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

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.