Interplay of the charged Higgs effects in $R_{D^{(\ast )}}$, $b\to s{\ell }^{+}{\ell }^{-}$ and $W$-mass

Abstract

Current data on semileptonic charged- and neutral-current $B$ decays show deviations from the predictions of the Standard Model. It is well known that a charged Higgs boson, belonging to the two-Higgs doublet model without $Z_2$ symmetry, offers one of the simplest solution to the charged-current $B$ decays. We show that this solution naturally induces a negative shift of $\mathcal{O}(1)$ in the Wilson coefficient ($C_{9\ell }$) of operator $({\bar{s}}_L{\gamma }_{\mu }{b}_L)(\bar{\ell }{\gamma }^{\mu }\ell )$, potentially resolving the tension in neutral-current $B$ decays as well. Interestingly, the lepton universality ratios in $b\to s{\ell }^{+}{\ell }^{-}$ decays, in tune with the recent LHCb result, remain SM-like. Precision constraints from neutral $B$ and $K$ meson mixing, decays $B_c\to \tau \bar{\nu }$, $B\to X_s\gamma$, and leptonic decays of $\tau$ and $Z$ can be satisfied. Furthermore, a positive shift in $W$-boson mass, nicely in agreement with the CDF measurement, is also possible, requiring the neutral scalars to be heavier than the charged Higgs but within the sub-TeV region.

Comments: 11 pages, 2 captioned figures, extended discussion in sec III.A and IV, and added an appendix; matches published version