Explaining $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$ anomaly by radiatively induced coupling in $U(1{)}_{\mu -\tau }$ gauge symmetry

Abstract

We propose an extension of the standard model (SM) with $U(1{)}_{\mu -\tau }$ gauge symmetry, extra vectorlike quark doublets $Q_a^{\prime }$ and singlet scalar $\chi$, both of which are charged under $U(1{)}_{\mu -\tau }$ and carry {odd} dark $Z_2$ parity. Then assuming that $\chi$ is the dark matter (DM) of the universe and imposing various constraints from dark matter search, flavor physics and collider search for $Q_a^{\prime }$, one can show that radiative corrections to $b\to s{Z}^{{}^{\prime }\ast }\to s{l}^{+}{l}^{-}$ involving $Q_a^{\prime }$ and $\chi$ can induce $\Delta C_9\sim -1$ which can resolve the LHCb anomalies related with $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$. Therefore both DM and $B$ physics anomalies could be accommodated in the model.

Comments: 6 pages, 2 figures, references added and discussions are extended