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.

Comments: 15 pages, 3 figures