  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 $h\to Z\gamma$.
