Phenomenology of an $SU(2) \times SU(2) \times U(1)$ model with lepton-flavour non-universality

Abstract: We investigate a gauge extension of the Standard Model in light of the observed hints of lepton universality violation in $b \to c \ell \nu$ and $b \to s \ell^+ \ell^-$ decays at BaBar, Belle and LHCb. The model consists of an extended gauge group $\mathrm{SU(2)}{1} \times \mathrm{SU(2)}{2} \times \mathrm{U(1)}_Y$ which breaks spontaneously around the TeV scale to the electroweak gauge group. Fermion mixing effects with vector-like fermions give rise to potentially large new physics contributions in flavour transitions mediated by $W^{\prime}$ and $Z^{\prime}$ bosons. This model can ease tensions in $B$-physics data while satisfying stringent bounds from flavour physics, tau decays, and electroweak precision data. Possible ways to test the proposed new physics scenario with upcoming experimental measurements are discussed. Among other predictions, the lepton flavour violating ratios $R_M$, with $M = K^*, \phi$, are found to be reduced with respect to the Standard Model expectation $R_M \simeq 1$.