== 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 model with b-s-l-l FCNC terms. 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}) + \\
\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:
{{{ 
#!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_{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}
}}}

The presumed scale and coupling of the new physics, is estimated by defining:
{{{ 
#!latex 
\begin{align}
	C_{bs\mu} = g_{*}^2 v^2 / \Lambda^2.
\end{align}  
}}}


* Please note that the model is normalized according to Λ = 1TeV and g^*^ = 1. For example, if you want to set Λ = 2TeV and g^*^ = 1 for electrons coupling to b-s quarks, just set Celbs in the param_card to be 0.25.

* A more simple model is also attached, contains only the b-s-l-l non-diagonal terms for simplicity.


== Model Files:
* [http://http://feynrules.irmp.ucl.ac.be/wiki/FCNC4F/bsll_5FS_full.zip bsll_5FS_full.zip] : the full model.
* [http://http://feynrules.irmp.ucl.ac.be/wiki/FCNC4F/bsll_5FS_non-diagonal.zip bsll_5FS_non-diagonal.zip] : only the non-diagonal terms.

== 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 
}}}

== References:
[1] 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