Next-to-leading-order electroweak correction to H→ Z⁰γ

Inspired by the recent observation of the Higgs boson radiative decay into Z⁰ by { ATLAS} and { CMS} Collaborations, we investigate the next-to-leading-order (NLO) electroweak correction to this rare decay process in Standard Model (SM). Implementing the on-shell renormalization scheme, we find that the magnitude of the NLO electroweak correction may reach $7%$ of the leading order (LO) prediction, much more significant than that of the NLO QCD correction, which is merely about $0.3%$. After incorporating the O(α) correction, the predicted partial width from various α schemes tend to converge to each other. Including both NLO electroweak and QCD corrections, we present the most accurate SM prediction for the branching fraction of this rare decay channel to be Bₜₕ[H→ Z⁰γ]=(1.55± 0.06)× 10⁻³, considerably lower than the measured value Bₑₓₚ[H→ Z⁰γ]=(3.4± 1.1)× 10⁻³. Resolving this alarming discrepancy clearly calls for further theoretical investigations, and, more importantly, experimental efforts from { HL-LHC} and the prospective Higgs factories such as { CEPC} and { FCC}.