Generalized screening theorem for Higgs decay processes in the two - doublet model

The radiative corrections to the decay processes of the neutral (CP -even) Higgs boson (H) into a longitudinal gauge boson pair, i.e., H → ZLZL and H → W L W− L are analyzed in the two-Higgs doublet model by assuming that all of the Higgs boson masses are much greater than the W and Z bosons’. These calculations are motivated to see if one could see potentially large virtual effects to these decay rates due to the charged and CP -odd neutral Higgs boson masses (mG and mA, respectively) which are supposed to be larger than mH . It is pointed out that, although the radiative corrections to the decay width Γ(H → W L W− L ) depend sensitively in general onmG andmA, there occurs a screening effect, i.e., cancellation in leading terms once we set mG = mA, so that the radiative corrections tend to be minimized. It is also pointed out that the decay rate Γ(H → ZLZL) is fairly insensitive to the other heavier Higgs masses and is possibly a good measuring tool of the Higgs mixing angle. The mechanism of these screening phenomena in the Higgs decays is explained on the basis of a new screening theorem, which we postulate with reference to the custodial symmetry in the Higgs potential.