Complete Lagrangian and set of Feynman rules for scalar leptoquarks

Leptoquarks (LQs) have attracted increasing attention within recent years, mainly since they can explain the flavor anomalies found in $R(D^{(*)})$, $b \rightarrow s \ell^+ \ell^-$ transitions and the anomalous magnetic moment of the muon. In this article, we lay the groundwork for further automated analyses by presenting the complete Lagrangian and the corresponding set of Feynman rules for scalar leptoquarks. This means we consider the five representations $\Phi_1, \Phi_{\tilde1}, \Phi_2, \Phi_{\tilde2}$ and $\Phi_3$ and include the triple and quartic self-interactions, as well as couplings to the Standard Model (SM) fermions, gauge bosons and the Higgs. The calculations are performed using FeynRules and all model files are publicly available online at https://gitlab.com/lucschnell/SLQrules.