Explaining $h\toμ^\pmτ^\mp$, $B\to K^* μ^+μ^-$ and $B\to K μ^+μ^-/B\to K e^+e^-$ in a two-Higgs-doublet model with gauged $L_μ-L_τ$

The LHC observed so far three deviations from the Standard Model (SM) predictions in flavour observables: LHCb reported anomalies in $B\to K^* μ^+μ^-$ and $R(K)=B\to K μ^+μ^-/B\to K e^+e^-$ while CMS found an excess in $h\toμτ$. 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 $L_μ-L_τ$ symmetry. We find that, despite the constraints from $τ\toμμμ$ and $B_s$--$\overline{B}_s$ mixing, one can explain $h \toμτ$, $B\to K^* μ^+μ^-$ and $R(K)$ simultaneously, obtaining interesting correlations among the observables.

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