New Physics Fit results: Summer 2016

Input used are the same as in Standard Model 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.

Parameter Input value Prediction
\bar{\rho} - 0.149 \pm 0.027
\bar{\eta} - 0.363 \pm 0.025
\rho - 0.153 \pm 0.027
\eta - 0.372 \pm 0.025
A - 0.810 \pm 0.020
\lambda 0.22534 \pm 0.00089 0.22494 \pm 0.00078
|V_{ub}| 0.00373 \pm 0.00021 0.00366 \pm 0.00012
|V_{cb}| 0.04170 \pm 0.00100 0.04256 \pm 0.00069
\alpha [^{\circ}] 94.2 \pm 5.0 \text{ and } 166.4 \pm 0.8 88.7 \pm 4.2
\beta [^{\circ}] - 22.9 \pm 1.4
\gamma [^{\circ}] -109.5 \pm 5.7 \text{ and } 70.5 \pm 5.7 65.3 \pm 2.0
C_{B_{d}} - 1.03 \pm 0.11
\phi_{B_{d}} [^{\circ}] - -1.8 \pm 1.7
C_{B_{s}} - 1.070 \pm 0.088
\phi_{B_{s}} [^{\circ}] - 0.054 \pm 0.951
C_{\epsilon_{K}} - 1.04 \pm 0.11
A_{SL_{d}} 0.00020 \pm 0.00200 -0.0019 \pm 0.0015
A_{SL_{s}} 0.0017 \pm 0.0030 -0.00016 \pm 0.00052

CKM matrix thus looks like V_{CKM}=\left(\begin{array}{ccc} (0.97434 \pm 0.00015) & (0.22504 \pm 0.00070) & (0.00365 \pm 0.00012)e^{i(-68.4 \pm 3.7)^\circ}\\ ( -0.22489 \pm 0.00070)e^{i(0.0351 \pm 0.0024)^\circ} & (0.97351 \pm 0.00016)e^{i(-0.00187 \pm 0.00012)^\circ} & (0.04255 \pm 0.00069) \\ (0.00858 \pm 0.00032)e^{i(-23.1 \pm 1.3)^\circ} & ( -0.04035 \pm 0.00093)e^{i(1.101 \pm 0.073)^\circ} & (0.999148 \pm 0.000039)\end{array}\right)




Full fit result for \,\bar{\rho}
0.149 \pm 0.027
95% prob:[0.097, 0.209]
99% prob:[0.077, 0.247]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\bar{\eta}
0.363 \pm 0.025
95% prob:[0.313, 0.413]
99% prob:[0.287, 0.438]
EPS - PDF - PNG - JPG - GIF



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



EPS - PDF - PNG - JPG - GIF




Full fit result for \,\rho
0.153 \pm 0.027
95% prob:[0.099, 0.214]
99% prob:[0.079, 0.253]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\eta
0.372 \pm 0.025
95% prob:[0.321, 0.424]
99% prob:[0.291, 0.449]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,A
0.810 \pm 0.020
95% prob:[0.772, 0.850]
99% prob:[0.752, 0.869]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,\lambda
0.22534 \pm 0.00089
95% prob:[0.22356, 0.22712]
99% prob:[0.22257, 0.22801]
EPS - PDF - PNG - JPG - GIF



Prediction for \,\lambda
0.22494 \pm 0.00078
95% prob:[0.22366, 0.22643]
99% prob:[0.22297, 0.22712]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,|V_{ub}|
0.00366 \pm 0.00012
95% prob:[0.00341, 0.00391]
99% prob:[0.00330, 0.00405]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,|V_{cb}|
0.04256 \pm 0.00069
95% prob:[0.04117, 0.04399]
99% prob:[0.04051, 0.04469]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\alpha [^{\circ}]
88.7 \pm 4.2
95% prob:[81.2, 99.0]
99% prob:[78.4, 105.2]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\beta [^{\circ}]Sorted ascending
22.9 \pm 1.4
95% prob:[20.0, 25.8]
99% prob:[18.6, 27.4]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\gamma [^{\circ}]
65.3 \pm 2.0
95% prob:[61.1, 69.5]
99% prob:[59.0, 71.9]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,C_{B_{d}}
1.03 \pm 0.11
95% prob:[0.81, 1.28]
99% prob:[0.73, 1.47]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\phi_{B_{d}} [^{\circ}]
-1.8 \pm 1.7
95% prob:[-5.2, 1.5]
99% prob:[-7.0, 3.3]
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}}
1.070 \pm 0.088
95% prob:[0.899, 1.252]
99% prob:[0.833, 1.371]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\phi_{B_{s}} [^{\circ}]
0.054 \pm 0.951
95% prob:[-1.849, 1.959]
99% prob:[-2.819, 2.912]
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}}
1.04 \pm 0.11
95% prob:[0.83, 1.28]
99% prob:[0.75, 1.45]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,A_{SL_{d}}
Gaussian likelihood used
0.00020 \pm 0.00200

EPS - PDF - PNG - JPG - GIF



Prediction for \,A_{SL_{d}}
-0.0019 \pm 0.0015
95% prob:[-0.0053, 0.0005]
99% prob:[-0.0066, 0.0021]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,A_{SL_{s}}
Gaussian likelihood used
0.0017 \pm 0.0030

EPS - PDF - PNG - JPG - GIF



Prediction for \,A_{SL_{s}}
-0.00016 \pm 0.00052
95% prob:[-0.00113, 0.00088]
99% prob:[-0.00141, 0.00131]
EPS - PDF - PNG - JPG - GIF

 
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