Revisiting the Higgs Boson Decay into a Photon and a Neutrino Pair

We present new calculations of the leading-order one-loop amplitude and the decay rate for $H\to \nu \bar{\nu }\gamma$ within the standard model, employing reduction to a set of basic Passarino-Veltman functions resulting in more concise expressions compared to prior works. Our result for the total decay rate is $\mathrm{\Gamma }(H\to \nu \bar{\nu }\gamma )=1.33\text{keV}$, in close agreement with the narrow width approximation (NWA) for the intermediate Z boson. A comparison with previous results available in the literature is also provided. We evaluate the differential decay rate with respect to the energy of the photon and find that the non-resonant contributions from box diagrams beyond the NWA notably affect the kinematic region associated with high-energy photons, where the intermediate Z boson is offshell. This suggests potential implications for searches of dark sector mediators, particularly in future lepton collider experiments.