Mass bounds of the lightest CP-even Higgs boson in the two-Higgs-doublet model

The upper and the lower bounds of the lightest CP-even Higgs-boson mass ($m_h$) are discussed in the two-Higgs-doublet model (2HDM) with a softly-broken discrete symmetry. They are obtained as a function of a cut-off scale $\Lambda$ ($\leq 10^{19}$ GeV) by imposing the conditions in which the running coupling constants neither blow up nor fall down below $\Lambda$. In comparison with the standard model (SM), although the upper bound does not change very much, the lower bound is considerably reduced. In the decoupling regime where only one Higgs boson ($h$) becomes much lighter than the others, the lower bound is given, for example, by about 100 GeV for $\Lambda = 10^{19}$ GeV and $m_t = 175$ GeV, which is smaller by about 40 GeV than the corresponding lower bound in the SM. In generic cases, $m_h$ is no longer bounded from below by these conditions. If we consider the $b \to s \gamma$ constraint, small values of $m_h$ are excluded in Model II of the 2HDM.