The SM expected branching ratio for $h \to \gamma \gamma$ and an excess for $h \to Z \gamma$

The recent measurements of $h \to Z \gamma$ from ATLAS and CMS show an excess of the signal strength $\mu_Z = (\sigma\cdot{\cal B})_{\mathrm{obs}}/(\sigma\cdot{\cal B})_{\mathrm{SM}}=2.2\pm 0.7$, normalized as 1 in the standard model~(SM). If confirmed, it would be a signal of new physics (NP) beyond the SM. We study NP explanation for this excess. In general, for a given model, it also affects the process $h \to \gamma \gamma$. Since the measured branching ratio for this process agrees well with the SM prediction, the model is severely constrained. We find that a minimally fermion singlets and doublet extended NP model can explain simultaneously the current data for $h \to Z \gamma$ and $h\to \gamma\gamma$. There are two solutions. Although both solutions enhance the amplitude of $h \to Z \gamma$ to the observed one, in one of the solutions the amplitude of $h \to \gamma \gamma$ flips sign to give the observ ed branching ratio. This seems to be a contrived solution although cannot be ruled out simply using branching ratio measurements alone. However, we find another solution that naturally enhances $h \to Z \gamma$ to the measured value, but keeps the amplitude of $h \to \gamma\gamma$ close to its SM prediction. We also comment on the phenomenology associated with these new fermions.