Explaining $h\to {\mu }^{\pm }{\tau }^{\mp }$, $B\to K^{\ast }{\mu }^{+}{\mu }^{-}$ and $B\to K{\mu }^{+}{\mu }^{-}/B\to K{e}^{+}{e}^{-}$ in a two-Higgs-doublet model with gauged $L_{\mu }-L_{\tau }$

Abstract

The LHC observed so far three deviations from the Standard Model (SM) predictions in flavour observables: LHCb reported anomalies in $B\to K^{\ast }{\mu }^{+}{\mu }^{-}$ and $R(K)=B\to K{\mu }^{+}{\mu }^{-}/B\to K{e}^{+}{e}^{-}$ while CMS found an excess in $h\to \mu \tau$. We show, for the first time, how these deviations from the SM can be explained within a single well-motivated model: a two-Higgs-doublet model with gauged $L_{\mu }-L_{\tau }$ symmetry. We find that, despite the constraints from $\tau \to \mu \mu \mu$ and $B_s$--${\overline{B}}_s$ mixing, one can explain $h\to \mu \tau$, $B\to K^{\ast }{\mu }^{+}{\mu }^{-}$ and $R(K)$ simultaneously, obtaining interesting correlations among the observables.

Comments: 6 pages, 2 figures, corrected formula for LFV tau decay with new HFAG limit. References added, accepted for publication in PRL