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.

                
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 -
A - 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

Constraints, Parameters Value Gaussian Error Flat Error Comments
\lambda 0.2258 0.0014 - -
\left | V_{cb} \right |~[10^{-3}] 39.2 1.1 - Average of exclusive
\left | V_{cb} \right |~[10^{-3}] 41.7 0.7 - Average of inclusive
\left | V_{ub} \right |~[10^{-4}] \mathrm{(excl.)} 35.0 4.0 - HFAG BR + Lattice QCD
\left | V_{ub} \right |~[10^{-4}] \mathrm{(incl.)} 39.9 1.5 4.0 HFAG average
m_b 4.21 0.08 - -
m_c 1.3 0.1 - -
\Delta m_d~[ps^{-1}] 0.507 0.005 - WA (CDF/CLEO/LEP/BaBar/Belle)
\Delta m_s~[ps^{-1}] 17.77 0.12 - CDF Likelihood is used
m_t~[GeV/c^2] 161.2 1.7 - (CDF/D0)
f_{B_s}\sqrt{B_{B_s}}~[MeV] 270 30 - Lattice QCD
\xi 1.21 0.04 - Lattice QCD
|\varepsilon_K|~[10^{-3}] 2.228 0.011 - -
B_K 0.75 0.07 - Lattice QCD
f_K~[GeV] 0.160 - - -
\Delta m_K~[10^{-2}~ps^{-1}] 0.5301 - - -
M_{K^0}~[GeV/c^2] 0.497648 - - -

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