# Spontaneous breakdown of charge in the MSSM and in the NMSSM: Possibilities and Implications

## TL;DR

This paper investigates the potential for spontaneous charge breaking in the MSSM and NMSSM, analyzing the conditions, implications, and constraints on the models' parameter space with quantum and thermal corrections.

## Contribution

It provides a detailed analysis of charge-breaking minima in MSSM and NMSSM, including the effects of radiative and thermal corrections, and derives constraints based on vacuum stability and experimental data.

## Key findings

- In MSSM, radiative corrections do not create deeper charge-breaking minima.
- In NMSSM, charge-breaking minima can occur due to singlet scalar states.
- Constraints on NMSSM parameters ensure vacuum stability and compatibility with Higgs data.

## Abstract

We study the possibilities and the implications of a spontaneous breakdown of charge in the MSSM and in the $Z_3$-symmetric NMSSM. The breakdown is triggered by the charged states of the Higgs doublets acquiring vacuum expectation values. In the MSSM, it is known that the presence of a charge conserving minimum for the tree-level Higgs potential precludes a deeper (global) charge-breaking minimum. We find that the inclusion of radiative correction to the potential does not alter the situation while a deeper charge-conserving minimum could arise, albeit with no major practical consequences. In the NMSSM scenario, a charge-breaking global minimum, with or without an accompanying charge-conserving deeper minimum, could appear even with the tree-level Higgs potential thanks to the presence of a charge-neutral scalar state which transforms as a singlet under the Standard Model gauge group. Use of the NMSSM Higgs potential that includes both quantum and thermal corrections and the requirement of a viable (stable or long-lived) vacuum that breaks the electroweak symmetry, along with its compatibility with the latest Higgs data, lead to nontrivial constraints on the NMSSM parameter space.