Fit results: Summer 2013 (post-EPS13)

Some Input Combinations

Standard Model Fit

Parameter Input value Full fit SM Prediction
\bar{\rho} - 0.127 \pm 0.023 -
\bar{\eta} - 0.353 \pm 0.014 -
\rho - 0.13 \pm 0.024 -
\eta - 0.362 \pm 0.014 -
A - 0.822 \pm 0.012 -
\lambda 0.2253 \pm 0.0009 0.22535 \pm 0.00065 -
|V_{ub}| 0.00375 \pm 0.00046 0.00362 \pm 0.00012 0.00361 \pm 0.00012
|V_{cb}| 0.0409 \pm 0.001 0.04172 \pm 0.00056 0.04212 \pm 0.0007
\sin\theta_{12} - 0.22535 \pm 0.00059 -
\sin\theta_{23} - 0.04173 \pm 0.00057 -
\sin\theta_{13} - 0.00362 \pm 0.00012 -
\delta [^{\circ}] - 70.3 \pm 3.5 -
m_{b}\mathrm{ [GeV/c^{2}]} 4.19 \pm 0.04 - -
m_{c}\mathrm{ [GeV/c^{2}]} 1.28 \pm 0.04 - -
m_{t}\mathrm{ [GeV/c^{2}]} 164.1 \pm 0.9 164.1 \pm 0.9 161.8 \pm 7.1
\Delta m_{s} \mathrm{[ps^{-1}]} 17.768 \pm 0.024 17.768 \pm 0.024 17.4 \pm 1.1
\Delta m_{d} \mathrm{[ps^{-1}]} 0.51 \pm 0.004 - -
\Delta m_{K} \mathrm{[ps^{-1}]} 1.8 \pm 1.8 - -
f_{B_{s}} 0.2277 \pm 0.0045 0.2272 \pm 0.0039 0.2266 \pm 0.0075
f_{B_{s}}/f_{B_{d}} 1.202 \pm 0.022 1.199 \pm 0.021 1.183 \pm 0.061
B_{B_{s}}/B_{B_{d}} 1.06 \pm 0.11 1.109 \pm 0.063 1.136 \pm 0.077
B_{B_{s}} 0.875 \pm 0.04 0.876 \pm 0.029 0.876 \pm 0.046
B_{k} 0.766 \pm 0.010 0.766 \pm 0.011 0.836 \pm 0.078
\alpha [^{\circ}] 90.9 \pm 8.0 87.7 \pm 3.3 86.3 \pm 3.8
\beta [^{\circ}] - 22.01 \pm 0.86 24.4 \pm 1.8
\sin(2\beta) 0.68 \pm 0.023 0.695 \pm 0.021 0.754 \pm 0.042
\cos(2\beta) 0.87 \pm 0.13 0.719 \pm 0.021 0.66 \pm 0.048
2\beta+\gamma [^{\circ}] -89 \pm 54 \text{ and } 90 \pm 54 114.2 \pm 3.4 114.4 \pm 3.4
\gamma [^{\circ}] -109.9 \pm 7.1 \text{ and } 70.1 \pm 7.1 70.3 \pm 3.5 69.8 \pm 3.9
|\epsilon_{k}| 2.228 \pm 0.011 2.228 \pm 0.039 2.04 \pm 0.19
B(B\rightarrow\tau\nu), 10^{-4} 1.14 \pm 0.22 0.834 \pm 0.071 0.806 \pm 0.07
J_{cp}, 10^{-5} - 3.12 \pm 0.09 -
B(B_{s}\rightarrow ll), 10^{-9} 2.9 \pm 0.7 3.87 \pm 0.16 3.91 \pm 0.16
B(B_{d}\rightarrow ll), 10^{-9} 0.37 \pm 0.15 0.1142 \pm 0.0069 0.1145 \pm 0.007
\Delta\Gamma_{d}/\Gamma_{d} - 0.00516 \pm 0.00037 -
\Delta\Gamma_{s}/\Gamma_{s} - 0.152 \pm 0.013 -
\beta_{s} [^{\circ}] - 1.073 \pm 0.042 -

The fit results for all the nine CKM elements are V_{CKM}=\left(\begin{array}{ccc} (0.97426 \pm 0.00014) & (0.22535 \pm 0.00059) & (0.00362 \pm 0.00012)e^{i(-70.2 \pm 3.3)^\circ}\\ ( -0.22525 \pm 0.00059)e^{i(0.0352 \pm 0.001)^\circ} & (0.97342 \pm 0.00013)e^{i(-0.00188333 \pm 0.00005)^\circ} & (0.04172 \pm 0.00056) \\ (0.00884 \pm 0.00019)e^{i(-22.0 \pm 0.8)^\circ} & ( -0.04092 \pm 0.00057)e^{i(1.071 \pm 0.042)^\circ} & (0.999121 \pm 0.000021)\end{array}\right)




Full fit result for \,\bar{\rho}
0.127 \pm 0.023
95% prob:[0.085, 0.175]
99% prob:[0.062, 0.197]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\bar{\eta}
0.353 \pm 0.014
95% prob:[0.326, 0.381]
99% prob:[0.314, 0.396]
EPS - PDF - PNG - JPG - GIF




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

\bar\rho=0.127 \pm 0.023
\bar\eta=0.353 \pm 0.014
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Angles only result for \,\bar{\rho} - \bar{\eta}

\bar\rho=0.134 \pm 0.029
\bar\eta=0.339 \pm 0.017
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Sides only result for \,\bar{\rho} - \bar{\eta}

\bar\rho=0.144 \pm 0.046
\bar\eta=0.376 \pm 0.030
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Full fit result for \,\rho
0.13 \pm 0.024
95% prob:[0.087, 0.179]
99% prob:[0.064, 0.202]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\eta
0.362 \pm 0.014
95% prob:[0.334, 0.390]
99% prob:[0.322, 0.406]
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Full fit result for \,A
0.822 \pm 0.012
95% prob:[0.798, 0.846]
99% prob:[0.785, 0.858]
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Fit Input for \,\lambda
0.2253 \pm 0.0009
95% prob:[0.2235, 0.2271]
99% prob:[0.2226, 0.228]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,\lambda
0.22535 \pm 0.00065
95% prob:[0.2241, 0.2266]
99% prob:[0.2235, 0.2273]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,|V_{ub}|
Gaussian likelihood used
0.00375 \pm 0.00046
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,|V_{ub}|
0.00362 \pm 0.00012
95% prob:[0.00339, 0.00388]
99% prob:[0.00328, 0.00402]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,|V_{ub}|
0.00361 \pm 0.00012
95% prob:[0.00337, 0.00387]
99% prob:[0.00326, 0.00402]
EPS - PDF - PNG - JPG - GIF



Compatibility Plot for \,|V_{ub}|



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Fit Input for \,|V_{cb}|
Gaussian likelihood used
0.0409 \pm 0.001

EPS - PDF - PNG - JPG - GIF



Full Fit result for \,|V_{cb}|
0.04172 \pm 0.00056
95% prob:[0.04059, 0.04285]
99% prob:[0.04006, 0.04341]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,|V_{cb}|
0.04204 \pm 0.00069
95% prob:[0.04072, 0.04347]
99% prob:[0.04003, 0.0441]
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Compatibility Plot for \,|V_{cb}|



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Full fit result for \,\sin\theta_{12}
0.22535 \pm 0.00059
95% prob:[0.22415, 0.22663]
99% prob:[0.22346, 0.22722]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\sin\theta_{23}
0.04173 \pm 0.00057
95% prob:[0.04060, 0.04286]
99% prob:[0.04006, 0.04341]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\sin\theta_{13}
0.00362 \pm 0.00012
95% prob:[0.00339, 0.00388]
99% prob:[0.00328, 0.00402]
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Full fit result for \,\delta [^{\circ}]
70.3 \pm 3.5
95% prob:[63.1, 76.5]
99% prob:[60.5, 79.7]
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Fit Input for \,m_{t}\mathrm{ [GeV/c^{2}]}
Gaussian likelihood used
164.1 \pm 0.9
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Full Fit result for \,m_{t}\mathrm{ [GeV/c^{2}]}
164.1 \pm 0.9
95% prob:[162., 165.]
99% prob:[161., 166.]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,m_{t}\mathrm{ [GeV/c^{2}]}
161.8 \pm 7.1
95% prob:[148.7, 176.8]
99% prob:[140.2, 142.2] U [143.9, 184.5]
EPS - PDF - PNG - JPG - GIF



Compatibility Plot for \,m_{t}\mathrm{ [GeV/c^{2}]}



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Fit Input for \,\Delta m_{s} \mathrm{[ps^{-1}]}
Gaussian likelihood used
17.768 \pm 0.024
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,\Delta m_{s} \mathrm{[ps^{-1}]}
17.768 \pm 0.024
95% prob:[17.72, 17.81]
99% prob:[17.69, 17.84]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,\Delta m_{s} \mathrm{[ps^{-1}]}
17.4 \pm 1.1
95% prob:[15.2, 19.7]
99% prob:[14.2, 20.9] U [20.9, 21]
EPS - PDF - PNG - JPG - GIF



Compatibility Plot for \,\Delta m_{s} \mathrm{[ps^{-1}]}



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Fit Input for \,f_{B_{s}}
Gaussian likelihood used
0.2277 \pm 0.0045
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,f_{B_{s}}
0.2272 \pm 0.0039
95% prob:[0.2201, 0.2349]
99% prob:[0.2165, 0.2388]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,f_{B_{s}}
0.2266 \pm 0.0075
95% prob:[0.2148, 0.2409]
99% prob:[0.2085, 0.2469]
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Compatibility Plot for \,f_{B_{s}}



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Fit Input for \,f_{B_{s}}/f_{B_{d}}
Gaussian likelihood used
1.202 \pm 0.022
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Full Fit result for \,f_{B_{s}}/f_{B_{d}}
1.199 \pm 0.021
95% prob:[1.159, 1.242]
99% prob:[1.136, 1.263]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,f_{B_{s}}/f_{B_{d}}
1.183 \pm 0.061
95% prob:[1.074, 1.321]
99% prob:[1.028, 1.402]
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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 0.11
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Full Fit result for \,B_{B_{s}}/B_{B_{d}}
1.109 \pm 0.063
95% prob:[0.99, 1.234]
99% prob:[0.939, 1.3]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,B_{B_{s}}/B_{B_{d}}
1.136 \pm 0.077
95% prob:[0.983, 1.287]
99% prob:[0.908, 1.381]
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Compatibility Plot for \,B_{B_{s}}/B_{B_{d}}



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Fit Input for \,B_{B_{s}}
Gaussian likelihood used
0.875 \pm 0.04
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Full Fit result for \,B_{B_{s}}
0.876 \pm 0.029
95% prob:[0.818, 0.936]
99% prob:[0.791, 0.97]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,B_{B_{s}}
0.876 \pm 0.046
95% prob:[0.795, 0.976]
99% prob:[0.761, 1.033]
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Compatibility Plot for \,B_{B_{s}}



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Fit Input for \,B_{k}
0.766 \pm 0.010
95% prob:[0.746, 0.787]
99% prob:[0.74, 0.794]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,B_{k}
0.766 \pm 0.011
95% prob:[0.747, 0.787]
99% prob:[0.739, 0.798]
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SM Fit prediction for \,B_{k}
0.836 \pm 0.078
95% prob:[0.692, 1.002]
99% prob:[0.632, 1.099]
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Compatibility Plot for \,B_{k}



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Fit Input for \,\alpha [^{\circ}]
90.9 \pm 8.0
95% prob:[78.5, 103.] U [162, 170.]
99% prob:[72.6, 110.] U [158, 172.] U [178., 180]
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Full Fit result for \,\alpha [^{\circ}]
87.7 \pm 3.3
95% prob:[81.6, 94.4]
99% prob:[78.1, 97.6]
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SM Fit prediction for \,\alpha [^{\circ}]
86.3 \pm 3.8
95% prob:[78.8, 94.5]
99% prob:[74.8, 98.2]
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Compatibility Plot for \,\alpha [^{\circ}]



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Full Fit result for \,\beta [^{\circ}]
22.01 \pm 0.86
95% prob:[20.4, 23.8]
99% prob:[19.6, 24.8]
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SM Fit prediction for \,\beta [^{\circ}]
24.4 \pm 1.8
95% prob:[20.8, 28.2]
99% prob:[19.2, 30.1]
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Fit Input for \,\sin(2\beta)
0.68 \pm 0.023
95% prob:[0.635, 0.729]
99% prob:[0.613, 0.755]
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Full Fit result for \,\sin(2\beta)
0.695 \pm 0.021
95% prob:[0.655, 0.74]
99% prob:[0.635, 0.763]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,\sin(2\beta)
0.754 \pm 0.042
95% prob:[0.67, 0.836]
99% prob:[0.625, 0.871]
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Compatibility Plot for \,\sin(2\beta)



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Fit Input for \,\cos(2\beta)
0.87 \pm 0.13
95% prob:[0.44, 0.99]
99% prob:[0.12, 0.99]
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Full Fit result for \,\cos(2\beta)
0.719 \pm 0.021
95% prob:[0.674, 0.757]
99% prob:[0.648, 0.773]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,\cos(2\beta)
0.66 \pm 0.048
95% prob:[0.555, 0.748]
99% prob:[0.498, 0.784]
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Compatibility Plot for \,\cos(2\beta)



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Fit Input for \,2\beta+\gamma [^{\circ}]
-89 \pm 54 \text{ and } 90 \pm 54
95% prob:[-173, -6.4] U [6.8, 173.]
99% prob:[-179, -0.6] U [0.5, 180]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,2\beta+\gamma [^{\circ}]
114.2 \pm 3.4
95% prob:[107.5, 120.8]
99% prob:[103.9, 124]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,2\beta+\gamma [^{\circ}]
114.4 \pm 3.4
95% prob:[107.7, 121]
99% prob:[104.1, 104.3] U [104.5, 124.4]
EPS - PDF - PNG - JPG - GIF



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



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Fit Input for \,\gamma [^{\circ}]
-109.9 \pm 7.1 \text{ and } 70.1 \pm 7.1
95% prob:[-124, -96.] U [55.7, 83.7]
99% prob:[-132, -90.] U [47.9, 89.7]
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Full Fit result for \,\gamma [^{\circ}]
70.3 \pm 3.5
95% prob:[63, 76.5]
99% prob:[60, 80.2]
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SM Fit prediction for \,\gamma [^{\circ}]
69.8 \pm 3.9
95% prob:[62.6, 77.6]
99% prob:[58.9, 81.5]
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Compatibility Plot for \,\gamma [^{\circ}]



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Fit Input for \,|\epsilon_{k}|
Gaussian likelihood used
2.228 \pm 0.011
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Full Fit result for \,|\epsilon_{k}|
2.228 \pm 0.039
95% prob:[2.205, 2.249]
99% prob:[2.195, 2.261]
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SM Fit prediction for \,|\epsilon_{k}|
2.04 \pm 0.19
95% prob:[1.68, 2.45]
99% prob:[1.55, 2.68]
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Compatibility Plot for \,|\epsilon_{k}|



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Fit Input for \,B(B\rightarrow\tau\nu), 10^{-4}
Gaussian likelihood used
1.14 \pm 0.22
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,B(B\rightarrow\tau\nu), 10^{-4}
0.834 \pm 0.071
95% prob:[0.705, 0.985]
99% prob:[0.649, 1.069]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,B(B\rightarrow\tau\nu), 10^{-4}
0.806 \pm 0.07
95% prob:[0.677, 0.953]
99% prob:[0.626, 1.044]
EPS - PDF - PNG - JPG - GIF



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



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Full fit result for \,J_{cp}, 10^{-5}
3.12 \pm 0.09
95% prob:[2.948, 3.305]
99% prob:[2.862, 3.4]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,B(B_{s}\rightarrow ll), 10^{-9}
2.9 \pm 0.7

EPS - PDF - PNG - JPG - GIF



Full Fit result for \,B(B_{s}\rightarrow ll), 10^{-9}
3.865 \pm 0.155
95% prob:[3.56,4.18]
99% prob:[3.469,4.323]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,B(B_{s}\rightarrow ll), 10^{-9}
3.91 \pm 0.16
95% prob:[3.60, 4.24]
99% prob:[3.46, 4.46]
EPS - PDF - PNG - JPG - GIF



Compatibility Plot for \,B(B_{s}\rightarrow ll), 10^{-9}



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Fit Input for \,B(B_{d}\rightarrow ll), 10^{-9}
0.37 \pm 0.15
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Full Fit result for \,B(B_{d}\rightarrow ll), 10^{-9}
0.1142 \pm 0.0069
95% prob:[0.1007, 0.1283]
99% prob:[0.0943, 0.1356]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,B(B_{d}\rightarrow ll), 10^{-9}
0.1145 \pm 0.007
95% prob:[0.1009, 0.1288]
99% prob:[0.0943, 0.1367]
EPS - PDF - PNG - JPG - GIF



Compatibility Plot for \,B(B_{d}\rightarrow ll), 10^{-9}



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Full fit result for \,\Delta\Gamma_{d}/\Gamma_{d}
0.00516 \pm 0.00037
95% prob:[0.00448, 0.00595]
99% prob:[0.00418, 0.0064]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\Delta\Gamma_{s}/\Gamma_{s}
0.152 \pm 0.013
95% prob:[0.129, 0.179]
99% prob:[0.119, 0.194]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\beta_{s} [^{\circ}]
1.073 \pm 0.042
95% prob:[0.994, 1.161]
99% prob:[0.956, 1.208]
EPS - PDF - PNG - JPG - GIF

Standard Model Inclusive Measurements Fit

Parameter Input value Full fit SM Prediction
\bar{\rho} - 0.144 \pm 0.024 -
\bar{\eta} - 0.358 \pm 0.021 -
A - 0.825 \pm 0.011 -
\lambda 0.2253 \pm 0.0009 0.2254 \pm 0.0006 -
|V_{ub}| 0.00440 \pm 0.00031 0.00374 \pm 0.00013 -
|V_{cb}| 0.04170 \pm 0.00070 0.04195 \pm 0.00051 -
\alpha [^{\circ}] 90.9 \pm 8.0 89.6 \pm 3.2 86.3 \pm 3.8
\beta [^{\circ}] - 22.61 \pm 0.89 24.4 \pm 1.8
\sin(2\beta) 0.680 \pm 0.023 0.711 \pm 0.022 0.754 \pm 0.042
\cos(2\beta) 0.87 \pm 0.13 0.705 \pm 0.022 0.660 \pm 0.048
2\beta+\gamma [^{\circ}] -89 \pm 54 \text{ and } 90 \pm 54 113.4 \pm 3.5 -
\gamma [^{\circ}] -109.9 \pm 7.1 \text{ and } 70.1 \pm 7.1 67.7 \pm 3.5 -
B(B\rightarrow\tau\nu), 10^{-4} 1.14 \pm 0.22 0.889 \pm 0.078 0.806 \pm 0.070
B(B_{s}\rightarrow ll), 10^{-9} - 3.60 \pm 0.12 -
B(B_{d}\rightarrow ll), 10^{-9} - 0.1118 \pm 0.0070 -

The fit results for all the nine CKM elements are V_{CKM}=\left(\begin{array}{ccc} 0.97426 \pm 0.00011 & (0.22535 \pm 0.00059) & (0.00374 \pm 0.00013)e^{i(-68.4 \pm 3.5)^\circ}\\ ( -0.2252 \pm 0.00054)e^{i(0.0361 \pm 0.0010)^\circ} & (0.97339 \pm 0.00013)e^{i(-0.00193 \pm 0.00005)^\circ} & (0.04195 \pm 0.00051) \\ (0.00876 \pm 0.00019)e^{i(-22.60 \pm 0.87)^\circ} & (0.041245 \pm 0.000455)e^{i(1.084 \pm 0.041)^\circ} & (0.999115 \pm 0.000021)\end{array}\right)




Full fit result for \,\bar{\rho}
0.144 \pm 0.024
95% prob:[0.097, 0.190]
99% prob:[0.075, 0.212]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\bar{\eta}
0.358 \pm 0.021
95% prob:[0.328, 0.387]
99% prob:[0.315, 0.401]
EPS - PDF - PNG - JPG - GIF



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



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Full fit result for \,A
0.825 \pm 0.011
95% prob:[0.803, 0.847]
99% prob:[0.792, 0.858]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,\lambda
0.2253 \pm 0.0009
95% prob:[0.2235, 0.2271]
99% prob:[0.2226, 0.228]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,\lambda
0.2254 \pm 0.0006
95% prob:[0.2241, 0.2266]
99% prob:[0.2235, 0.2272]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,|V_{ub}|
Gaussian likelihood used
0.00440 \pm 0.00031
EPS - PDF - PNG - JPG - GIF



Fit Input for \,|V_{cb}|
Gaussian likelihood used
0.0417 \pm 0.0007
EPS - PDF - PNG - JPG - GIF

Standard Model Exclusive Measurements Fit

Parameter Input value Full fit SM Prediction
\bar{\rho} - 0.113 \pm 0.021 -
\bar{\eta} - 0.358 \pm 0.021 -
A - 0.811 \pm 0.011 -
\lambda 0.2253 \pm 0.0009 0.22535 \pm 0.00065 -
|V_{ub}| 0.00342 \pm 0.00022 0.00357 \pm 0.00011 -
|V_{cb}| 0.03955 \pm 0.00088 0.04121 \pm 0.0005 -
\alpha [^{\circ}] 90.9 \pm 8.0 85.6 \pm 2.9 86.3 \pm 3.8
\beta [^{\circ}] - 21.91 \pm 0.75 24.4 \pm 1.8
\sin(2\beta) 0.68 \pm 0.023 0.693 \pm 0.019 0.754 \pm 0.042
\cos(2\beta) 0.87 \pm 0.13 0.722 \pm 0.018 0.66 \pm 0.048
2\beta+\gamma [^{\circ}] -89 \pm 54 \text{ and } 90 \pm 54 116.1 \pm 3.1 -
\gamma [^{\circ}] -109.9 \pm 7.1 \text{ and } 70.1 \pm 7.1 72.5 \pm 3.1 -
B(B\rightarrow\tau\nu) 10^{-4} 1.14 \pm 0.22 0.818 \pm 0.065 0.806 \pm 0.07
B(B_{s}\rightarrow ll), 10^{-9} - 3.52 \pm 0.12 -
B(B_{d}\rightarrow ll), 10^{-9} - 0.1162 \pm 0.0066 -

The fit results for all the nine CKM elements are V_{CKM}=\left(\begin{array}{ccc} (0.97426 \pm 0.00014) & (0.22545 \pm 0.00059) & (0.00357 \pm 0.00011)e^{i(-72.6 \pm 3.1)^\circ}\\ ( -0.22525 \pm 0.00059)e^{i(0.03476 \pm 0.00096)^\circ} & (0.97342 \pm 0.00013)e^{i(-0.00186 \pm 0.00005)^\circ} & (0.04121 \pm 0.0005) \\ (0.00886 \pm 0.00018)e^{i(-21.93 \pm 0.73)^\circ} & ( -0.04042 \pm 0.0005)e^{i(1.08 \pm 0.033)^\circ} & (0.999142 \pm 0.000018)\end{array}\right)




Full fit result for \,\bar{\rho}
0.113 \pm 0.021
95% prob:[0.072, 0.155]
99% prob:[0.049, 0.179]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\bar{\eta}
0.358 \pm 0.021
95% prob:[0.329, 0.385]
99% prob:[0.316, 0.401]
EPS - PDF - PNG - JPG - GIF



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



EPS - PDF - PNG - JPG - GIF




Full fit result for \,A
0.811 \pm 0.011
95% prob:[0.788, 0.832]
99% prob:[0.779, 0.846]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,\lambda
0.2253 \pm 0.0009
95% prob:[0.2235, 0.2271]
99% prob:[0.2226, 0.228]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,\lambda
0.22535 \pm 0.00065
95% prob:[0.2241, 0.2266]
99% prob:[0.2235, 0.2272]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,|V_{ub}|
0.00342 \pm 0.00022
95% prob:[0.00297, 0.00385]
99% prob:[0.00276, 0.00407]
EPS - PDF - PNG - JPG - GIF



Fit Input for \,|V_{cb}|
Gaussian likelihood used
0.03955 \pm 0.00088
EPS - PDF - PNG - JPG - GIF

Tree level Fit

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} - -0.136 \pm 0.051 \text{ and } 0.132 \pm 0.049
\bar{\eta} - -0.367 \pm 0.050 \text{ and } 0.369 \pm 0.050
\rho - 0.135 \pm 0.051
\eta - 0.378 \pm 0.050
A - 0.806 \pm 0.020
\lambda - 0.2253 \pm 0.0006
\alpha, [^{\circ}] - 86.2 \pm 7.6
\beta, [^{\circ}] - 23.1 \pm 3.0
\sin(2\beta) - 0.726 \pm 0.071
\gamma, [^{\circ}] -109.9 \pm 7.1 \text{ and } 70.1 \pm 7.1 69.4 \pm 7.1

The fit results for all the nine CKM elements are V_{CKM}=\left(\begin{array}{ccc} (0.97428 \pm 0.00014) & (0.22532 \pm 0.00063) & (0.00375 \pm 0.00046)e^{i(-69.5 \pm 7.1)^\circ}\\ ( -0.22512 \pm 0.00063)e^{i(0.0353 \pm 0.0045)^\circ} & (0.97347 \pm 0.00015)e^{i(-0.00188 \pm 0.00023)^\circ} & (0.039915 \pm 0.000015 \text{ and } 0.04092 \pm 0.00098) \\ (0.00869 \pm 0.00048 \text{ and } 0.01101 \pm 0.00050)e^{i(-23.1 \pm 2.7)^\circ} & ( -0.0398 \pm 0.0010)e^{i(1.12 \pm 0.12)^\circ} & (0.999155 \pm 0.000040)\end{array}\right)




Full fit result for \,\bar{\rho}
-0.136 \pm 0.051 \text{ and } 0.132 \pm 0.049
95% prob:[-0.23, -0.04] U [0.041, 0.238]
99% prob:[-0.28, 0.285]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\bar{\eta}
-0.367 \pm 0.050 \text{ and } 0.369 \pm 0.050
95% prob:[-0.46, -0.26] U [0.27, 0.469]
99% prob:[-0.52, -0.22] U [0.223, 0.522]
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 0.051
95% prob:[0.042, 0.245]
99% prob:[0, 0.292]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\eta
0.378 \pm 0.050
95% prob:[0.281, 0.476]
99% prob:[0.242, 0.5]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,A
0.806 \pm 0.020
95% prob:[0.766, 0.846]
99% prob:[0.746, 0.867]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\lambda
0.2253 \pm 0.0006
95% prob:[0.2241, 0.2266]
99% prob:[0.2234, 0.2272]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\alpha, [^{\circ}]
86.2 \pm 7.6
95% prob:[72.6, 102.]
99% prob:[68, 109.]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\beta, [^{\circ}]
23.1 \pm 3.0
95% prob:[17.1, 29.1]
99% prob:[15, 31.7]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\sin(2\beta)
0.726 \pm 0.071
95% prob:[0.574, 0.858]
99% prob:[0.506, 0.899]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,\gamma, [^{\circ}]
-109.9 \pm 7.1 \text{ and } 70.1 \pm 7.1
95% prob:[-124, -96.] U [54.6, 83.4]
99% prob:[-132, -90.] U [47.8, 89.7]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,\gamma, [^{\circ}]
69.4 \pm 7.1
95% prob:[54.5, 83.1]
99% prob:[47.8, 90.2]
EPS - PDF - PNG - JPG - GIF

Standard Model No Lattice Fit

Parameter Full fit
\bar{\rho} 0.132 \pm 0.028
\bar{\eta} 0.34 \pm 0.017
A 0.808 \pm 0.019
\lambda 0.2253 \pm 0.0006
f_{B_{s}} 0.192 \pm 0.023
f_{B_{s}}/f_{B_{d}} 0.66045 \pm 0.0005 \text{ and } 0.79684 \pm 0.10092 \text{ and } 0.91973 \pm 0.01798
B_{B_{s}}/B_{B_{d}} 1.613 \pm 0.045 \text{ and } 2.185 \pm 0.453 \text{ and } 2.776 \pm 0.133
B_{B_{s}} 1.18 \pm 0.22 \text{ and } 1.5 \pm 0.05
B_{k} 0.855 \pm 0.09




Full fit result for \,\bar{\rho}
0.132 \pm 0.028
95% prob:[0.078, 0.188]
99% prob:[0.049, 0.219]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\bar{\eta}
0.34 \pm 0.017
95% prob:[0.307, 0.373]
99% prob:[0.289, 0.389] U [0.390, 0.394]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,A
0.808 \pm 0.019
95% prob:[0.768, 0.84] U [0.842, 0.848]
99% prob:[0.755, 0.861]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\lambda
0.2253 \pm 0.0006
95% prob:[0.2241, 0.2267]
99% prob:[0.2235, 0.2272]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,f_{B_{s}}
0.192 \pm 0.023
95% prob:[0.149, 0.239]
99% prob:[0.129, 0.256] U [0.257, 0.258]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,f_{B_{s}}/f_{B_{d}}
0.66045 \pm 0.0005 \text{ and } 0.79684 \pm 0.10092 \text{ and } 0.91973 \pm 0.01798
95% prob:[0.62, 1.07]
99% prob:[0.60, 1.28]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,B_{B_{s}}/B_{B_{d}}
1.613 \pm 0.045 \text{ and } 2.185 \pm 0.453 \text{ and } 2.776 \pm 0.133
95% prob:[1.34, 1.36] U [1.38, 3.6]
99% prob:[0.93, 3.6]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,B_{B_{s}}
1.18 \pm 0.22 \text{ and } 1.5 \pm 0.05
95% prob:[0.842, 1.803]
99% prob:[0.744, 1.917]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,B_{k}
0.855 \pm 0.09
95% prob:[0.697, 1.045]
99% prob:[0.619, 1.147] U [1.183, 1.19]
EPS - PDF - PNG - JPG - GIF

New Physics Fit

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} - 0.147 \pm 0.045
\bar{\eta} - 0.368 \pm 0.048
\rho - 0.151 \pm 0.046
\eta - 0.377 \pm 0.049
A - 0.799 \pm 0.020
\lambda 0.2253 \pm 0.0009 0.2253 \pm 0.0006
C_{B_{d}} - 1.07 \pm 0.17
\phi_{B_{d}} [^{\circ}] - -2.0 \pm 3.2
C_{B_{s}} - 1.066 \pm 0.083
\phi_{B_{s}} [^{\circ}] - 0.6 \pm 2.0
C_{\epsilon_{K}} - 1.05 \pm 0.16
A_{SL_{d}} 0.0032 \pm 0.0029 -0.0019 \pm 0.0018
A_{SL_{s}} -0.0047 \pm 0.0052 -0.00011 \pm 0.00064

The fit results for all the nine CKM elements are V_{CKM}=\left(\begin{array}{ccc} (0.97428 \pm 0.00014) & (0.22527 \pm 0.00063) & (0.00376 \pm 0.00045)e^{i(-67.8 \pm 6.2)^\circ}\\ ( -0.22517 \pm 0.00063)e^{i(0.0347 \pm 0.0044)^\circ} & (0.97347 \pm 0.00015)e^{i(-0.00186 \pm 0.00022)^\circ} & (0.04061 \pm 0.00097) \\ (0.00847 \pm 0.00044)e^{i(-23.4 \pm 2.7)^\circ} & ( -0.03989 \pm 0.00095)e^{i(1.11 \pm 0.12)^\circ} & (0.999169 \pm 0.000039)\end{array}\right)




Full fit result for \,\bar{\rho}
0.147 \pm 0.045
95% prob:[0.065, 0.235]
99% prob:[0.034, 0.288]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\bar{\eta}
0.368 \pm 0.048
95% prob:[0.272, 0.466]
99% prob:[0.220, 0.525]
EPS - PDF - PNG - JPG - GIF



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



EPS - PDF - PNG - JPG - GIF




Full fit result for \,\rho
0.151 \pm 0.046
95% prob:[0.066, 0.241]
99% prob:[0.035, 0.295]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\eta
0.377 \pm 0.049
95% prob:[0.279, 0.478]
99% prob:[0.225, 0.538]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,A
0.799 \pm 0.020
95% prob:[0.76, 0.839]
99% prob:[0.741, 0.859]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,\lambda
0.2253 \pm 0.0009
95% prob:[0.2235, 0.2271]
99% prob:[0.2226, 0.228]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,\lambda
0.2253 \pm 0.0006
95% prob:[0.224, 0.2265]
99% prob:[0.2234, 0.2272]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\Phi^{NP}_{B_{d}} - A^{NP}_{d}/A^{SM}_{d}
 
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\Phi^{NP}_{B_{s}} - A^{NP}_{d}/A^{SM}_{s}
 
EPS - PDF - PNG - JPG - GIF




Full fit result for \,C_{B_{d}}
1.07 \pm 0.17
95% prob:[0.77, 1.44]
99% prob:[0.65, 1.69]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\phi_{B_{d}} [^{\circ}]
-2.0 \pm 3.2
95% prob:[-8., 4.2]
99% prob:[-12, 7.8]
EPS - PDF - PNG - JPG - GIF



correlations for \,\Phi_{B_{d}} - C_{B_{d}}



EPS - PDF - PNG - JPG - GIF




Full fit result for \,C_{B_{s}}
1.066 \pm 0.083
95% prob:[0.912, 1.245]
99% prob:[0.847, 1.351]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\phi_{B_{s}} [^{\circ}]
0.6 \pm 2.0
95% prob:[-3., 4.6]
99% prob:[-5., 6.7]
EPS - PDF - PNG - JPG - GIF



correlations for \,\Phi_{B_{s}} - C_{B_{s}}



EPS - PDF - PNG - JPG - GIF




Full fit result for \,C_{\epsilon_{K}}
1.05 \pm 0.16
95% prob:[0.77, 1.41]
99% prob:[0.66, 1.73]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,A_{SL_{d}}
Gaussian likelihood used
0.0032 \pm 0.0029
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,A_{SL_{d}}
-0.0019 \pm 0.0018
95% prob:[-0.0057, 0.00128]
99% prob:[-0.0074, 0.00336]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,A_{SL_{s}}
Gaussian likelihood used
-0.0047 \pm 0.0052
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,A_{SL_{s}}
-0.00011 \pm 0.00064
95% prob:[-0.0013, 0.00114]
99% prob:[-0.0019, 0.00181]
EPS - PDF - PNG - JPG - GIF

 
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