| 1 |  |  | 
          
            |  | 1 | == 4-fermion EFT ttll (l=e,mu) | 
          
            |  | 2 |  | 
          
            |  | 3 | == Authors: | 
          
            |  | 4 | * Yoav Afik (yoavafik@campus.technion.ac.il) (1) | 
          
            |  | 5 | * Shaouly Bar-Shalom (shaouly@physics.technion.ac.il) (2) | 
          
            |  | 6 | * Kuntal Pal (3) | 
          
            |  | 7 | * Amarjit Soni (4) | 
          
            |  | 8 | * Jose Wudka (3) | 
          
            |  | 9 |  | 
          
            |  | 10 | (1) Experimental Physics Department, CERN, Geneva, Switzerland | 
          
            |  | 11 |  | 
          
            |  | 12 | (2) Department of Physics, Technion: Israel Institute of Technology Haifa, Israel | 
          
            |  | 13 |  | 
          
            |  | 14 | (3) Department of Physics, University of California, Riverside, CA, US | 
          
            |  | 15 |  | 
          
            |  | 16 | (4) Department of Physics, Brookhaven National Laboratory, Upton, NY, US | 
          
            |  | 17 |  | 
          
            |  | 18 | == Description of the model: | 
          
            |  | 19 | 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: | 
          
            |  | 20 |  | 
          
            |  | 21 | {{{ | 
          
            |  | 22 | #!latex | 
          
            |  | 23 | \begin{align*} | 
          
            |  | 24 | {\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] ~. | 
          
            |  | 25 | \end{align*} | 
          
            |  | 26 | }}} | 
          
            |  | 27 |  | 
          
            |  | 28 |  | 
          
            |  | 29 |  | 
          
            |  | 30 |  | 
          
            |  | 31 |  | 
          
            |  | 32 | == Model Files: | 
          
            |  | 33 | * [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. | 
          
            |  | 34 | * 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. | 
          
            |  | 35 |  | 
          
            |  | 36 | == 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): | 
          
            |  | 37 | {{{ | 
          
            |  | 38 | define p = g u c d s b u~ c~ d~ s~ b~ | 
          
            |  | 39 | define j = g u c d s b u~ c~ d~ s~ b~ | 
          
            |  | 40 | generate p p > mu+ mu- t t~ NP^2==4 | 
          
            |  | 41 | add process p p > mu+ mu- t t~ j NP^2==4 | 
          
            |  | 42 | ... | 
          
            |  | 43 | set lambdas... | 
          
            |  | 44 | set fSrr ... | 
          
            |  | 45 | set fTrr ... | 
          
            |  | 46 | set fVlr ... | 
          
            |  | 47 | set fVrl ... | 
          
            |  | 48 | set fVrr ... | 
          
            |  | 49 | set fVll ... | 
          
            |  | 50 | }}} | 
          
            |  | 51 | 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: | 
          
            |  | 52 | {{{ | 
          
            |  | 53 | ... | 
          
            |  | 54 | generate p p > mu+ mu- t t~ NP^2==2 | 
          
            |  | 55 | add process p p > mu+ mu- t t~ j NP^2==2 | 
          
            |  | 56 | ... | 
          
            |  | 57 | }}} | 
          
            |  | 58 |  | 
          
            |  | 59 | 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: | 
          
            |  | 60 | {{{ | 
          
            |  | 61 | #!latex | 
          
            |  | 62 | \begin{align*} | 
          
            |  | 63 | {\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) ~. | 
          
            |  | 64 | \end{align*} | 
          
            |  | 65 | }}} | 
          
            |  | 66 |  | 
          
            |  | 67 |  | 
          
            |  | 68 | Note that only operators with the couplings fSrr, fTrr, fVlr, fVrl, fVrr, fVll are generated by this UFO. | 
          
            |  | 69 |  | 
          
            |  | 70 |  | 
          
            |  | 71 | == References: | 
          
            |  | 72 | [1] Afik, Yoav and Bar-Shalom, Shaouly and Pal, Kuntal and Soni, Amarjit and Wudka, Jose. 2111.13711. | 
          
            |  | 73 | * Link to paper: https://arxiv.org/abs/2111.13711 |