Massive gravitino scattering amplitudes and the unitarity cutoff of the new Fayet-Iliopoulos terms

Abstract

We compute the 2 → 2 gravitino scattering amplitudes at tree level in supergravity theories where supersymmetry is spontaneously broken. In the unitary gauge, the gravitino becomes massive (of mass m3/2) by absorbing the Goldstino, and the scattering amplitudes of its longitudinal polarisations grow with energy as $$ {\kappa}^2{E}^4/{m}_{3/2}^2 $$ κ 2 E 4 / m 3 / 2 2 , signaling a potential breakdown of unitarity at a scale $$ {\Lambda}^2\sim {m}_{3/2}/\kappa \sim {M}_{\textrm{SUSY}}^2 $$ Λ 2 ∼ m 3 / 2 / κ ∼ M SUSY 2 . As we show explicitly in the Polonyi model, this leading term is cancelled by the contributions coming from the scalar partner of the Goldstino (sgoldstino), restoring perturbative unitarity up to the Planck scale. This is expected since supersymmetry is spontaneously broken, in analogy with the situation occuring in the Standard Model, where massive gauge bosons scattering preserves unitarity at high energy once we consider the contributions from the Higgs boson. However, when supersymmetry is broken by the new Fayet-Iliopoulos D-term, with ungauged R-symmetry, the above cancellation does not occur. In this case, the unbroken phase is singular and there is no contribution able to cancel the quartic divergences of the amplitudes, leading to a cutoff Λ ~ MSUSY where the effective theory breaks down. The same behaviour is obtained when supersymmetry is non-linearly realised.

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

“…Also, to avoid confusion, we call standard FI term the one from standard supersymmetry [8] which implies a gauged R-symmetry. As in [1], we find that since the new FI terms modify the scalar potential without contributing to JHEP04(2023)002 the amplitudes, they generically lead to uncanceled leading terms O(κ 2 E 4 /|m 3/2 | 2 ) in the latter and a perturbative cutoff at the SUSY breaking scale. In concrete examples, we can find particular values of the parameters for which the contribution of the new FI terms to the potential vanishes at the minimum, restoring the cancellation in the amplitudes and a cutoff at the Planck scale.…”

“…This time, there are three channels contributing to the 2 → 2 gravitino scattering at tree level, with propagation of the graviton, the scalar, and the gauge vector, in their respective multiplets. The contribution of the gravitational channel is not modified with respect to [1] in this setup; we will recall the result later. The contributions to compute are the ones from the scalar and vector channels.…”

“…In [1], we computed the massive gravitino scattering amplitudes in the Polonyi model, which includes a chiral multiplet with canonical Kähler potential and a constant+linear superpotential. There are two channels contributing to these amplitudes at tree level, with propagation of the graviton or the scalar comprised in the chiral multiplet.…”

“…In a recent paper [1], we started an investigation of the massive gravitino 2 → 2 scattering amplitudes. We computed them in the Polonyi model [2] and found that, as for the standard Higgs mechanism, there is a cancellation of the leading terms at high energy (in…”

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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(κ 2 E 4 /|m 3/2 | 2 ), that would lead to a breakdown of perturbative unitarity at a scale Λ ∼ M SUSY , is a consequence of the vanishing of the scalar potential at its minimum, which is implied by the flat background.

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