Lepton-flavour violating $B$ decays in generic $Z^{\prime }$ models

Abstract

LHCb has reported deviations from the Standard Model in $b\to s{\mu }^{+}{\mu }^{-}$ transitions for which a new neutral gauge boson is a prime candidate for an explanation. As this gauge boson has to couple in a flavour non-universal way to muons and electrons in order to explain $R_K$, it is interesting to examine the possibility that also lepton flavour is violated, especially in the light of the CMS excess in $h\to {\tau }^{\pm }{\mu }^{\mp }$. In this article, we investigate the perspectives to discover the lepton-flavour violating modes $B\to K^{(\ast )}{\tau }^{\pm }{\mu }^{\mp }$, $B_s\to {\tau }^{\pm }{\mu }^{\mp }$ and $B\to K^{(\ast )}{\mu }^{\pm }{e}^{\mp }$, $B_s\to {\mu }^{\pm }{e}^{\mp }$. 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 $\tau \to 3\mu$, $\tau \to \mu \nu \bar{\nu }$, $\mu \to e\gamma$, $g_{\mu }-2$, semi-leptonic $b\to s{\mu }^{+}{\mu }^{-}$ decays, $B\to K^{(\ast )}\nu \nu$ and $B_s$--${\overline{B}}_s$ mixing are examined. From these decays, we determine upper bounds on the decay rates of lepton flavour violating $B$ decays. $Br(B\to K\nu \nu )$ limits the branching ratios of LFV $B$ decays to be smaller than $8\times 10^{-5}(2\times 10^{-5})$ for vectorial (left-handed) lepton couplings. However, much stronger bounds can be obtained by a combined analysis of $B_s$--${\overline{B}}_s$, $\tau \to 3\mu$, $\tau \to \mu \nu \bar{\nu }$ and other rare decays. The bounds depend on the amount of fine-tuning among the contributions to $B_s$--${\overline{B}}_s$ mixing. Allowing for a fine-tuning at the percent level we find upper bounds of the order of $10^{-6}$ for branching ratios into $\tau \mu$ final states, while $B_s\to {\mu }^{\pm }{e}^{\mp }$ is strongly suppressed and only $B\to K^{(\ast )}{\mu }^{\pm }{e}^{\mp }$ can be experimentally accessible (with a branching ratio of order $10^{-7}$).

7 pages, 4 figures, constraints from B->Knunu added, typos corrected

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