4-fermion EFT bbll including interference with the SM

Authors:

• Yoav Afik (yoavafik@…)
• 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:

\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 $m_{\ell \ell}$:

\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:

\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:

• ​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