A complete and minimal catalogue of MSSM gauge invariant monomials

TL;DR

This paper provides a comprehensive, minimal set of gauge invariant monomials for the MSSM, including generational structure, enabling systematic construction of operators and analysis of flat directions.

Contribution

It extends the existing catalogue of MSSM monomials to include generational details and demonstrates the lifting of flat directions with lower order superpotentials.

Findings

Catalogue contains 712 monomials plus 3 generations of right-handed neutrinos.

All MSSM flat directions can be lifted by a 6th order superpotential.

The catalogue allows systematic construction of gauge invariant operators.

Abstract

We present a complete and minimal catalogue of MSSM gauge invariant monomials. That is, the catalogue of Gherghetta, Kolda and Martin is elaborated to include generational structure for all monomials. Any gauge invariant operator can be built as a linear combination of elements of the catalogue lifted to nonnegative integer powers. And the removal of any one of the monomials would deprive the catalogue of this feature. It contains 712 monomials - plus 3 generations of righthanded neutrinos if one extends the model to the $\nu$MSSM. We note that $\nu$MSSM flat directions can all be lifted by the 6th order superpotential - compared to the 9th order needed in MSSM.