  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.

High Energy Physics - Phenomenology