Fit results: Winter 2013 (pre-Moriond13)

Standard Model Fit

Parameter Input value Full fit SM Prediction
\bar{\rho} - 0.132 \pm 0.021 -
\bar{\eta} - 0.350 \pm 0.014 -
\rho - 0.136 \pm 0.021 -
\eta - 0.359 \pm 0.014 -
A - 0.827 \pm 0.013 -
\lambda 0.2254 \pm 0.0009 0.22535 \pm 0.00065 -
|V_{ub}| 0.00382 \pm 0.00056 0.00365 \pm 0.00013 0.00364 \pm 0.00013
|V_{cb}| 0.041 \pm 0.001 0.04207 \pm 0.00064 0.04273 \pm 0.00077
\sin\theta_{12} - 0.2254 \pm 0.0007 -
\sin\theta_{23} - 0.04207 \pm 0.00064 -
\sin\theta_{13} - 0.00364 \pm 0.00013 -
\delta [^{\circ}] - 69.2 \pm 3.1 -
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 0.9 170 \pm 11
\Delta m_{s} \mathrm{[ps^{-1}]} 17.72 \pm 0.04 17.72 \pm 0.04 17.5 \pm 1.3
\Delta m_{d} \mathrm{[ps^{-1}]} 0.507 \pm 0.004 - -
\Delta m_{K} \mathrm{[ps^{-1}]} 1.8 \pm 1.8 - -
f_{B_{s}} 0.233 \pm 0.010 0.2281 \pm 0.0057 0.2262 \pm 0.0066
f_{B_{s}}/f_{B_{d}} 1.2 \pm 0.02 1.204 \pm 0.018 1.239 \pm 0.053
B_{B_{s}}/B_{B_{d}} 1.05 \pm 0.07 1.093 \pm 0.051 1.144 \pm 0.076
B_{B_{s}} 0.87 \pm 0.04 0.856 \pm 0.036 0.814 \pm 0.073
B_{k} 0.75 \pm 0.02 0.757 \pm 0.019 0.866 \pm 0.086
\alpha [^{\circ}] 90.9 \pm 8.0 88.7 \pm 3.1 87.7 \pm 3.6
\beta [^{\circ}] - 21.95 \pm 0.86 24.3 \pm 1.9
\sin(2\beta) 0.680 \pm 0.023 0.692 \pm 0.021 0.751 \pm 0.044
\cos(2\beta) 0.87 \pm 0.13 0.722 \pm 0.021 0.664 \pm 0.050
2\beta+\gamma [^{\circ}] -89 \pm 54 \text{ and } 90 \pm 54 113.3 \pm 3.3 113.5 \pm 3.3
\gamma [^{\circ}] -109.0 \pm 7.8 \text{ and } 70.8 \pm 7.8 69.2 \pm 3.2 68.6 \pm 3.6
|\epsilon_{k}| 0.002228 \pm 0.000013 0.002228 \pm 0.000011 0.00188 \pm 0.0002
B(B\rightarrow\tau\nu) 10^{-4} 0.99 \pm 0.25 0.839 \pm 0.078 0.826 \pm 0.079
J_{cp} 10^{-5} - 3.15 \pm 0.11 -
B(B_{s}\rightarrow ll), 10^{-9} - 3.45 \pm 0.26 -
\Delta\Gamma_{d}/\Gamma_{d} - 0.00493 \pm 0.00042 -
\Delta\Gamma_{s}/\Gamma_{s} - 0.147 \pm 0.014 -
\beta_{s} [^{\circ}] - 1.067 \pm 0.043 -

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) & (0.00365 \pm 0.00013)e^{i(-69.1 \pm 3.1)^\circ}\\ ( -0.22535 \pm 0.00065)e^{i(0.0355 \pm 0.0012)^\circ} & (0.97339 \pm 0.00013)e^{i(-0.001906 \pm 0.000061)^\circ} & (0.04207 \pm 0.00064) \\ (0.00888 \pm 0.00020)e^{i(-21.86 \pm 0.80)^\circ} & ( -0.04128 \pm 0.00064)e^{i(1.064 \pm 0.043)^\circ} & (0.999106 \pm 0.000024)\end{array}\right)




Full fit result for \,\bar{\rho}
0.132 \pm 0.021
95% prob:[0.090, 0.174]
99% prob:[0.070, 0.195]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\bar{\eta}
0.35 \pm 0.014
95% prob:[0.323, 0.379]
99% prob:[0.311, 0.395]
EPS - PDF - PNG - JPG - GIF




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



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Angles only result for \,\bar{\rho} - \bar{\eta}



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Sides only result for \,\bar{\rho} - \bar{\eta}



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Full fit result for \,\rho
0.136 \pm 0.021
95% prob:[0.093, 0.178]
99% prob:[0.072, 0.200]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\eta
0.359 \pm 0.014
95% prob:[0.331, 0.389]
99% prob:[0.319, 0.405]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,A
0.827 \pm 0.013
95% prob:[0.802, 0.855]
99% prob:[0.788, 0.869]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,\lambda
0.2254 \pm 0.0009
95% prob:[0.2236, 0.2272]
99% prob:[0.2226, 0.228]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,\lambda
0.22535 \pm 0.00065
95% prob:[0.2242, 0.2267]
99% prob:[0.2235, 0.2273]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,|V_{ub}|
Gaussian likelihood used
0.00382 \pm 0.00056
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,|V_{ub}|
0.00365 \pm 0.00013
95% prob:[0.00340, 0.00391]
99% prob:[0.00329, 0.00405]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,|V_{ub}|
0.00364 \pm 0.00013
95% prob:[0.00338, 0.00390]
99% prob:[0.00326, 0.00405]
EPS - PDF - PNG - JPG - GIF



Compatibility Plot for \,|V_{ub}|



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Fit Input for \,|V_{cb}|
Gaussian likelihood used
0.041 \pm 0.001
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,|V_{cb}|
0.04207 \pm 0.00064
95% prob:[0.0408, 0.04332]
99% prob:[0.04018, 0.04396]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,|V_{cb}|
0.04273 \pm 0.00077
95% prob:[0.04118, 0.04432]
99% prob:[0.04033, 0.04531]
EPS - PDF - PNG - JPG - GIF



Compatibility Plot for \,|V_{cb}|



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Full fit result for \,\sin\theta_{12}
0.2254 \pm 0.0007
95% prob:[0.2242, 0.2267]
99% prob:[0.2236, 0.2274]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\sin\theta_{23}
0.04207 \pm 0.00064
95% prob:[0.04081, 0.04334]
99% prob:[0.04017, 0.04402]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\sin\theta_{13}
0.00364 \pm 0.00013
95% prob:[0.00340, 0.00391]
99% prob:[0.00329, 0.00406]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\delta [^{\circ}]
69.2 \pm 3.1
95% prob:[63.3, 75.8]
99% prob:[60.1, 78.8]
EPS - PDF - PNG - JPG - GIF




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}]}
170 \pm 11
95% prob:[148.7, 192.7]
99% prob:[141.8, 200]
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
17.72 \pm 0.04
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,\Delta m_{s} \mathrm{[ps^{-1}]}
17.72 \pm 0.04
95% prob:[17.64, 17.8]
99% prob:[17.61, 17.84]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,\Delta m_{s} \mathrm{[ps^{-1}]}
17.5 \pm 1.3
95% prob:[14.9, 20.2]
99% prob:[13.8, 21.7]
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
0.233 \pm 0.010
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,f_{B_{s}}
0.2281 \pm 0.0057
95% prob:[0.2173, 0.2398]
99% prob:[0.212, 0.2459]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,f_{B_{s}}
0.2262 \pm 0.0066
95% prob:[0.2134, 0.2395]
99% prob:[0.208, 0.2481]
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
1.2 \pm 0.02
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,f_{B_{s}}/f_{B_{d}}
1.204 \pm 0.018
95% prob:[1.168, 1.242]
99% prob:[1.15, 1.261]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,f_{B_{s}}/f_{B_{d}}
1.239 \pm 0.053
95% prob:[1.14, 1.35]
99% prob:[1.105, 1.398]
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
1.05 \pm 0.07
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,B_{B_{s}}/B_{B_{d}}
1.093 \pm 0.051
95% prob:[0.993, 1.197]
99% prob:[0.944, 1.249]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,B_{B_{s}}/B_{B_{d}}
1.144 \pm 0.076
95% prob:[1.012, 1.291]
99% prob:[0.944, 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}}
0.856 \pm 0.036
95% prob:[0.785, 0.929]
99% prob:[0.749, 0.965]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,B_{B_{s}}
0.814 \pm 0.073
95% prob:[0.679, 0.977]
99% prob:[0.622, 1.06] U [1.062, 1.069]
EPS - PDF - PNG - JPG - GIF



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



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Fit Input for \,B_{k}
0.733 \pm 0.029
95% prob:[0.674, 0.791]
99% prob:[0.645, 0.819]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,B_{k}
0.748 \pm 0.028
95% prob:[0.694, 0.803]
99% prob:[0.667, 0.831]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,B_{k}
0.866 \pm 0.086
95% prob:[0.71, 1.048]
99% prob:[0.638, 1.151]
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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:[78.4, 103.] U [162., 170.]
99% prob:[72.6, 110.] U [158, 172.] U [178., 180]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,\alpha [^{\circ}]
88.7 \pm 3.1
95% prob:[82.3, 94.6]
99% prob:[79.5, 97.9]
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SM Fit prediction for \,\alpha [^{\circ}]
87.7 \pm 3.6
95% prob:[80.4, 95]
99% prob:[76.9, 98.7]
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Compatibility Plot for \,\alpha [^{\circ}]



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Full Fit result for \,\beta [^{\circ}]
21.95 \pm 0.87
95% prob:[20.3, 23.8]
99% prob:[19.6, 24.7]
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SM Fit prediction for \,\beta [^{\circ}]
24.4 \pm 1.9
95% prob:[20.6, 28.3]
99% prob:[18.9, 30.4]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,\sin(2\beta)
0.680 \pm 0.023
95% prob:[0.635, 0.729]
99% prob:[0.613, 0.755]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,\sin(2\beta)
0.693 \pm 0.021
95% prob:[0.653, 0.739]
99% prob:[0.633, 0.762]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,\sin(2\beta)
0.755 \pm 0.044
95% prob:[0.665, 0.84]
99% prob:[0.619, 0.877]
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)
0.721 \pm 0.021
95% prob:[0.675, 0.759]
99% prob:[0.65, 0.776]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,\cos(2\beta)
0.659 \pm 0.051
95% prob:[0.551, 0.753]
99% prob:[0.49, 0.791]
EPS - PDF - PNG - JPG - GIF



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}]
113.3 \pm 3.3
95% prob:[106.8, 119.9]
99% prob:[103.5, 123]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,2\beta+\gamma [^{\circ}]
113.5 \pm 3.3
95% prob:[107.1, 120.2]
99% prob:[103.7, 123.3]
EPS - PDF - PNG - JPG - GIF



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



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Fit Input for \,\gamma [^{\circ}]
-109.0 \pm 7.8 \text{ and } 70.8 \pm 7.8
95% prob:[-124, -94.] U [55, 85.6]
99% prob:[-132, -87.] U [47.3, 92.4]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,\gamma [^{\circ}]
69.2 \pm 3.2
95% prob:[63.2, 75.7]
99% prob:[60.1, 78.8]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,\gamma [^{\circ}]
68.6 \pm 3.6
95% prob:[62, 75.7]
99% prob:[58.4, 78.2] U [78.4, 79]
EPS - PDF - PNG - JPG - GIF



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



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Fit Input for \,|\epsilon_{k}|
0.00223 \pm 0.000013
95% prob:[0.00220, 0.00225]
99% prob:[0.00219, 0.00226]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,|\epsilon_{k}|
0.002223 \pm 0.000011
95% prob:[0.00221, 0.00224]
99% prob:[0.00220, 0.00226]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,|\epsilon_{k}|
0.00188 \pm 0.0002
95% prob:[0.00150, 0.00230]
99% prob:[0.00135, 0.00255]
EPS - PDF - PNG - JPG - GIF



Compatibility Plot for \,|\epsilon_{k}|



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Fit Input for \,B(B\rightarrow\tau\nu) 10^{-4}
Gaussian likelihood used
0.99 \pm 0.25
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,B(B\rightarrow\tau\nu) 10^{-4}
0.839 \pm 0.078
95% prob:[0.7, 1.005]
99% prob:[0.641, 1.1]
EPS - PDF - PNG - JPG - GIF



SM Fit prediction for \,B(B\rightarrow\tau\nu) 10^{-4}
0.826 \pm 0.079
95% prob:[0.685, 0.997]
99% prob:[0.627, 1.1]
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}
3.15 \pm 0.11
95% prob:[2.93, 3.37]
99% prob:[2.83, 3.49]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,B(B_{s}\rightarrow ll), 10^{-9}
3.45 \pm 0.26
95% prob:[2.94, 4]
99% prob:[2.7, 4.3]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\Delta\Gamma_{d}/\Gamma_{d}
0.00493 \pm 0.00042
95% prob:[0.00417, 0.00583]
99% prob:[0.00383, 0.0063]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\Delta\Gamma_{s}/\Gamma_{s}
0.147 \pm 0.014
95% prob:[0.122, 0.175]
99% prob:[0.111, 0.191]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\beta_{s} [^{\circ}]
1.067 \pm 0.043
95% prob:[0.985, 1.156]
99% prob:[0.948, 1.204]
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} - -0.128 \pm 0.055 \text{ and } 0.128 \pm 0.055
\bar{\eta} - -0.376 \pm 0.060 \text{ and } 0.375 \pm 0.060
\rho - 0.131 \pm 0.055
\eta - 0.385 \pm 0.058
A - 0.807 \pm 0.020
\lambda - 0.22535 \pm 0.00065
\alpha, [^{\circ}] - 85.2 \pm 8.2
\beta, [^{\circ}] - 23.5 \pm 3.5
\sin(2\beta) - 0.736 \pm 0.084
\gamma, [^{\circ}] 70.8 \pm 7.8 71.1 \pm 7.5

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) & (0.00383 \pm 0.00056)e^{i(-71.3 \pm 7.6)^\circ}\\ ( -0.22515 \pm 0.00059)e^{i(0.0361 \pm 0.0050)^\circ} & (0.97344 \pm 0.00015)e^{i(-0.00192 \pm 0.00026)^\circ} & (0.041 \pm 0.001) \\ (0.00876 \pm 0.00052 \text{ and } 0.01100 \pm 0.00053)e^{i(-23.3 \pm 3.0)^\circ} & ( -0.0399 \pm 0.0010)e^{i(1.14 \pm 0.13)^\circ} & (0.999151 \pm 0.000039)\end{array}\right)




Full fit result for \,\bar{\rho}
-0.128 \pm 0.055 \text{ and } 0.128 \pm 0.054
95% prob:[-0.24, -0.02] U [0.027, 0.244]
99% prob:[-0.30, 0.298]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\bar{\eta}
-0.376 \pm 0.06 \text{ and } 0.375 \pm 0.061
95% prob:[-0.49, -0.25] U [0.258, 0.495]
99% prob:[-0.55, -0.20] U [0.204, 0.559]
EPS - PDF - PNG - JPG - GIF



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



EPS - PDF - PNG - JPG - GIF




Full fit result for \,\rho
0.131 \pm 0.055
95% prob:[0.027, 0.250]
99% prob:[0, 0.307]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\eta
0.385 \pm 0.058
95% prob:[0.279, 0.494]
99% prob:[0.226, 0.5]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,A
0.807 \pm 0.020
95% prob:[0.767, 0.847]
99% prob:[0.747, 0.868]
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




Full fit result for \,\alpha, [^{\circ}]
85.2 \pm 8.2
95% prob:[70, 102.]
99% prob:[63.5, 112.]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\beta, [^{\circ}]
23.5 \pm 3.5
95% prob:[16.5, 30.4]
99% prob:[15, 33.3]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\sin(2\beta)
0.736 \pm 0.084
95% prob:[0.559, 0.885]
99% prob:[0.5, 0.923]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,\gamma, [^{\circ}]
70.8 \pm 7.7
95% prob:[55.1, 85.6]
99% prob:[47.3, 92.3]
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,\gamma, [^{\circ}]
71.1 \pm 7.5
95% prob:[55.1, 85.7]
99% prob:[47.3, 92.6]
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 0.048
\bar{\eta} - 0.370 \pm 0.057
\rho - 0.151 \pm 0.050
\eta - 0.378 \pm 0.058
A - 0.802 \pm 0.020
\lambda 0.2254 \pm 0.0009 0.22535 \pm 0.00065
C_{B_{d}} - 1.01 \pm 0.15
\phi_{B_{d}} [^{\circ}] - -2.2 \pm 3.7
C_{B_{s}} - 1.03 \pm 0.10
\phi_{B_{s}} [^{\circ}] - -0.84 \pm 2.47
C_{\epsilon_{K}} - 1.08 \pm 0.18
A_{SL_{d}} -0.0003 \pm 0.0021 -0.0013 \pm 0.0015
A_{SL_{s}} -0.0109 \pm 0.0040 -0.00033 \pm 0.00068

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) & (0.00379 \pm 0.00054)e^{i(-67.5 \pm 6.4)^\circ}\\ ( -0.22525 \pm 0.00059)e^{i(0.0352 \pm 0.0049)^\circ} & (0.97344 \pm 0.00015)e^{i(-0.00187 \pm 0.00024)^\circ} & (0.04075 \pm 0.00097) \\ (0.00851 \pm 0.00046)e^{i(-23.6 \pm 2.9)^\circ} & ( -0.04002 \pm 0.00095)e^{i(1.12 \pm 0.13)^\circ} & (0.999163 \pm 0.000039)\end{array}\right)




Full fit result for \,\bar{\rho}
0.147 \pm 0.048
95% prob:[0.060, 0.241]
99% prob:[0.027, 0.305]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\bar{\eta}
0.370 \pm 0.057
95% prob:[0.257, 0.484]
99% prob:[0.191, 0.558]
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 0.050
95% prob:[0.061, 0.247]
99% prob:[0.028, 0.312]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\eta
0.378 \pm 0.058
95% prob:[0.264, 0.497]
99% prob:[0.196, 0.572]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,A
0.802 \pm 0.020
95% prob:[0.763, 0.841]
99% prob:[0.744, 0.862]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,\lambda
0.2254 \pm 0.0009
95% prob:[0.2236, 0.2272]
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




Full fit result for \,C_{B_{d}}
1.01 \pm 0.15
95% prob:[0.73, 1.35]
99% prob:[0.62, 1.59]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\phi_{B_{d}} [^{\circ}]
-2.2 \pm 3.7
95% prob:[-9., 5.2]
99% prob:[-14, 9.8]
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}}
1.03 \pm 0.10
95% prob:[0.84, 1.26]
99% prob:[0.77, 1.40]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\phi_{B_{s}} [^{\circ}]
-0.84 \pm 2.47
95% prob:[-5., 3.8]
99% prob:[-8., 6.5]
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}}
1.08 \pm 0.18
95% prob:[0.76, 1.52]
99% prob:[0.64, 1.91]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,A_{SL_{d}}
Gaussian likelihood used
-0.0003 \pm 0.0021
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,A_{SL_{d}}
-0.0013 \pm 0.0015
95% prob:[-0.0047, 0.00162]
99% prob:[-0.0064, 0.00344]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,A_{SL_{s}}
Gaussian likelihood used
-0.0109 \pm 0.0040
EPS - PDF - PNG - JPG - GIF



Full Fit result for \,A_{SL_{s}}
-0.00033 \pm 0.00068
95% prob:[-0.0017, 0.00102]
99% prob:[-0.0024, 0.00173]
EPS - PDF - PNG - JPG - GIF

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