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Next-to-leading order corrections to decays of the heavier CP-even Higgs boson in the two Higgs doublet model

We investigate the impact of electroweak (EW), scalar and QCD corrections to the full set of decay branching ratios of an additional CP-even Higgs boson ($H$) in the two Higgs doublet model with a softly broken $Z_2$ symmetry. We employ the improved gauge independent on-shell scheme in the renormalized vertices. We particularly focus on the scenario near the alignment limit in which couplings of the discovered 125 GeV Higgs boson ($h$) coincide with those of the standard model while the $Hhh$ coupling vanishes at tree level. The renormalized decay rate for $H\to hh$ can significantly be changed from the prediction at tree level due to non-decoupling loop effects of additional Higgs bosons, even in the near alignment case. We find that the radiative corrections to the branching ratio of $H\to hh$ can be a few ten percent level in the case with the masses of additional Higgs bosons being degenerate under the constraints of perturbative unitarity, vacuum stability and the EW precision data. Further sizable corrections can be obtained for the case with a mass difference among the additional Higgs bosons.