Difference: ResultsSummer2022NP (r2 vs. r1)

r2 - 29 Aug 2023 - 18:59 - MarcellaBona r1 - 25 Jul 2022 - 03:05 - DenisDerkach

New Physics Fit results: Summer 2022

New Physics Fit results: Summer 2022

Input used are the same as in Standard Model Fit .

Input used are the same as in Standard Model Fit .

  

The fit presented here is meant to constrain the NP contributions to |? 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 parameterised, 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

The fit presented here is meant to constrain the NP contributions to |? 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),
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

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}
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.

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 new physics parameters can also be rewritten as A_q = ( 1 + \frac{A^{NP}}{A^{SM}}) e^{2i}) e^{2 i \phi_{B_q}}

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:

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} \,,\;   \\
\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.

in a self-explanatory notation.

All the measured observables can be written as a function of these NP parameters and the SM ones ? and ?, and additional parameters such as masses, form factors, and decay constants.

All the measured observables can be written as a function of these NP parameters and the SM ones ? and ?, and additional parameters such as masses, form factors, and decay constants.

Table of inputs, posterior values and predictions from the global fit beyond the SM.

ParameterFit Results
\bar{\rho}0.169 \pm 0.025
\bar{\eta}0.365 \pm 0.026
C_{\epsilon_{K}}1.12 \pm 0.12
C_{B_{d}}1.14 \pm 0.11
\phi_{B_{d}} [^{\circ}]-3.4 \pm 2.0
C_{B_{s}}1.14 \pm 0.08
\phi_{B_{s}} [^{\circ}]-0.3 \pm 0.6

Fit Results for the new physics global fit:




Full-fit result for \,\bar{\rho} - \bar{\eta}
All constraints are used, the tree-only constraints are drawn
EPS - PDF - PNG - JPG - GIF



Full-fit result for \,C_{B_{d}} - \phi_{B_{d}}
B_{d} system new physics parameters
C_{B_{d}} = 1.14 \pm 0.11
\phi_{B_{d}} = -3.4 \pm 2.0 [^{\circ}]
EPS - PDF - PNG - JPG - GIF



Full-fit result for \,C_{B_{s}} - \phi_{B_{s}}
B_{s} system new physics parameters
C_{B_{s}} = 1.14 \pm 0.08
\phi_{B_{s}} = -0.3 \pm 0.6 [^{\circ}]
EPS - PDF - PNG - JPG - GIF



Full-fit result for \,A^{NP}_{B_{d}}/A^{SM}_{B_{d}} - \phi_{B_{d}}
B_{d} system new physics parameters
A^{NP}/A^{SM} less than 25% @68% prob.
A^{NP}/A^{SM} less than 35% @95% prob.
EPS - PDF - PNG - JPG - GIF



Full-fit result for \,A^{NP}_{B_{s}}/A^{SM}_{B_{s}} - \phi_{B_{s}}
B_{s} system new physics parameters
A^{NP}/A^{SM} less than 25% @68% prob.
A^{NP}/A^{SM} less than 30% @95% prob.
EPS - PDF - PNG - JPG - GIF

New physics scale analysis:




Generic scenario scale analysis for \,\Lambda_{NP}
\Lambda_{NP} > \alpha_{NP} \times 4.4 \cdot 10^{5} \;\textrm{TeV}
EPS - PDF - PNG - JPG - GIF



NMFV scenario scale analysis for \,\Lambda_{NP}
\Lambda_{NP} > \alpha_{NP} \times 95 \;\textrm{TeV}
EPS - PDF - PNG - JPG - GIF

Table of inputs, posterior values and predictions from the global fit beyond the SM.

ParameterFit Results
\bar{\rho}0.169 \pm 0.025
\bar{\eta}0.365 \pm 0.026
C_{\epsilon_{K}}1.12 \pm 0.12
C_{B_{d}}1.14 \pm 0.11
\phi_{B_{d}} [^{\circ}]-3.4 \pm 2.0
C_{B_{s}}1.14 \pm 0.08
\phi_{B_{s}} [^{\circ}]-0.3 \pm 0.6

Fit Results for the new physics global fit:




Full-fit result for \,\bar{\rho} - \bar{\eta}
All constraints are used, the tree-only constraints are drawn
EPS - PDF - PNG - JPG - GIF



Full-fit result for \,C_{B_{d}} - \phi_{B_{d}}
B_{d} system new physics parameters
C_{B_{d}} = 1.14 \pm 0.11
\phi_{B_{d}} = -3.4 \pm 2.0 [^{\circ}]
EPS - PDF - PNG - JPG - GIF



Full-fit result for \,C_{B_{s}} - \phi_{B_{s}}
B_{s} system new physics parameters
C_{B_{s}} = 1.14 \pm 0.08
\phi_{B_{s}} = -0.3 \pm 0.6 [^{\circ}]
EPS - PDF - PNG - JPG - GIF



Full-fit result for \,A^{NP}_{B_{d}}/A^{SM}_{B_{d}} - \phi_{B_{d}}
B_{d} system new physics parameters
A^{NP}/A^{SM} less than 25% @68% prob.
A^{NP}/A^{SM} less than 35% @95% prob.
EPS - PDF - PNG - JPG - GIF



Full-fit result for \,A^{NP}_{B_{s}}/A^{SM}_{B_{s}} - \phi_{B_{s}}
B_{s} system new physics parameters
A^{NP}/A^{SM} less than 25% @68% prob.
A^{NP}/A^{SM} less than 30% @95% prob.
EPS - PDF - PNG - JPG - GIF

New physics scale analysis:




Generic scenario scale analysis for \,\Lambda_{NP}
\Lambda_{NP} > \alpha_{NP} \times 4.4 \cdot 10^{5} \;\textrm{TeV}
EPS - PDF - PNG - JPG - GIF



NMFV scenario scale analysis for \,\Lambda_{NP}
\Lambda_{NP} > \alpha_{NP} \times 95 \;\textrm{TeV}
EPS - PDF - PNG - JPG - GIF
r2 - 29 Aug 2023 - 18:59 - MarcellaBona r1 - 25 Jul 2022 - 03:05 - DenisDerkach

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