One PI and Wilsonian Actions in SUSY theories

TL;DR

This paper explores the relationship between high-scale soft breaking terms and physical parameters in SUSY theories, emphasizing the role of Wilsonian and 1PI actions in determining physical masses and gaugino mass contributions.

Contribution

It clarifies how IR effects and non-renormalization theorems influence the relation between Wilsonian and 1PI actions in supersymmetric models.

Findings

Infrared effects violating non-renormalization theorems are absent at generic field points.

If gaugino mass is absent in the Wilsonian action, it remains absent in the 1PI action.

Physical masses are determined by the poles in the full quantum propagator.

Abstract

The soft breaking terms in supersymmetric theories are calculated at some high scale characterizing the hidden supersymmetry breaking sector, and then evolved down to the TeV scale. These parameters are usually presented as the ones that should be compared to experiment. The physical parameters however are those occurring in the quantum effective (1PI) action - in particular the physical mass is the location of the pole in the full quantum propagator. Here we discuss the relation between the two and the possible existence of additive contributions to the gaugino mass. We argue that infra red effects which violate non-renormalization theorems are absent (for the 1PI action) if the calculation is done at a generic point in field space so that an effective IR cutoff is present. It follows that if a gaugino mass term is absent in the Wilsonian action it is absent in the 1PI action.