Decay of CP-Even Higgs <i>H → hγγ</i> in the Two-Higgs Doublet Model: One-Loop Analytic Results and Ward Identity Checks

Abstract The first analytic expressions for one-loop-induced contributions for the decay of CP-even Higgs H → hγγ, with $h$ being the Standard-Model-like Higgs boson within the framework of the two-Higgs doublet model, are presented in this paper. The one-loop form factors for the decay processes are written in terms of scalar one-loop Passarino–Veltman functions following the input notations of both the LoopTools and Collier packages. Subsequently, physical results for the decay processes can be generated numerically by using one of the above-mentioned packages. The analytic expressions shown in this paper are verified by several numerical checks, e.g. the ultraviolet and infrared finiteness of the one-loop amplitude. Furthermore, the amplitude satisfies the Ward identity due to on-shell photons in final states. The identity is also checked numerically in this work. In phenomenological studies, the differential decay rates for H → hγγ as a function of the invariant mass of two photons in final states are first examined in the parameter space of the two-Higgs doublet models.