$-90 \pm 56 \text{ and } 94 \pm 52$ 95% prob:[-166, 166.] 99% prob:[-179, 179]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,2\beta+\gamma, [^{\circ}]$

$114.7 \pm 3.1$ 95% prob:[108.3, 120.7] 99% prob:[105.6, 123.4]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,2\beta+\gamma, [^{\circ}]$

$114.9 \pm 3.1$ 95% prob:[108.6, 120.9] 99% prob:[105.8, 123.6]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,2\beta+\gamma, [^{\circ}]$


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Fit Input for $\,\gamma, [^{\circ}]$

$-106 \pm 11 \text{ and } 74 \pm 11$ 95% prob:[-128, -85.] U [52.1, 94.4] 99% prob:[-139, -75.] U [41.4, 104.]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\gamma, [^{\circ}]$

$69.8 \pm 3.0$ 95% prob:[63.9, 75.7] 99% prob:[61, 78.5]
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SM Fit prediction for $\,\gamma, [^{\circ}]$

$69.6 \pm 3.1$ 95% prob:[63.4, 75.6] 99% prob:[60.5, 78.8]
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Compatibility Plot for $\,\gamma, [^{\circ}]$


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Fit Input for $\,\|\varepsilon_{K}\|$

$0.00222994 \pm 1.04974\times 10^{-5}$ 95% prob:[0.00220745, 0.00224944] 99% prob:[0.00219845, 0.00225644]
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,\|\varepsilon_{K}\|$

$0.00222854 \pm 9.98004\times 10^{-06}$ 95% prob:[0.00220858, 0.0022485] 99% prob:[0.0021986, 0.00225848]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,\|\varepsilon_{K}\|$

$0.00192 \pm 0.00018$ 95% prob:[0.00157, 0.00230] 99% prob:[0.00141, 0.00252]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,\|\varepsilon_{K}\|$


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Fit Input for $\,B(B\rightarrow\tau u),10^{-4}$

Gaussian likelihood used $1.72 \pm 0.28$
EPS - PDF - PNG - JPG - GIF

Full Fit result for $\,B(B\rightarrow\tau u),10^{-4}$

$0.867 \pm 0.078$ 95% prob:[0.721, 1.031] 99% prob:[0.661, 1.127]
EPS - PDF - PNG - JPG - GIF

SM Fit prediction for $\,B(B\rightarrow\tau u),10^{-4}$

$0.805 \pm 0.071$ 95% prob:[0.674, 0.958] 99% prob:[0.619, 1.051]
EPS - PDF - PNG - JPG - GIF

Compatibility Plot for $\,B(B\rightarrow\tau u),10^{-4}$


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Full fit result for $\,J_{cp}\times 10^{-5}$

$3.09 \pm 0.11$ 95% prob:[2.87, 3.30] 99% prob:[2.77, 3.42]
EPS - PDF - PNG - JPG - GIF

Constraints, Parameters	Gaussian Error	Flat Error	Comments
$\lambda$		-	-
$\left \| V_{cb} \right \|~[10^{-3}]$		-	Average of exclusive
$\left \| V_{cb} \right \|~[10^{-3}]$		-	Average of inclusive
$\left \| V_{ub} \right \|~[10^{-4}] \mathrm{(excl.)}$		-	HFAG BR + Lattice QCD
$\left \| V_{ub} \right \|~[10^{-4}] \mathrm{(incl.)}$			HFAG average
		-	-
		-	-
$\Delta m_d~[ps^{-1}]$		-	WA (CDF/CLEO/LEP/BaBar/Belle)
$\Delta m_s~[ps^{-1}]$		-	CDF Likelihood is used
		-	(CDF/D0)
$f_{B_s}\sqrt{B_{B_s}}~[MeV]$		-	Lattice QCD
$\xi$		-	Lattice QCD
$\|\varepsilon_K\|~[10^{-3}]$		-	-
		-	Lattice QCD
	-	-	-
$\Delta m_K~[10^{-2}~ps^{-1}]$	-	-	-
$M_{K^0}~[GeV/c^2]$	-	-	-

Under construction

Revision 5

Changes from r3 to r5

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Summer 2008 Standard Model fit resultsSummer 2008 Standard Model fit results

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Winter 2008 Standard Model fit resultsWinter 2008 Standard Model fit results

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Revision 3

Changes from r1 to r3

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Software version

What versions of Foswiki (or TWiki) was the tip tested on?

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Current Standard Model fit resultsCurrent Standard Model fit results
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Summer 2008 Standard Model fit resultsSummer 2008 Standard Model fit results
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Winter 2008 Standard Model fit resultsWinter 2008 Standard Model fit results
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Fit results: Summer 2023: work in progress. See EPS-HEP2023 talk and CKM workshop talk

Fit results: Summer 2023: work in progress. See EPS-HEP2023 talk and CKM workshop talk

Fit results: Winter 2022 ?

Fit results: Winter 2022 ?

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