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

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 $U_1^{\mu }(3,1,2/3)$ which has been suggested to address the lepton universality anomalies $R_{K^{(\ast )}}$ and $R_{D^{(\ast )}}$ 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 $U_1^{\mu }(3,1,2/3)$ 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 $R_{D^{(\ast )}}$ anomaly, given its current value.

Comments: Version published in JHEP