New limits on $\mathbf{\tan\beta}$ for 2HDMs with $\mathbf{Z_2}$ symmetry

In two-Higgs-doublet models with exact $Z_2$ symmetry, putting $m_h \simeq 125$ GeV at the alignment limit, the following limits on the heavy scalar masses are obtained from the conditions of unitarity and stability of the scalar potential: $m_H,~m_A,~m_{H^+} < 1$ TeV and $1/8 <\tan\beta <8$. The constraints from $b \to s \gamma$ and neutral meson mass differences, when superimposed on the unitarity constraints, put a tighter lower limit on $\tan\beta$ depending on $m_{H^+}$. It has also been shown that larger values of $\tan\beta$ can be allowed by introducing soft breaking term in the potential at the expense of a correlation between $m_H$ and the soft breaking parameter.