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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 $b\to sγ$ transitions and $ΔM_{B_d}$ restrict the coupling $λ_{tt}$ of the top quark (corresponding to $\cotβ$ in models with a $Z_2$ symmetry) to $|λ_{tt}|<1$ for $m_{H^+}\lesssim 500$ GeV. Stringent constraints from $B$ meson decays are obtained also on the other third generation couplings $λ_{bb}$ and $λ_{ττ}$, but with stronger dependence on $m_{H^+}$. For the second generation, we obtain constraints on combinations of $λ_{ss}$, $λ_{cc}$, and $λ_{μμ}$ 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 $(m_{H^+},\tanβ)$ plane. The flavor constraints are most excluding in the type II model which lacks a decoupling limit in $\tanβ$. 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.