More on massive gravitino scattering amplitudes and the unitarity cutoff of the new Fayet-Iliopoulos terms

TL;DR

This paper investigates gravitino scattering amplitudes in supergravity models with supersymmetry breaking, revealing how new Fayet-Iliopoulos terms influence the unitarity cutoff and the conditions under which it can be raised to the Planck scale.

Contribution

It extends gravitino scattering amplitude analysis to models with both F- and D-term breaking and examines the impact of new FI terms on the unitarity cutoff.

Findings

Cancellation of leading unitarity-violating terms depends on scalar potential vanishing.

New FI terms generally lower the perturbative cutoff to the SUSY breaking scale.

In special cases, the cutoff can be increased to the Planck scale.

Abstract

We extend the $2\rightarrow2$ gravitino scattering amplitude computed in [1] to an arbitrary $\mathcal{N}=1$ supergravity model of one chiral and one vector multiplet, in a Minkowski background with supersymmetry breaking driven by both $F$- and $D$-terms. We find that the cancellation of the leading term in $\mathcal{O}(\kappa^2 E^4/|m_{3/2}|^2)$, that would lead to a breakdown of perturbative unitarity at a scale $\Lambda\sim M_\mathrm{SUSY}$, is a consequence of the vanishing of the scalar potential at its minimum, which is implied by the flat background. We then analyse the inclusion of the new Fayet-Iliopoulos (FI) terms. We find that, since they modify the scalar potential without contributing to the amplitudes, they generically lead to uncanceled leading terms in the latter and a perturbative cutoff at the supersymmetry breaking scale, except for particular cases where the new FI term does not modify the potential at its minimum and the cutoff is pushed up to the Planck scale.