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 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. For $\Lambda = 10^{19}$ GeV and $m_t = 175$ GeV, the mass is not bounded from below in Model I of the 2HDM, whereas in Model II the mass less than about 100 GeV is excluded because of the $b \to s \gamma$ constraint. In the decoupling regime where only one Higgs boson becomes lighter than others, the lower bound is given by about 100 GeV for Model I and II, which is smaller by about 40 GeV than the corresponding lower bound in the SM.