Decoupling and Destabilizing in Spontaneously Broken Supersymmetry

TL;DR

This paper explores how the low energy effective theory of spontaneously broken supersymmetry is constructed, emphasizing the role of the Goldberger-Treiman relation, and discusses implications for stability and operator generation in supersymmetric models.

Contribution

It introduces a consistent power counting scheme for the low energy effective theory in models with spontaneous supersymmetry breaking, including the effects of Goldstino loops.

Findings

Goldstino loops can destabilize the weak scale if not properly accounted for.

The low energy operators are generated with magnitudes fixed by the power counting scheme.

The couplings of the Goldstino are determined by soft supersymmetry breaking terms.

Abstract

The supersymmetric analog of the Goldberger-Treiman relation plays a critical role in the low energy effective theory of models in which supersymmetry is spontaneously broken in a hidden sector. The interactions that connect the hidden and visible sectors break a global symmetry, which implies that the low energy theory must be constructed consistently in inverse powers of the messenger scale. The Goldberger-Treiman relation determines the couplings of the Goldstino to the visible sector fields. These couplings are fixed by the soft supersymmetry breaking terms within a power counting scheme that is stable under radiative corrections. We describe the power counting of the low energy effective theory, first for a toy model of extended technicolor and then for the supersymmetric standard model. One implication of this work for supersymmetry phenomenology is the observation that Goldstino loops can destabilize the weak scale if the low energy theory is not constructed consistently. Another is that Goldstino loops induce all visible sector operators not forbidden by symmetries. The magnitudes of these operators are determined by the consistent power counting of the low energy effective theory.