$B_{s,d} \to \ell^{+}\ell^{-}$ in a Two-Higgs-Doublet Model

We compute the branching ratios of $B_{s,d} \to \ell^+ \ell^-$ in the type-II two-Higgs-doublet model with large $\tan\beta$. We find a significant enhancement over the Standard Model branching ratios of up to an order of magnitude for values of $\tan\beta \sim 50$ and charged Higgs masses $M_{H^+}$ above the bound from $b \to s \gamma$. We point out that previous calculations in the literature are gauge-dependent due to the omission of an important diagram, which gives the dominant contribution in the 't Hooft-Feynman gauge. We have analyzed in detail the region of the $(M_{H^+}, \tan \beta)$ plane to be probed by searches for $B_s \to \mu^+ \mu^-$ in Run II of the Tevatron. Since the branching ratio increases like $\tan^4 \beta$, this decay mode is complementary to $ b \to s \gamma$ and efficiently probes the large $\tan \beta$ region. For $\tan \beta=50$ an integrated luminosity of 20 fb$^{-1}$ in an extended Run II will probe charged Higgs masses up to 700 GeV, if the background to $B_s \to \mu^+ \mu^-$ is small