Destabilising Divergences in the NMSSM

TL;DR

This paper analyzes the destabilising divergences arising when introducing a gauge singlet into the MSSM (the NMSSM). It shows that, in the absence of extra symmetries, certain tadpole/tensorial diagrams can destabilise the gauge hierarchy, with a detailed supergravity-based power-counting framework identifying which operators are dangerous. It then presents two symmetry-based cures: a gauged $U(1)_R$-symmetry and a target-space duality symmetry, each forbidding the problematic operators and enabling natural generation of the weak-scale $\mu$ and $\mu'$ terms without cosmological domain-wall issues. The results demonstrate that consistent, natural singlet extensions can avoid both fine-tuning and domain walls, having implications for Higgs phenomenology and low-energy SUSY models.

Abstract

The problem of destabilising divergences is discussed for singlet extensions of the MSSM. It is shown that models which possess either gauged-$R$ symmetry or target space duality at the Planck scale are able to circumvent this problem whilst avoiding cosmological domain walls.