On the effective interactions of a light gravitino with matter fermions

TL;DR

This paper derives the effective interactions between a light gravitino's goldstino components and matter fermions, revealing a novel coupling structure that differs from traditional non-linear supersymmetry realizations, with potential phenomenological relevance.

Contribution

It provides the first explicit derivation of the four-point goldstino-matter fermion coupling in a simple supersymmetry-breaking model, highlighting a new invariant interaction structure.

Findings

Derived the four-point effective coupling explicitly.

Discovered the coupling differs from the standard non-linear realization.

Identified the need to include a second invariant coupling.

Abstract

If the gravitino is light and all the other supersymmetric particles are heavy, we can consider the effective theory describing the interactions of its goldstino components with ordinary matter. To discuss the model-dependence of these interactions, we take the simple case of spontaneously broken supersymmetry and only two chiral superfields, associated with the goldstino and a massless matter fermion. We derive the four-point effective coupling involving two matter fermions and two goldstinos, by explicit integration of the heavy spin-0 degrees of freedom in the low-energy limit. Surprisingly, our result is not equivalent to the usual non-linear realization of supersymmetry, where a pair of goldstinos couples to the energy-momentum tensor of the matter fields. We solve the puzzle by enlarging the non-linear realization to include a second independent invariant coupling, and we show that there are no other independent couplings of this type up to this order in the low-energy expansion. We conclude by commenting on the interpretation of our results and on their possible phenomenological implications.