Next-to-leading-order electroweak correction to H Z⁰

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 () correction, the predicted partial width from various 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 B ₓ₇H Z⁰= (1. 55 0. 06) 10^-3, considerably lower than the measured value B ₄ₗ₏H Z⁰= (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.