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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 $\,\sin\theta_{12}$ <-- -->

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

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, 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]
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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Fit results: Summer 2010 (pre-ICHEP)

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prefix=" " mode="div" 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

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

%TWISTY{ prefix=" "

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mode="div" showlink="Universal Unitarity Triangle (UUT) Fit" hidelink="Universal Unitarity Triangle (UUT) Fit"

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

%TWISTY{

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mode="div" showlink="New Physics Fit" hidelink="New Physics Fit"

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

%TWISTY{

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showlink="Explanation of the page content" hidelink="Explanation of the page content"

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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.

Changed:

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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.

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

Added:

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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 $V_{cb}$ .

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

Revision 32

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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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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 :

Changed:

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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}}} \

>
>

\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

Changed:

<
<

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

>
>

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

Changed:

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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.

>
>

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

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

Line: 141 to 117

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

Added:

>
>

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.

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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 D( )π(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.

>
>

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.

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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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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.

>
>

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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showlink=" FIT : Summer 2010/before ICHEP " hidelink="FIT : Summer 2010/before ICHEP "

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showlink="Fit results: Summer 2010 (pre-ICHEP) " hidelink="Fit results: Summer 2010 (pre-ICHEP) "

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Click on the parameter name to jump to the corresponding plot

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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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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

>
>

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 D( )π(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 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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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 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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}% 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.

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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.]
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

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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}} \

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

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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]
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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}% 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]
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

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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

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{\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}\,, \

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\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]
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 26

Changes from r24 to r26

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	%TWISTY{ prefix="" mode="div"
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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
Changed:
< <	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
> >	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, DK 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.
Line: 126 to 126
	suffix="" remember="on" }%
Changed:
< <	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.
> >	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.
	woops, ordering error: got an ENDTWISTY before seeing a TWISTY
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	suffix="" remember="on" }%
Changed:
< <	The fit presented here is meant to constrain the NP contributions to DF\|=2 transitions by using the available experimental information on
> >	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,
Line: 168 to 168
	\label{eq:ceps}
Changed:
< <	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 $\Delta m_K$
> >	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:
Line: 182 to 180
	\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})\,,\; \
Added:
> >	\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} \,,\; \

Revision 24

Changes from r22 to r24

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

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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.

Changed:

<
<

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

Line: 23 to 23

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.

Changed:

<
<

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

Line: 61 to 61

}% 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 $\,\|V_{cb}\|$


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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 $0.87 \pm 0.04$
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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]
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]
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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]
EPS - PDF - PNG - JPG - GIF

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]
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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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 $V_{cs}$ .

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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

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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

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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 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 $C_{\epsilon_K} = \frac{\mathrm{Im}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{full}}|\bar{K}^0\rangle]} {\mathrm{Im}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{SM}}|\bar{K}^0\rangle]}\,,\qquad C_{\Delta m_K} = \frac{\mathrm{Re}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{full}}|\bar{K}^0\rangle]} {\mathrm{Re}[\langle K^0|H_{\mathrm{eff}}^{\mathrm{SM}}|\bar{K}^0\rangle]}\,. \label{eq:ceps}$ 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:

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

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

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

Revision 22

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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.

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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|, 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.

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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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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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%TWISTY{ mode="div"

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showlink="Summer 2010" hidelink="Summer 2010"

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showlink=" FIT : Summer 2010/before ICHEP " hidelink="FIT : Summer 2010/before ICHEP "

showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" suffix=""

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

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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" }% 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

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

showlink="Tree level Fit" hidelink="Tree Level Fit" showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png"

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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

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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

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 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 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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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.

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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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showlink="Compatibility Plots" hidelink="Compatibility Plots" showimgleft="/foswiki/pub/System/DocumentGraphics/toggleopen.png" hideimgleft="/foswiki/pub/System/DocumentGraphics/toggleclose.png" suffix="" remember="on" }% 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.

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 $\,\cos(2\beta)$


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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 $\,\gamma, [^{\circ}]$


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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 $\,\|\varepsilon_{K}\|$


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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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 :

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

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 $V_{cs}$ .

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

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Revision 16

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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 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
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< <	in that given Model. Let's consider for example the Standard Model. The comparison between these
> >	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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Revision 14

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+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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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 $\,\|V_{cb}\|$


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


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


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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]
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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]
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 $\,\sin(2\beta)$


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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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
	-	-	-
$\Delta m_K~[10^{-2}~ps^{-1}]$	-	-	-
$M_{K^0}~[GeV/c^2]$	-	-	-

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suffix="" remember="on" }% 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 $\,\cos(2\beta)$


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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 $\,\gamma, [^{\circ}]$


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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 $\,\|\varepsilon_{K}\|$


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]
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]
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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 $\,\|\varepsilon_{K}\|$


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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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
	-	-	-
$\Delta m_K~[10^{-2}~ps^{-1}]$	-	-	-
$M_{K^0}~[GeV/c^2]$	-	-	-

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Additional information on fit inputsAdditional information on fit inputs

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
	-	-	-
$\Delta m_K~[10^{-2}~ps^{-1}]$	-	-	-
$M_{K^0}~[GeV/c^2]$	-	-	-

Standard Model fit resultsStandard Model fit results

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 $\,\|V_{cb}\|$


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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 $\,f_{B_{s}}$


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 $\,\sin(2\beta)$


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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 $\,\cos(2\beta)$


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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.]
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 $\,\gamma, [^{\circ}]$


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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 $\,\|\varepsilon_{K}\|$


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

New Physics fit resultsNew Physics fit results

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Fit results: Summer 2023: work in progress. See EPS-HEP2023 talk for preliminary numbers

Fit results: Summer 2023: work in progress. See EPS-HEP2023 talk for preliminary numbers

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