Exploring Background Contributions in $H \to Z \gamma$ Decay

The rare decay $H \to Z\gamma$ has been investigated by both the ATLAS and CMS Collaborations, with each reporting an excess in Run~2 in 2023 characterized by $\mu = 2.2 \pm 0.7$. This anomaly was initially attributed to possible modifications of the $HZ\gamma$ vertex. However, because the $H \to Z\gamma$ signal is reconstructed via the $H \to \ell\ell\gamma$ channel, background effects -- particularly those from processes that mimic the same final state -- may have been underestimated. In this work, we re-examine these backgrounds in detail and propose that the observed excess could be explained by an additional BSM-induced contribution. We present both an effective field theory framework and a UV-complete model that provide the necessary rates and a consistent interpretation of the data. The proposed model reproduces the newest ATLAS result, $\mu = 1.3^{+0.6}_{-0.5}$, obtained using a narrower dilepton invariant-mass window.