Explaining $h\to {\mu }^{\pm }{\tau }^{\mp }$, $B\to K^{*}{\mu }^{+}{\mu }^{-}$, and $B\to K{\mu }^{+}{\mu }^{-}/B\to K{e}^{+}{e}^{-}$ in a Two-Higgs-Doublet Model with Gauged $L_{\mu }\text{−}{L}_{\tau }$

The LHC has observed, so far, 3 deviations from the Standard Model (SM) predictions in flavor observables: LHCb reported anomalies in $B\to K^{*}{\mu }^{+}{\mu }^{-}$ 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 $L_{\mu }\text{−}{L}_{\tau }$ symmetry. We find that, despite the constraints from $\tau \to \mu \mu \mu$ and $B_s\text{−}{\overline{B}}_s$ mixing, one can explain $h\to \mu \tau$, $B\to K^{*}{\mu }^{+}{\mu }^{-}$ and $R(K)$ simultaneously, obtaining interesting correlations among the observables.

Figure 1

Left panel: Allowed regions in the $\cos (\alpha -\beta )\text{−}\sin ({\theta }_R)$ plane. The blue (light blue) region corresponds to the $1\sigma$ ($2\sigma$) region of the CMS measurement of $h\to \mu \tau$ for $\tan \beta =50$; yellow stands for $\tan \beta =10$. The (dashed) red contours mark deviations of $h\to \tau \tau$ by 10% compared to the SM for $\tan \beta =50$ (10). The vertical green lines illustrate the naive LHC limit $|\cos (\alpha -\beta )|\lesssim 0.4$; horizontal lines denote the 90% C.L. limit on $\tau \to 3\mu$ via $Z^{\prime }$ exchange. Right panel: Allowed regions in the ${\mathrm{\Gamma }}_{23}^{dL}$-$m_{Z^{\prime }}/g^{\prime }$ plane from $B\to K^{*}{\mu }^{+}{\mu }^{-}$ and $R(K)$ (yellow) and $B_s$ mixing (blue). For $B_s$ mixing, (light) blue corresponds to ($m_Q=15m_{Z^{\prime }}/g^{\prime }$) $m_Q=m_{Z^{\prime }}/g^{\prime }$. The horizontal lines denote the lower bounds on $m_{Z^{\prime }}/g^{\prime }$ from $\tau \to 3\mu$ for $\sin ({\theta }_R)=0.005,0.02,0.05$. The gray region is excluded by neutrino trident production (NTP).

Figure 2

Allowed regions in the $m_{Z^{\prime }}/g^{\prime }$-$\sin ({\theta }_R)$ plane: The horizontal stripes correspond to $h\to \mu \tau$ ($1\sigma$) for $\tan \beta =85,50,25$ and $\cos (\alpha -\beta )=0.2$; (light) blue stands for (future) $\tau \to 3\mu$ limits at 90% C.L. The gray regions are excluded by NTP or $B_s\text{−}{\overline{B}}_s$ mixing in combination with the $1\sigma$ range for $C_9$ [see Eq. (18)].