4-fermion EFT with FCNC implementation

Authors:

• Yoav Afik (yoavafik@…)
• Jonathan Cohen (jcohen@…)
• Eitan Gozani
• Enrique Kajomovitz
• Yoram Rozen

Department of Physics, Technion: Israel Institute of Technology Haifa, Israel

Description of the model:

This is a Contact Interaction model.

The lagrangian of the model is described by:

\begin{eqnarray}
\mathcal{L}_{eff} = \frac{C_{ij}^{U \mu}}{v^2} (\bar{u}_{L}^{i} \gamma_{\mu} u_{L}^{j}) (\bar{\mu}_{L} \gamma_{\mu} \mu_{L}) + \frac{C_{ij}^{D \mu}}{v^2} (\bar{d}_{L}^{i} \gamma_{\mu} d_{L}^{j}) (\bar{\mu}_{L} \gamma_{\mu} \mu_{L}) + \\
\frac{C_{ij}^{U e}}{v^2} (\bar{u}_{L}^{i} \gamma_{\mu} u_{L}^{j}) (\bar{e}_{L} \gamma_{\mu} e_{L}) + \frac{C_{ij}^{D e}}{v^2} (\bar{d}_{L}^{i} \gamma_{\mu} d_{L}^{j}) (\bar{e}_{L} \gamma_{\mu} e_{L})
\end{eqnarray}

Only the off-diagonal elements for the b-s admixtures are considered, since those are the ones related to the observed b-s-l-l anomalies. The matrices take the form:

\begin{eqnarray}
C_{ij}^{U \mu} = 
\begin{pmatrix} C_{u \mu} & 0 & 0 \\ 0 & C_{c \mu} & 0 \\ 0 & 0 & C_{t \mu} \end{pmatrix} 
,
C_{ij}^{D \mu} = 
\begin{pmatrix} C_{d \mu} & 0 & 0 \\ 0 & C_{s \mu} & C_{b s \mu}^{*} \\ 0 & C_{b s \mu} & C_{b \mu} \end{pmatrix} 
\end{eqnarray}

\begin{eqnarray}
C_{ij}^{U e} = 
\begin{pmatrix} C_{u e} & 0 & 0 \\ 0 & C_{c e} & 0 \\ 0 & 0 & C_{t e} \end{pmatrix} 
,
C_{ij}^{D e} = 
\begin{pmatrix} C_{d e} & 0 & 0 \\ 0 & C_{s e} & C_{b s e}^{*} \\ 0 & C_{b s e} & C_{b e} \end{pmatrix} 
\end{eqnarray}

A more general model is also attached, contains the full diagonal and non-diagonal terms.

\begin{eqnarray}
C_{ij}^{U \mu} = 
\begin{pmatrix} C_{u \mu} & C_{c u \mu}^{*} & C_{t u \mu}^{*} \\ C_{c u \mu} & C_{c \mu} & C_{t c \mu}^{*} \\ C_{t u \mu} & C_{t c \mu} & C_{t \mu} \end{pmatrix} 
,
C_{ij}^{D \mu} = 
\begin{pmatrix} C_{d \mu} & C_{s d \mu}^{*} & C_{b d \mu}^{*} \\ C_{s d \mu} & C_{s \mu} & C_{b s \mu}^{*} \\ C_{b d \mu} & C_{b s \mu} & C_{b \mu} \end{pmatrix} 
\end{eqnarray}

\begin{eqnarray}
C_{ij}^{U e} = 
\begin{pmatrix} C_{u e} & C_{c u e}^{*} & C_{t u e}^{*} \\ C_{c u e} & C_{c e} & C_{t c e}^{*} \\ C_{t u e} & C_{t c e} & C_{t e} \end{pmatrix} 
,
C_{ij}^{D e} = 
\begin{pmatrix} C_{d e} & C_{s d e}^{*} & C_{b d e}^{*} \\ C_{s d e} & C_{s e} & C_{b s e}^{*} \\ C_{b d e} & C_{b s e} & C_{b e} \end{pmatrix} 
\end{eqnarray}

Sample commands for MadGraph5_aMC@NLO:

define p = g u c d s b u~ c~ d~ s~ b~ 
define j = g u c d s b u~ c~ d~ s~ b~ 
generate p p > mu+ mu- 
add process p p > mu+ mu- j 
add process p p > mu+ mu- j j 

Reference:

• Please cite as: Afik, Y., Cohen, J., Gozani, E. et al. J. High Energ. Phys. (2018) 2018: 56.
• Link to paper: ​https://link.springer.com/article/10.1007/JHEP08(2018)056