Vacuum (meta-)stability in the $\mu\nu$SSM

TL;DR

This paper analyzes the vacuum stability of the $$nuSSM, identifying regions with long-lived metastable vacua and emphasizing the importance of this analysis for phenomenological studies at the LHC.

Contribution

It provides a detailed vacuum stability analysis of the $$nuSSM, including tunneling rates and the impact of light right-handed sneutrinos, which was not previously explored.

Findings

Many parameter regions have long-lived vacua longer than the universe's age.

Some regions feature short-lived electroweak vacua, constraining the model.

Vacuum stability is crucial for the phenomenological viability of the $$nuSSM.

Abstract

We perform an analysis of the vacuum stability of the neutral scalar potential of the $\mu$-from-$\nu$ Supersymmetric Standard Model ($\mu\nu$SSM). As an example scenario, we discuss the alignment-without-decoupling limit of the $\mu\nu$SSM, for which the required conditions on the Higgs sector are derived. We demonstrate that in this limit large parts of the parameter space feature unphysical minima that are deeper than the electroweak minimum. In order to estimate the lifetime of the electroweak vacuum, we calculate the rates for the tunneling process into each unphysical minimum. We find that in many cases the resulting lifetime is longer than the age of the universe, such that the considered parameter region is not excluded. On the other hand, we also find parameter regions in which the electroweak vacuum is short-lived. We investigate how the different regions of stability are related to the presence of light right-handed sneutrinos. Accordingly, a vacuum stability analysis that accurately takes into account the possibility of long-lived metastable vacua is crucial for a reliable assessment of the phenomenological viability of the parameter space of the $\mu\nu$SSM and its resulting phenomenology at the (HL)-LHC.