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We consider the decays $h\to\gamma\gamma,\gamma Z$ in the context of anextension of the standard model with two inert doublets and an additional $S_3$symmetry. This model has contributions for these processes through new chargedscalar-loops. Comparing our $h\to\gamma\gamma$ with the more precise availableexperimental data we can predict the behaviour of $h\to\gamma Z$ due that theydepend on the same parameters, our estimation for this channel is 1.05 timesthe 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$-1\sigma$.

Prediction of $h\to\gamma Z$ from $h\to\gamma\gamma$ at LHC for the IMDS$_3$ Model