RG invariant solutions for the soft supersymmetry breaking parameters

TL;DR

This paper proves the equivalence of two methods for deriving soft supersymmetry breaking parameters in gauge theories and explores RG-invariant solutions, including finite cases, providing a comprehensive theoretical framework.

Contribution

It provides a full proof of the equivalence between superconformal anomaly results and RG-invariant trajectories for soft couplings in general supersymmetric theories.

Findings

Equivalence of superconformal anomaly and RG-invariant trajectory results.

Existence of a finite RG-invariant solution for soft couplings.

Comprehensive proof applicable to multi-coupling theories.

Abstract

We show that the results for the soft couplings in supersymmetric gauge theories recently derived via the superconformal anomaly are equivalent to results obtained earlier from a consideration of exact RG-invariant trajectories. We give a full proof of these results for a general multi-coupling theory. Moreover, we demonstrate the existence of a distinct finite RG-invariant solution for the soft couplings in the case when the unbroken supersymmetric theory is finite.