Flavor constraints on two-Higgs-doublet models with general diagonal Yukawa couplings

We consider constraints from flavor physics on two-Higgs-doublet models (2HDM) with general, flavor-diagonal, Yukawa couplings. Analyzing the charged Higgs contribution to different observables, we find that $b\to s\gamma$ transitions and $\mathrm{\Delta }{M}_{B_d}$ restrict the coupling ${\lambda }_{tt}$ of the top quark (corresponding to $\cot \beta$ in models with a $Z_2$ symmetry) to $\mathrm{\mid }{\lambda }_{tt}\mathrm{\mid }<1$ for $m_{H^{+}}\lesssim 500$ GeV. Stringent constraints from $B$ meson decays are obtained also on the other third generation couplings ${\lambda }_{bb}$ and ${\lambda }_{\tau \tau }$, but with stronger dependence on $m_{H^{+}}$. For the second generation, we obtain constraints on combinations of ${\lambda }_{ss}$, ${\lambda }_{cc}$, and ${\lambda }_{\mu \mu }$ from leptonic $K$ and $D_s$ decays. The limits on the general couplings are translated to the common 2HDM types I – IV with a $Z_2$ symmetry, and presented on the $(m_{H^{+}},\tan \beta )$ plane. The flavor constraints are most excluding in the type II model which lacks a decoupling limit in $\tan \beta$. We obtain a lower limit $m_{H^{+}}\gtrsim 300$ GeV in models of type II and III, while no lower bound on $m_{H^{+}}$ is found for types I and IV.