Abstract
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 ($h\to \gamma \gamma, Z\gamma$) deviate from the standard model, and large parameter region is excluded by the recent ATLAS and CMS combined analysis of $h\to \gamma \gamma$. Our result of the signal strength for $h\to \gamma \gamma$ is $R_{\gamma \gamma} \lesssim 1.1$, but its deviation is too small to observe at the LHC experiment.
Highlights
Current experimental results at the LHC are almost consistent with the predictions in the standard model (SM)
Rγ γ can be enhanced by both H ± and H ±± contributions for λ4 < 0, there is no parameter space in λ4 < 0 region for M ≤ 1 TeV. This result comes from the vacuum stability conditions, and we note that Rγ γ is not strongly enhanced compared to the literature; see for example Refs. [55,56]
We have studied the vacuum stability and perturbativity conditions in the minimal type-II seesaw model
Summary
Current experimental results at the LHC are almost consistent with the predictions in the standard model (SM). There are additional particles to the SM: the SM gauge singlet Majorana neutrinos, an SU (2)L triplet scalar field with hypercharge Y = 2, and an SU (2)L triplet fermion with hypercharge Y = 0 in type-I [2,3,4,5], II [6,7,8,9,10,11], and III [12] seesaw mechanism, respectively. We do not consider such a symmetry, but impose a naturalness condition that contributions of the heavy triplet scalar field should be lower than the measured Higgs mass.
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