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Correlation of $h\rightarrowγγ$ and $Zγ$ in Type-II seesaw neutrino model

We study the charged scalar contributions to the Higgs decay channels of $h\rightarrow γγ$ and $h\rightarrow Zγ$ in the Type-II seesaw neutrino model. In most of the allowed parameter space in the model, the new contribution to $h\rightarrow Zγ$ is positively correlated with that to $h\rightarrowγγ$. If the current excess of the $h\rightarrow γγ$ rate measured by the ATLAS Collaboration persists, the $h\rightarrow Zγ$ rate should be also larger than the corresponding standard model prediction. We demonstrate that the anti-correlation between $h\rightarrowγγ$ and $h\rightarrow Zγ$ only exists in some special region.