Motivated by a small but intriguing excess observed in the decay mode H → ℓ+ℓ−γ reported by both the ATLAS and CMS collaborations, we explore the possibility that new physics contributes directly to the effective \( H\overline{\mathcal{ll}}\gamma \) coupling rather than modifying the Z peak. Concretely, we consider a dimension-8 operator that could arise from new particles via box diagrams. Such non-resonant contribution may provide an alternative origin for current or future excesses. We examine how experimental cuts may distinguish between possible modifications of the Z peak and non-resonant contributions. The currently measured excess requires that the new physics scale is relatively low (ΛR ~ v). However, we show that it may remain within current experimental bounds. In particular, we illustrate this using a simplified model, motivated by the dark matter problem, and discuss its other experimental constraints.
