Prediction of htoγ Z from htoγγ at LHC for the IMDS₃ Model

We consider the decays $h\to\gamma\gamma,\gamma Z$ in the context of an extension of the standard model with two inert doublets and an additional $S_3$ symmetry. This model has contributions for these processes through new charged scalar-loops. Comparing our $h\to\gamma\gamma$ with the more precise available experimental data we can predict the behaviour of $h\to\gamma Z$ due that they depend on the same parameters, our estimation for this channel is 1.05 times the standard model value, but can be up to 1.16 if consider the $+1\sigma$ uncertainty from the $h\to\gamma\gamma$ data, and down to 0.96 if consider $-1\sigma$.