Minima of the Scalar Potential in the Type II Seesaw Model: From Local to Global

Abstract

The Type II seesaw model requires that its scalar doublet $H$ and triplet $\Delta$ get specific patterns of VEVs $⟨H⟩\propto (0,1{)}^T$ and $⟨\Delta ⟩\propto (0,0,1{)}^T$ to accommodate neutrino masses. However, other types of minima could also exist in the scalar potential, which may strongly contradict to experimental observations. This paper studies when the minimum at $⟨H⟩\propto (0,1{)}^T$ and $⟨\Delta ⟩\propto (0,0,1{)}^T$ will be global and finds the necessary and sufficient condition for that, assuming that the lepton number violating term $H^2\Delta$ in the potential is perturbatively small.

15 pages, 3 figures

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Cited by in corpus (6)

• Towards deconstructing the simplest seesaw mechanism
• Doubly-charged Higgs Boson at Future Electron-Proton Collider
• Tree-level vacuum stability of two-Higgs-doublet models and new constraints on the scalar potential
• Lepton and quark mixing patterns with generalized CP transformations
• Accidental symmetries in the scalar potential of the Standard Model extended with two Higgs triplets
• Prescription for finite oblique parameters $S$ and $U$ in extensions of the SM with $m_W\ne m_Z\cos {\theta }_W$