Correlating lepton flavour violating $b\to s$ and leptonic decay modes in a minimal abelian extension of the Standard Model

Abstract

We consider an abelian extension of the Standard Model (SM) comprising a new gauge group $U(1{)}^{\prime }$, with the neutral gauge boson $Z^{\prime }$ having flavour violating couplings to quarks and leptons. The fermion content is the same as in SM except for the addition of three right-handed neutrinos. The model, proposed in \cite{Aebischer:2019blw}, describes the couplings of $Z^{\prime }$ to fermions in terms of three rational parameters ${ϵ}_{1,2,3}$ that sum to zero imposing the cancellation of the gauge anomalies. Each ${ϵ}_i$ is common to all fermions in a generation, a feature producing correlations among quark and lepton observables. We focus on $b\to s{\ell }_1^{-}{\ell }_2^{+}$ transitions for the lepton flavour conserving ${\ell }_1={\ell }_2$ and lepton flavour violating case ${\ell }_1\ne {\ell }_2$. Small deviations with respect to the SM predictions are found in the first case, which reflects a feature of the model where quark and lepton sectors prevent each other to manifest large discrepancies with respect to SM. We investigate the correlations between rare $B$ and $B_s$ decays and the leptonic processes ${\tau }^{-}\to {\mu }^{-}{\mu }^{+}{\mu }^{-}$, ${\mu }^{-}\to e^{-}\gamma$, ${\mu }^{-}\to e^{-}{e}^{+}{e}^{-}$ and the ${\mu }^{-}\to e^{-}$ conversion in nuclei. We show that the current experimental upper bounds on these four channels play an increasingly important role in constraining the branching fractions of lepton flavour violating $B$ and $B_s$ decays. While the present bound on ${\tau }^{-}\to {\mu }^{-}{\mu }^{+}{\mu }^{-}$ does not impose significant restrictions, the other three modes set progressively more stringent limits, an important information for the planned new experimental facilities.

Comments: 43 pages, 23 figures. Revised version with improved numerical analysis, including new experimental constraints. Matches the version accepted for publication in JHEP