Electroweak phase transition with radiative symmetry breaking in Type-II seesaw with inert doublet

Abstract: We consider the Type-II seesaw model extended with another Higgs doublet, which is odd under the $Z_2$ symmetry. We look for the possibility of triggering the electroweak symmetry breaking via radiative effects. The Higgs mass parameter changes sign from being positive at higher energy scales to negative at lower energy scales in the presence of the TeV scalar triplet. The Planck scale perturbativity is demanded and the electroweak phase transition is studied using two-loop $\beta$-functions. The maximum allowed values for the interaction quartic coupling of the second doublet field and the triplet field with the Higgs field are $\lambda_3=0.15$ and $\lambda_{\Phi_{1\Delta}}=0.50$, respectively. Considering these EW values, the first-order phase transition, i.e., $\phi_{+}(T_c)/T_c\sim 0.6$ is satisfied only for vanishing doublet and triplet bare mass parameters, $m_{\Phi_2}=0.0$ GeV and $m_{\Delta}=0.0$ GeV. The small non-zero induced vacuum expectation value for the scalar triplet also generates the neutrino mass, and the lightest stable neutral particle from the inert doublet satisfies the dark matter constraints for the chosen parameter space. The impact of the thermal corrections on the stability of the electroweak vacuum is also studied, and the current experimental values of the Higgs mass and the top mass lie in the stable region both at the zero temperature and the finite temperature.