New Physics Fit results: Summer 2018

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} - 0.144 \pm 0.028
\bar{\eta} - 0.378 \pm 0.027
\rho - 0.147 \pm 0.028
\eta - 0.388 \pm 0.028
A - 0.785 \pm 0.021
\lambda 0.22574 \pm 0.00089 0.22550 \pm 0.00050
|V_{ub}| 0.00372 \pm 0.00023 0.00373 \pm 0.00023
|V_{cb}| 0.0405 \pm 0.0011 0.0398 \pm 0.0010
\alpha [^{\circ}] 93.3 \pm 5.6 \text{ and } 166.6 \pm 0.6 86.2 \pm 4.0
\beta [^{\circ}] - 23.8 \pm 1.6
\gamma [^{\circ}] -109.9 \pm 4.2 \text{ and } 70.0 \pm 4.2 69.8 \pm 3.9
C_{B_{d}} - 1.05 \pm 0.11
\phi_{B_{d}} [^{\circ}] - -2.0 \pm 1.8
C_{B_{s}} - 1.110 \pm 0.090
\phi_{B_{s}} [^{\circ}] 0.60 \pm 0.88 0.43 \pm 0.89
C_{\epsilon_{K}} - 1.11 \pm 0.12
A_{SL_{d}} -0.0020 \pm 0.0017 -0.0033 \pm 0.0014
A_{SL_{s}} -0.00059 \pm 0.00280 -0.00012 \pm 0.00051

CKM matrix thus looks like V_{CKM}=\left(\begin{array}{ccc} (0.97431 \pm 0.00012) & (0.22514 \pm 0.00055) & (0.00371 \pm 0.00023)e^{i(-69.7 \pm 3.7)^\circ}\\ ( -0.22504 \pm 0.00055)e^{i(0.0343 \pm 0.0025)^\circ} & (0.97353 \pm 0.00012)e^{i(-0.00183 \pm 0.00013)^\circ} & (0.0398 \pm 0.0010) \\ (0.00842 \pm 0.00033)e^{i(-23.6 \pm 1.6)^\circ} & ( -0.0390 \pm 0.0010)e^{i(1.142 \pm 0.077)^\circ} & (0.999200 \pm 0.000040)\end{array}\right)




Full fit result for \,\bar{\rho}
0.144 \pm 0.028
95% prob:[0.092, 0.199]
99% prob:[0.074, 0.231]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,\bar{\eta}
0.378 \pm 0.027
95% prob:[0.322, 0.436]
99% prob:[0.295, 0.296] U [0.298, 0.472]
EPS - PDF - PNG - JPG - GIF



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



EPS - PDF - PNG - JPG - GIF




Full fit result for \,\rho
0.147 \pm 0.028
95% prob:[0.094, 0.204]
99% prob:[0.075, 0.236]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\eta
0.388 \pm 0.028
95% prob:[0.331, 0.448]
99% prob:[0.305, 0.484]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,A
0.785 \pm 0.021
95% prob:[0.745, 0.830]
99% prob:[0.723, 0.853]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,\lambda
0.22574 \pm 0.00089
95% prob:[0.22386, 0.22762]
99% prob:[0.22118, 0.22871]
EPS - PDF - PNG - JPG - GIF



Prediction for \,\lambda
0.22550 \pm 0.00050
95% prob:[0.22405, 0.22623]
99% prob:[0.22356, 0.22683]
EPS - PDF - PNG - JPG - GIF

too many splits for range


Fit Input for \,|V_{ub}|
0.00372 \pm 0.00023
95% prob:to be defined
99% prob:[0.000000000000, 1.249] U [1.250, 1.996]
EPS - PDF - PNG - JPG - GIF



Prediction for \,|V_{ub}|
0.00373 \pm 0.00023
95% prob:[0.00325, 0.00424]
99% prob:[0.00303, 0.00452]
EPS - PDF - PNG - JPG - GIF

too many splits for range


Fit Input for \,|V_{cb}|
Gaussian likelihood used
0.0405 \pm 0.0011

EPS - PDF - PNG - JPG - GIF



Prediction for \,|V_{cb}|
0.0398 \pm 0.0010
95% prob:[0.0378, 0.0420]
99% prob:[0.0370, 0.0430]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,\alpha [^{\circ}]
93.3 \pm 5.6 \text{ and } 166.6 \pm 0.6
95% prob:[83.30, 103.10] U [163.00, 169.90]
99% prob:[78.59, 109.70] U [160.19, 171.60]
EPS - PDF - PNG - JPG - GIF



Prediction for \,\alpha [^{\circ}]
86.2 \pm 4.0
95% prob:[79.0, 95.4]
99% prob:[76.2, 100.0]
EPS - PDF - PNG - JPG - GIF




Prediction for \,\beta [^{\circ}]
23.8 \pm 1.6
95% prob:[20.5, 27.3]
99% prob:[19.0, 29.4]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,\gamma [^{\circ}]
-109.9 \pm 4.2 \text{ and } 70.0 \pm 4.2
95% prob:[-118.3, -101.5] U [61.7, 78.5]
99% prob:[-122.5, -97.2] U [57.5, 82.5]
EPS - PDF - PNG - JPG - GIF



Prediction for \,\gamma [^{\circ}]
69.8 \pm 3.9
95% prob:[61.3, 76.3]
99% prob:[57.4, 78.9]
EPS - PDF - PNG - JPG - GIF




Full fit result for \,C_{B_{d}}
1.05 \pm 0.11
95% prob:[0.83, 1.27]
99% prob:[0.75, 1.43]
EPS - PDF - PNG - JPG - GIF



Full fit result for \,\phi_{B_{d}} [^{\circ}]
-2.0 \pm 1.8
95% prob:[-6.0, 1.5]
99% prob:[-8.3, 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}}
1.110 \pm 0.090
95% prob:[0.942, 1.289]
99% prob:[0.875, 1.397]
EPS - PDF - PNG - JPG - GIF



Fit Input for \,\phi_{B_{s}} [^{\circ}]
0.60 \pm 0.88
95% prob:0
99% prob:0
EPS - PDF - PNG - JPG - GIF



Prediction for \,\phi_{B_{s}} [^{\circ}]
0.43 \pm 0.89
95% prob:[-1.35, 2.21]
99% prob:[-2.24, 3.10]
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}}
1.11 \pm 0.12
95% prob:[0.87, 1.38]
99% prob:[0.77, 1.55]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,A_{SL_{d}}
Gaussian likelihood used
-0.0020 \pm 0.0017

EPS - PDF - PNG - JPG - GIF



Prediction for \,A_{SL_{d}}
-0.0033 \pm 0.0014
95% prob:[-0.0059, -0.0004]
99% prob:[-0.0070, 0.0006]
EPS - PDF - PNG - JPG - GIF




Fit Input for \,A_{SL_{s}}
Gaussian likelihood used
-0.00059 \pm 0.00280

EPS - PDF - PNG - JPG - GIF



Prediction for \,A_{SL_{s}}
-0.00012 \pm 0.00051
95% prob:[-0.00110, 0.00089]
99% prob:[-0.00136, 0.00135]
EPS - PDF - PNG - JPG - GIF

 
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