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 (mh) 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 Λ (≤1019 GeV) by imposing the conditions in which the running coupling constants neither blow up nor fall down below Λ. 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 Λ=1019 GeV and mt=175 GeV, which is smaller by about 40 GeV than the corresponding lower bound in the SM. In generic cases, mh is no longer bounded from below by these conditions. If we consider the b→sγ constraint, small values of mh are excluded in Model II of the 2HDM.