Two-loop QCD corrections to $CP$-even Higgs boson decays into $Vγ$ in the Type-I Two-Higgs-Doublet Model
We investigate the QCD corrections to the loop-induced decays of the heavy $CP$-even Higgs boson, $H \to Vγ$ ($V = Z, γ$), within the framework of the Type-I Two-Higgs-Doublet Model (THDM). Owing to the similarity of the underlying loop topologies, the two decay channels exhibit closely correlated behaviour. After imposing relevant phenomenological constraints, we evaluate the decay widths for 5000 viable parameter points at next-to-leading order (NLO) in QCD under the alignment limit. The $H\toγγ$ width exceeds that of $H\to Zγ$ by roughly a factor of four. Both are dominated by the top-quark loop: the $W$ contribution vanishes in the alignment limit, and the charged-Higgs loop is suppressed throughout most of the viable parameter region. The corrections exhibit a pronounced dependence on the heavy Higgs boson mass $m_H$, attaining a maximum in the vicinity of the $t\bar{t}$ production threshold. To elucidate the individual parameter dependences, dedicated benchmark scenarios are analysed, revealing that the decay widths diminish monotonically with increasing $\tanβ$ while growing with $m_H$. The QCD corrections for both decay modes typically span approximately $-20\%$ to $+20\%$, with larger corrections in the non-alignment scenario: in the $H\toγγ$ channel they reach up to $+38\%$ at large $\tanβ$, and in the $H\to Zγ$ channel they cross zero to become positive. The $CP$ selection rule forces the $t\bar{t}$ pair into a $P$-wave configuration at threshold, which strongly suppresses the Coulomb corrections and secures the perturbative stability of the fixed-order prediction. A comparison with ATLAS limits shows that current data do not yet constrain the parameter space, whereas the $\mathcal{O}(15\%)$ NLO corrections may become relevant for interpreting exclusion bounds at the HL-LHC.