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Vacuum stability and naturalness in type-II seesaw

We study the vacuum stability and perturbativity conditions in the minimal type-II seesaw model. These conditions give characteristic constraints to model parameters. In the model, there is a $SU(2)_L$ triplet scalar field, which could cause a large Higgs mass correction. From the naturalness point of view, heavy Higgs masses should be lower than $350\,{\rm GeV}$, which can be testable by the LHC Run-II results. Due to effects of the triplet scalar field, branching ratios of the Higgs decay ($h\to γγ, Zγ$) deviate from the standard model, and large parameter region is excluded by the recent ATLAS and CMS combined analysis of $h\to γγ$. Our result of the signal strength for $h\to γγ$ is $R_{γγ} \lesssim 1.1$, but its deviation is too small to observe at the LHC experiment.