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

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