Twin Pati-Salam theory of flavour with a TeV scale vector leptoquark

TL;DR

This paper introduces a twin Pati-Salam model that explains fermion masses and predicts a TeV-scale vector leptoquark, which could address B decay anomalies but faces challenges with current experimental data.

Contribution

It develops a novel twin Pati-Salam framework that accounts for all fermion masses and mixings and predicts specific leptoquark couplings, extending previous models.

Findings

Predicts a dominant coupling of the leptoquark to third family left-handed doublets.

Successfully explains quark and lepton masses and mixings.

Mass matrix predictions are inconsistent with the current $R_{D^{(*)}}$ anomaly solution.

Abstract

We propose a twin Pati-Salam (PS) theory of flavour broken to the $G_{4321}$ gauge group at high energies, then to the Standard Model at low energies, yielding a TeV scale vector leptoquark $U^{\mu}_1(3,1,2/3)$ which has been suggested to address the lepton universality anomalies $R_{K^{(*)}}$ and $R_{D^{(*)}}$ in $B$ decays. Quark and lepton masses are mediated by vector-like fermions, with personal Higgs doublets for the second and third families, which may be replaced by a two Higgs doublet model (2HDM). The twin PS theory of flavour successfully accounts for all quark and lepton (including neutrino) masses and mixings, and predicts a dominant coupling of $U^{\mu}_1(3,1,2/3)$ to the third family left-handed doublets. However the predicted mass matrices, assuming natural values of the parameters, are not consistent with the single vector leptoquark solution to the $R_{D^{(*)}}$ anomaly, given its current value.