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

TL;DR

This paper analyzes the scalar potential of the Type II seesaw model to determine conditions under which the desired vacuum state is the global minimum, ensuring consistency with neutrino mass observations.

Contribution

It provides the necessary and sufficient conditions for the local minimum to be the global minimum in the scalar potential of the Type II seesaw model.

Findings

Derived conditions for the global minimum in the scalar potential

Assumed small lepton number violating term in analysis

Ensured the vacuum aligns with experimental neutrino mass data

Abstract

The Type II seesaw model requires that its scalar doublet $H$ and triplet $\Delta$ get specific patterns of VEVs $\langle H\rangle\propto(0,1)^{T}$ and $\langle\Delta\rangle\propto(0,0,1)^{T}$ 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 $\langle H\rangle\propto(0,1)^{T}$ and $\langle\Delta\rangle\propto(0,0,1)^{T}$ 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.