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Radiative corrections to decay branching ratios of the CP-odd Higgs boson in two Higgs doublet models

We calculate radiative corrections to decay rates of CP-odd Higgs boson $A$ for various decay modes in the four types of two Higgs doublet models with the softly broken discrete $Z_{2}$ symmetry. The decay branching ratios are evaluated at the next-to-leading order for electroweak corrections and the next-to-next-to-leading order for QCD corrections. We comprehensively study the impact of the electroweak corrections on the decay rates and the branching ratios. We find that the radiative corrections can sizably modify the branching ratios, especially for the $A\to Zh$ decay mode in the nearly alignment scenario, where coupling constants of the SM-like Higgs boson $h$ are close to those in the standard model. We also show correlations between the branching ratios of $A$ and the scaling factor of the SM-like Higgs boson coupling including higher-order corrections. In addition, we show characteristic predictions on the decay pattern depending on the types of Yukawa interaction, by which we can discriminate the types of Yukawa interaction in future collider experiments.