Renormalization group invariants in supersymmetric theories: one- and two-loop results

TL;DR

This paper systematically searches for renormalization group invariants in supersymmetric theories, identifying known and new invariants at one-loop and analyzing their reduction at two-loop levels, with implications for probing supersymmetry breaking.

Contribution

It introduces a comprehensive method combining symmetry arguments and automated search to find RG invariants in MSSM, pMSSM, and dMSSM, extending previous results and exploring two-loop effects.

Findings

All known one-loop invariants for MSSM are recovered and extended.

Additional invariants are found for pMSSM and dMSSM.

Number of invariants significantly decreases at two-loop level.

Abstract

We stress the potential usefulness of renormalization group invariants. Especially particular combinations thereof could for instance be used as probes into patterns of supersymmetry breaking in the MSSM at inaccessibly high energies. We search for these renormalization group invariants in two systematic ways: on the one hand by making use of symmetry arguments and on the other by means of a completely automated exhaustive search through a large class of candidate invariants. At the one-loop level, we find all known invariants for the MSSM and in fact several more, and extend our results to the more constrained pMSSM and dMSSM, leading to even more invariants. Extending our search to the two-loop level we find that the number of invariants is considerably reduced.