$wgUseTeX = true;

== 4-fermion EFT with FCNC implementation

== Authors:
* Yoav Afik (yoavafik@campus.technion.ac.il)
* Jonathan Cohen (jcohen@campus.technion.ac.il)
* 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 (CI) model. 

The lagrangian of the model is described by: \\

{{{ 
#!latex 
\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}),
\end{eqnarray}
}}} 

At the first model, 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:
{{{ 
#!latex 
\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_{t \mu} \end{pmatrix} 
\end{eqnarray}
}}}


A more general model is also attached, contains the full terms:
#!latex 
\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_{t \mu} \end{pmatrix} 
\end{eqnarray}
}}}

Similar couplings to electrons are considered as well for complicity.




== 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