Large $h\to bs$ in generic two-Higgs-doublet models

We investigate the possible size of $h\to bs$ in two-Higgs-doublet models with generic Yukawa couplings. Even though the corresponding rates are in general expected to be small due to the indirect constraints from $B_s\to {\mu }^{+}{\mu }^{-}$ and $B_s–{\overline{B}}_s$ mixing, we find regions in parameter space where $h\to bs$ can have a sizable branching ratio well above 10%. This requires a tuning of the neutral scalar masses and their couplings to muons, but then all additional constraints such as $B\to X_s\gamma$, $(g-2{)}_{\mu }$, and $h\to {\mu }^{+}{\mu }^{-}$ are satisfied. In this case, $h\to bs$ can be a relevant background in $h\to b\overline{b}$ searches and vice versa due to the imperfect $b$-tagging purity. Furthermore, if $h\to bs$ is sizeable, one expects two more scalar resonances in the proximity of $m_h$. We briefly comment on other flavor-violating Higgs decays and on the 95 GeV $\gamma \gamma$ resonance within generic two-Higgs-doublet models.

Figure 1

Allowed regions in the ${ϵ}_{23}^d–{ϵ}_{32}^d$ plane for $m_H=150\mathrm{GeV}$ and $c_{\beta \alpha }=0.1$, requiring that the 2HDM contribution to $B_s–{\overline{B}}_s$ mixing should not exceed 10% compared to the SM which is of the order of the uncertainty in the lattice calculation of the matrix elements. Here we scanned over $m_A$ from 100 to 200 GeV. Note that the dependence on $c_{\beta \alpha }$ is very weak. As one can see, in order to get potentially large effects in $h\to bs$, either ${ϵ}_{23}^d$ or ${ϵ}_{32}^d$ must be very small.

Figure 2

$\mathrm{BR}(h\to bs)$ contours and the allowed $2\sigma$ regions from $B_s\to {\mu }^{+}{\mu }^{-}$. Left: setting all ${ϵ}^f=0$ except for ${ϵ}_{23}^d$, with $m_A$ given by Eq. (15). Right: Same as left plot but with nonzero ${ϵ}_{\mu \mu }^{\ell }$ given by Eq. (23) instead. The darker gray region is excluded by the upper limit on the total decay width of the Higgs of 13 MeV [30] and the lighter gray region is excluded by the global-fit constraint $\mathrm{BR}(h\to \text{anything})<34\%$ [32].

Figure 3

$\mathrm{BR}(h\to bs)$ vs $m_H$ for our ansatz from Eqs. (15), (23), and (26) for different values of $c_{\beta \alpha }$. Note that for degenerate masses of the neutral scalars $h\to bs$ is in principle unbounded.

Figure 4

Allowed region from $B\to \mu \nu$ for our ansatz from Eqs. (15), (23), and (26) with ${ϵ}_{32}^d=0$.