B-anomalies in a twin Pati-Salam theory of flavour including the 2022 LHCb $$ {R}_{K^{\left(\ast \right)}} $$ analysis

Abstract

Abstract We perform a comprehensive phenomenological analysis of the twin Pati-Salam theory of flavour, focussing on the parameter space relevant for interpreting the B-anomalies via vector leptoquark U1 exchange. This model provides a very predictive framework in which the U1 couplings and the Yukawa couplings find a common origin via mixing of chiral quarks and leptons with vector-like fermions, providing a direct link between the B-anomalies and the fermion masses and mixing. We propose and study a simplified model with three vector-like fermion families, in the massless first family approximation, and show that the second and third family charged fermion masses and mixings and the B-anomalies can be simultaneously explained and related. The model has the proper flavour structure to be compatible with all low-energy observables, and leads to predictions in promising observables such as τ → 3μ, τ → μγ and $$ B\to {K}^{\left(\ast \right)}\nu \overline{\nu} $$ B → K ∗ ν ν ¯ at Belle II and LHCb. The model also predicts a rich spectrum of TeV scale gauge bosons and vector-like fermions, all accessible to the LHC. In this updated version we have included an extended analysis considering the new 2022 LHCb data on $$ {R}_{K^{\left(\ast \right)}} $$ R K ∗ , which has slightly shifted the preferred parameter space with respect to the 2021 case. The model can still explain the $$ {R}_{D^{\left(\ast \right)}} $$ R D ∗ anomalies at 1σ in a narrow window, however we expect small deviations from the SM on the $$ {R}_{K^{\left(\ast \right)}} $$ R K ∗ ratios, to be tested in the future via more precise measurements by the LHCb collaboration. We also predict RD = $$ {R}_{D^{\ast }} $$ R D ∗ , with future measurements shifting the world averages to slightly smaller central values.