Screening Theorem for the Higgs Decays into the Gauge Boson Pairs

The radiative corrections to the decays of the neutral CP-even Higgs boson $H$ into a longitudinal gauge boson pair, {\it i.e.}, $H \rightarrow Z_LZ_L$ and $W^+_LW^-_L$ are analyzed in the two Higgs doublet model by making use of the equivalence theorem. The sensitivity of the decay rates to the masses of the heavier Higgs bosons, charged $G^{\pm}$ and CP-odd neutral $A$ bosons as well as CP-even neutral $h$ boson, is investigated. Though the width $\Gamma (H \rightarrow Z_LZ_L)$ is insensitive to the masses of heavier Higgs bosons, $\Gamma (H \rightarrow W^+_LW^-_L)$ is sensitive and the radiative corrections are minimized for $m_G = m_A$. These results are explained completely on the basis of a new screening theorem for the vertices, which is closely connected with the custodial $SU(2)_V$ symmetry.