Disentangling SMEFT and UV contributions in $h\to Z\gamma$ and $h\to\gamma\gamma$ decays

LHC searches have revealed that the Higgs boson decay to a photon pair is nearly consistent with the Standard Model (SM), whereas recently, there is evidence for the decay of the Higgs boson to a $Z$-boson and a photon. These decays are governed by the same set of Wilson-coefficients at the tree level in Standard Model Effective Field Theory (SMEFT). In this study, we aim to explain this potential discrepancy between the decays $h\to \gamma \gamma$ and $h\to Z\gamma$. We conduct a model-independent analysis in SMEFT to determine the magnitude and features of the Wilson coefficients required to account for the observed distinction between the two signal strengths. Following this, we adopt a top-down approach, considering all single and two field extensions of the SM, including scalars and fermions, as candidates for new interactions. We perform the matching of these models to one loop using automated packages and compare the models' predictions regarding $h\to Z\gamma$.