Theorem on vacuum stability

TL;DR

This paper proves a theorem in extended Standard Model scenarios, showing that the vacuum with only the Higgs doublet acquiring a VEV is a local minimum and energetically favored over configurations with additional scalar fields also acquiring VEVs.

Contribution

It establishes a general theorem about vacuum stability in models with extra scalar multiplets and arbitrary hypercharges, extending previous results.

Findings

The vacuum with only the Higgs VEV is a local minimum.

Configurations with additional scalar VEVs have higher potential energy.

The theorem applies to models with arbitrary scalar hypercharges.

Abstract

We consider an extension of the Standard Model with one or more scalar multiplets beyond the Higgs doublet $\Phi$. The additional scalar multiplets are supposed to carry arbitrary hypercharges. We prove that, in such a model, if the field configuration where only $\Phi$ has a nonzero vacuum expectation value (VEV) is a local minimum of the potential, then it has a lower value of the potential than any field configuration where both $\Phi$ and other scalar multiplets have nonzero VEVs.