Leptoquark toolbox for precision collider studies

We implement scalar and vector leptoquark (LQ) models in the universal FeynRules output (UFO) format assuming the Standard Model fermion content and conservation of baryon and lepton numbers. Scalar LQ implementations include next-to-leading order (NLO) QCD corrections. We report the NLO QCD inclusive cross sections in proton-proton collisions at 13 TeV, 14 TeV, and 27 TeV for all on-shell LQ production processes. These comprise (i) LQ pair production ($p p \to \Phi \Phi$) and (ii) single LQ + lepton production ($p p \to \Phi \ell$) for all initial quark flavours ($u$, $d$, $s$, $c$, and $b$). Vector LQ implementation includes adjustable non-minimal QCD coupling. We discuss several aspects of LQ searches at a hadron collider, emphasising the implications of $SU(2)$ gauge invariance, electroweak and flavour constraints, on the possible signatures. Finally, we outline the high-$p_T$ search strategy for LQs recently proposed in the literature to resolve experimental anomalies in $B$-meson decays. In this context, we stress the importance of complementarity of the three LQ related processes, namely, $p p \to \Phi \Phi$, $p p \to \Phi \ell$, and $p p \to \ell \ell$.