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

== Authors:
* Yoav Afik (yoavafik@campus.technion.ac.il)
* Shaouly Bar-Shalom
* Jonathan Cohen
* Yoram Rozen

Department of Physics, Technion: Israel Institute of Technology Haifa, Israel


== Description of the model:
This is a Contact Interaction model with b-b-l-l Contact-Interaction terms, including interference with the SM. The effective Lagrangian of the model is described by:

{{{ 
#!latex 
\begin{align*}
\mathcal{L}_{eff} = \frac{g^2}{\Lambda^2}\sum_{i,j=L,R} \eta_{ij}(\bar{b}_{i} \gamma_{\mu} b_{i}) (\bar{\ell}_{j} \gamma^{\mu} \ell_{j}),
\end{align*}
}}} 
where here $\ell=e,\mu$, $\Lambda$ is the NP scale and we have summed over all possible chirality structures with $\eta_{ij}=\pm1$, which will be useful for accounting for constructive/destructive interference with the SM Drell-Yan process $pp\to Z/\gamma^*\to\ell^+\ell^- + X$.

The behavior of the cross section for the corresponding $p p \to \ell^+ \ell^- + X$ processes can be parametrized by the contribution of three terms, which depend on the di-lepton invariant mass $m_{\ell \ell}$:

{{{ 
#!latex 
\begin{align*}
\sigma(m_{\ell \ell})=\sigma^{SM}(m_{\ell \ell}) + \sigma^{NP}(g,\Lambda,m_{\ell \ell}) ~,
\end{align*}
}}} 

where $\sigma^{SM}$ is the pure SM term and $\sigma^{NP}(\Lambda,m_{\ell \ell})$ contain only the NP contributions: 
{{{ 
#!latex 
\begin{align*}
\sigma^{NP}(g,\Lambda,m_{\ell \ell})=\frac{g^2}{\Lambda^2} \cdot \sigma^{SM \times NP}(m_{\ell \ell}) + \frac{g^4}{\Lambda^4} \cdot \sigma^{NP \times NP}(m_{\ell \ell}) ~,
\end{align*}
}}} 




== Model Files:
* [https://feynrules.irmp.ucl.ac.be/attachment/wiki/FCNC4F/bsll_5FS_full.zip bsll_5FS_full.zip] : the full model.

== 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 > 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.

== 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