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

We extend the 2 -> 2 gravitino scattering amplitude computed in [1] to an arbitrary 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 O( kappa E-2(4)/vertical bar m(3/2)vertical bar(2)), that would lead to a breakdown of perturbative unitarity at a scale Lambda similar to M-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.

Automated summary

We extend the 2 -> 2 gravitino scattering amplitude computed in [1] to an arbitrary N = 1 supergravity model with supersymmetry breaking. We find that the cancellation of leading terms in the amplitude at a certain scale is a consequence of the vanishing of the scalar potential at its minimum. We also analyze the inclusion of new Fayet-Iliopoulos terms and find that they generally lead to uncanceled leading terms in the amplitude.