== 4-fermion EFT bbll including interference with the SM

== Authors:
* Yoav Afik (yoavafik@campus.technion.ac.il) (1)
* Shaouly Bar-Shalom (shaouly@physics.technion.ac.il) (1)
* Amarjit Soni (2)
* Jose Wudka (3)

(1) Department of Physics, Technion: Israel Institute of Technology Haifa, Israel
(2) Department of Physics, Brookhaven National Laboratory, Upton, NY, US
(3) Department of Physics, University of California, Riverside, CA, US

== Description of the model:
This is a Contact Interaction model with t-u-l-l and t-c-l-l terms, for scalar, vector and tensor couplings. The effective Lagrangian of the model is described by:

{{{ 
#!latex 
\begin{align*}
{\cal L}_{tu\ell \ell} =  {1\over\Lambda^2} \sum_{i,j=L,R} \biggl[ V_{ij}^\ell \left({\bar \ell} \gamma_\mu P_i \ell \right) \left( \bar t \gamma^\mu P_j u \right)  + S_{ij}^\ell \left( {\bar \ell} P_i \ell \right) \left( \bar t P_j u \right)  + T_{ij}^\ell \left( {\bar \ell} \sigma_{\mu \nu} P_i \ell \right) \left( \bar t \sigma_{\mu \nu} P_j u \right) \biggr] \label{4fermimatrix}~
\end{align*}
}}} 





== Model Files:
* [https://feynrules.irmp.ucl.ac.be/attachment/wiki/FourFermionbbll/bbll_UFO.zip bbll_UFO.zip] : the full model.

== Commands for MadGraph5_aMC@NLO, for a production of an electron and a positron with jets:
{{{
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 > e+ e- NP^2>0
add process p p > e+ e- j NP^2>0
add process p p > e+ e- j j NP^2>0
...
set LambdaS ...
set Celbbll ...
set Celbblr ...
set Celbbrr ...
set Celbbrl ...
}}}

Where LambdaS is the scale of new physics in GeV, Celbbll is the bbee coupling with left-left chirality, etc. Note especially that the sign of Celbbll / Celbblr / Celbbrr / Celbbrl determines if the interference with the SM is constructive or destructive.

== Similarly, commands for MadGraph5_aMC@NLO, for a production of a muon and an anti-muon with jets:
{{{
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- NP^2>0
add process p p > mu+ mu- j NP^2>0
add process p p > mu+ mu- j j NP^2>0
...
set LambdaS ...
set Cmubbll ...
set Cmubblr ...
set Cmubbrr ...
set Cmubbrl ...
}}}



== References:
[1] Afik, Yoav and Bar-Shalom, Shaouly and Cohen, Jonathan and Rozen, Yoram. Phys. Lett. B. 807:135541, 2020, 1912.00425.
 * Link to paper: https://www.sciencedirect.com/science/article/pii/S0370269320303452?via%3Dihub