Effective interactions and on-shell recursion relation for massive spin 3/2

TL;DR

This paper develops on-shell methods to compute interactions and amplitudes for massive spin-3/2 particles, providing a Lagrangian-free approach that reproduces known supergravity results and unitarity bounds.

Contribution

It introduces a novel on-shell recursion framework for massive spin-3/2 particles, connecting interactions with supergravity and unitarity bounds without relying on traditional Lagrangian techniques.

Findings

Derived three-point interactions with smooth massless limits.

Constructed four-point amplitudes matching supergravity contact interactions.

Reproduced unitarity bounds and the Polonyi model scaling.

Abstract

We use on-shell methods to compute all three-point interactions of massive spin-3/2 particles involving a graviton and particles of spin $\leq 1$. By employing the massive spinor-helicity formalism we identify the interactions which have a smooth massless limit as expected from the superHiggs mechanism. These interactions are then used to on-shell construct four-point massive spin-3/2 amplitudes using an all-line transverse shift for the external momenta, which correctly reproduces the contact gravitino interactions in the $N=1$ supergravity Lagrangian. The on-shell constructed four-point amplitudes are also used to derive well-known unitarity bounds in supergravity. In particular, by adding scalar and pseudoscalar interactions to construct the four-point massive spin-3/2 amplitudes that scale as $E^2$ in the high-energy limit, we recover the on-shell Polonyi model with a Planck scale unitarity bound. These effective three-point interactions and on-shell recursion relations provide an alternative and simpler way to study the interactions of massive spin-3/2 particles without a Lagrangian or the use of Feynman diagrams.