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

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 $U_1$ exchange. This model provides a very predictive framework in which the $U_1$ 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 $\tau \to 3\mu$, $\tau \to \mu \gamma$ and $B\to K^{(\ast )}\nu \bar{\nu }$ 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 $R_{K^{(\ast )}}$, which has slightly shifted the preferred parameter space with respect to the 2021 case. The model can still explain the $R_{D^{(\ast )}}$ anomalies at 1$\sigma$ in a narrow window, however we expect small deviations from the SM on the $R_{K^{(\ast )}}$ ratios, to be tested in the future via more precise measurements by the LHCb collaboration. We also predict $\Delta R_D=\Delta R_{D^{\ast }}$, with future measurements shifting the world averages to slightly smaller central values.

Comments: 44 pages + appendices and references, 14 figures. v5: Typos corrected