| | 1 | == 4-fermion EFT bbll including interference with the SM |
| | 2 | |
| | 3 | == Authors: |
| | 4 | * Yoav Afik (yoavafik@campus.technion.ac.il) |
| | 5 | * Shaouly Bar-Shalom |
| | 6 | * Jonathan Cohen |
| | 7 | * Yoram Rozen |
| | 8 | |
| | 9 | Department of Physics, Technion: Israel Institute of Technology Haifa, Israel |
| | 10 | |
| | 11 | |
| | 12 | == Description of the model: |
| | 13 | 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: |
| | 14 | |
| | 15 | {{{ |
| | 16 | #!latex |
| | 17 | \begin{align*} |
| | 18 | \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}), |
| | 19 | \end{align*} |
| | 20 | }}} |
| | 21 | 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 $pp\to Z/\gamma^*\to\ell^+\ell^- + X$. |
| | 22 | |
| | 23 | 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 $m_{\ell \ell}$: |
| | 24 | |
| | 25 | {{{ |
| | 26 | #!latex |
| | 27 | \begin{align*} |
| | 28 | \sigma(m_{\ell \ell})=\sigma^{SM}(m_{\ell \ell}) + \sigma^{NP}(g,\Lambda,m_{\ell \ell}) ~, |
| | 29 | \end{align*} |
| | 30 | }}} |
| | 31 | |
| | 32 | where $\sigma^{SM}$ is the pure SM term and $\sigma^{NP}(\Lambda,m_{\ell \ell})$ contain only the NP contributions: |
| | 33 | {{{ |
| | 34 | #!latex |
| | 35 | \begin{align*} |
| | 36 | \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}) ~, |
| | 37 | \end{align*} |
| | 38 | }}} |
| | 39 | |
| | 40 | |
| | 41 | |
| | 42 | |
| | 43 | == Model Files: |
| | 44 | * [https://feynrules.irmp.ucl.ac.be/attachment/wiki/FCNC4F/bsll_5FS_full.zip bsll_5FS_full.zip] : the full model. |
| | 45 | |
| | 46 | == Commands for MadGraph5_aMC@NLO: |
| | 47 | {{{ |
| | 48 | define p = g u c d s b u~ c~ d~ s~ b~ |
| | 49 | define j = g u c d s b u~ c~ d~ s~ b~ |
| | 50 | generate p p > e+ e- NP^2>0 |
| | 51 | add process p p > e+ e- j NP^2>0 |
| | 52 | add process p p > e+ e- j j NP^2>0 |
