On new physics off the Z peak in $H\to {\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}\gamma$

Motivated by a small but intriguing excess observed in the decay mode $H\to {\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}\gamma$ reported by both the ATLAS and CMS collaborations, we explore the possibility that new physics contributes directly to the effective $H\mathrm{\ell }\bar{\mathrm{\ell }}\gamma$ 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 $({\mathrm{\Lambda }}_R\sim v$). 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.