== 4-fermion EFT ttll (l=e,mu)

== Authors:
* Yoav Afik (yoavafik@campus.technion.ac.il) (1)
* Shaouly Bar-Shalom (shaouly@physics.technion.ac.il) (2)
* Kuntal Pal (3)
* Amarjit Soni (4)
* Jose Wudka (3)

(1) Experimental Physics Department, CERN, Geneva, Switzerland

(2) Department of Physics, Technion: Israel Institute of Technology Haifa, Israel

(3) Department of Physics, University of California, Riverside, CA, US

(4) Department of Physics, Brookhaven National Laboratory, Upton, NY, US

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

{{{ 
#!latex 
\begin{align*}
{\cal L}_{tt\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 t \right)  + S_{ij}^\ell \left( {\bar \ell} P_i \ell \right) \left( \bar t P_j t \right)  + T_{ij}^\ell \left( {\bar \ell} \sigma_{\mu \nu} P_i \ell \right) \left( \bar t \sigma_{\mu \nu} P_j t \right) \biggr] ~.
\end{align*}
}}} 





== Model Files:
* [https://feynrules.irmp.ucl.ac.be/attachment/wiki/FourFermionFCNCtqll/4fermion-tqll-models.zip 4fermion-tqll-models.zip] : the full model both at the 4FS and at the 5FS. In the paper we use the 5FS.
* Please note there are four models: t-u-l-l Contact Interactions at the 4FS / 5FS, and t-c-l-l Contact Interactions at the 4FS / 5FS.

== Commands for MadGraph5_aMC@NLO, for a production of a muon and an anti-muon with a top quark and up to one more jet (NP only):
{{{
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- t t~ NP^2==4
add process p p > mu+ mu- t t~ j NP^2==4
...
set lambdas...
set fSrr ...
set fTrr ...
set fVlr ...
set fVrl ...
set fVrr ...
set fVll ...
}}}
For the scenario of vector coupling, interference with the SM should be considered. This can be done by changing the coupling order in the generation commands:
{{{
...
generate p p > mu+ mu- t t~ NP^2==2
add process p p > mu+ mu- t t~ j NP^2==2
...
}}}

Where lambdas is the scale of new physics in GeV, fSrr is the coupling of the t-u-l-l scalar operator with right-right chirality of the fermions, etc. For example, if we set fSrr=1 and all other couplings to 0, we get a scalar operator with:
{{{ 
#!latex 
\begin{align*}
{\cal L}_{t\bar t\ell \ell} =  {1\over\Lambda^2} \left( {\bar \ell} P_R \ell \right) \left( \bar t P_R t \right) ~.
\end{align*}
}}} 


Note that only operators with the couplings fSrr, fTrr, fVlr, fVrl, fVrr, fVll are generated by this UFO.


== References:
[1] Afik, Yoav and Bar-Shalom, Shaouly and Pal, Kuntal and Soni, Amarjit and Wudka, Jose. 2111.13711.
 * Link to paper: https://arxiv.org/abs/2111.13711