TTP15-018 Lepton-flavour violating B decays in generic Z' models

LHCb has reported deviations from the SM expectations in $B\to K^* \mu^+\mu^-$ angular observables, in $B_s\to\phi\mu^+\mu^-$ and in ratio $R(K)=Br[B\to K \mu^+\mu^-]/Br[B\to K e^+e^-]$. For all three decays, a heavy neutral gauge boson mediating $b\to s\mu^+\mu^-$ transitions is a prime candidate for an explanation. As $R(K)$ measures violation of lepton-flavour universality, it is interesting to examine the possibility that also lepton flavour is violated. In this article, we investigate the perspectives to discover the lepton-flavour violating modes $B\to K^{(*)}\tau^\pm\mu^\mp$, $B_s\to \tau^\pm\mu^\mp$ and $B\to K^{(*)} \mu^\pm e^\mp$, $B_s\to \mu^\pm e^\mp$. For this purpose we consider a simplified model in which new-physics effects originate from an additional neutral gauge boson ($Z^\prime$) with generic couplings to quarks and leptons. The constraints from $\tau\to3\mu$, $\tau\to\mu\nu\bar{\nu}$, $\mu\to e\gamma$, $g_\mu-2$, neutrino trident production, $Z\to\ell^+\ell^{\prime-}$, semi-leptonic $b\to s\mu^+\mu^-$ decays and $B_s$–$\overline{B}_s$ mixing are examined. Taking into account these limits, we determine upper bounds on the decay rates of $B\to K^{(*)}\tau^\pm\mu^\mp$, $B_s\to \tau^\pm\mu^\mp$, $B\to K^{(*)}\mu^\pm e^\mp$ and $B_s\to \mu^\pm e^\mp$ as a function of fine-tuning in $B_s$–$\overline{B}_s$ mixing. We find that for a significant degree of fine-tuning the effect in all considered decays with $\tau\mu$ final states can be sizable (leading to branching ratios of the order of $\times 10^{-6}$). For $\mu e$ final states, $B_s\to \mu^\pm e^\mp$ is strongly suppressed and only $B\to K^{(*)} \mu^\pm e^\mp$ can be relevant (of the order of $\times 10^{-7}$). However, this is only possible in a region of the parameter space disfavoured by the current LHCb data on $b\to s\mu^+\mu^-$ transitions.