Massive Spin-5/2 Fields Coupled to Gravity: Tree-Level Unitarity vs. the Equivalence Principle

TL;DR

This paper investigates the gravitational interactions of massive spin-5/2 fields, revealing unitarity violations at certain energies with minimal coupling, and proposing non-minimal interactions that restore unitarity but violate the equivalence principle.

Contribution

It demonstrates the unitarity violation in spin-5/2 gravitational scattering and introduces non-minimal couplings to restore unitarity, highlighting a tension with the equivalence principle.

Findings

Tree-level unitarity violation at energies ~√(m M_{Pl}) with minimal coupling.

Restoration of unitarity at Planck scale with non-minimal interactions.

Non-minimal interactions violate the strong equivalence principle.

Abstract

I show that the gravitational scattering amplitudes of a spin-5/2 field with mass $m\ll M_{Pl}$ violate tree-level unitarity at energies $\sqrt{s}\approx\sqrt{mM_{Pl}}$ if the coupling to gravity is minimal. Unitarity up to energies $\sqrt{s}\approx M_{Pl}$ is restored by adding a suitable non-minimal term, which gives rise to interactions violating the (strong) equivalence principle. These interactions are only relevant at distances $d\lequiv 1/m$.