Simplified models of vector $SU(4)$ leptoquarks at the TeV

Abstract

Assuming confirmation of the anomalies in semi-leptonic $B$-decays, their explanation in terms of the exchange of a massive vector leptoquark field, $U_{\mu }^a$, of charge 2/3, appears to require the inclusion of $U_{\mu }^a$ in the vector multiplet of the adjoint of Pati-Salam $SU(4)$, ${\mathcal{G}}_{\mu }^A$, as well as the introduction of vector-like fermions, $F_j$, in the fundamental of $SU(4)$. We consider simplified models characterised by the nature of the $SU(4)$ symmetry (global or local), by the number of vector-like fermions, and by the couplings of the Higgs boson to SM fermions (direct or induced by mixing with the vector-like fermions). In all cases, we implement a minimal breaking of a $U(2{)}_f^n$ flavour symmetry, with a single motivated exception. We then perform a global fit including the main observables sensitive to exchanges of the ${\mathcal{G}}_{\mu }^A$ at tree level and in loops dominated by logs insensitive to the UV completion.

Comments: 17 pages, 3 figures, 3 tables