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

Authors:

• Yoav Afik (yoavafik@…) (1)
• Shaouly Bar-Shalom (shaouly@…) (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:

\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:

• ​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 ...

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:

\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*}

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
...

Both the interference and pure NP contributions can be generated together with:

...
generate p p > mu+ mu- t t~ NP^2>0
add process p p > mu+ mu- t t~ j NP^2>0
...

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