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

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(*) and R-D(*) in B decays. Quark and lepton masses are mediated by vectorlike 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( * ) anomaly, given its current value.