Paper detail

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

The Type II seesaw model requires that its scalar doublet $H$ and triplet $Δ$ get specific patterns of VEVs $\langle H\rangle\propto(0,1)^{T}$ and $\langleΔ\rangle\propto(0,0,1)^{T}$ 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 $\langleΔ\rangle\propto(0,0,1)^{T}$ will be global and finds the necessary and sufficient condition for that, assuming that the lepton number violating term $H^{2}Δ$ in the potential is perturbatively small.