$\nu$MSSM superpotential to 6th order - normalised and with no superfluous couplings

TL;DR

This paper expands the $ u$MSSM superpotential to sixth order, ensuring all flat directions are lifted and all couplings are independent, providing a comprehensive framework for analyzing gauge-invariant potentials.

Contribution

It provides a complete sixth-order expansion of the $ u$MSSM superpotential with normalized couplings, enabling detailed studies of flat directions and gauge-invariant potentials.

Findings

All 5179 couplings are independent.

Superpotential cannot be zero unless all couplings are zero.

A specific normalization choice is adopted.

Abstract

We expand the superpotential of $\nu$MSSM to 6th order. This is the order at which all flat directions can be lifted. All 5179 couplings are independent ie. the superpotential cannot be zero for all fields, without all couplings being zero. Likewise, any gauge invariant potential to the 6th order can be made by fixing the constants. A specific and welldefined choice of normalisation has been adopted. The case for investigating this potential, rather than looking at one or several generalised flat directions is made.