Tree-Level Unitarity Constraints on the Gravitational Couplings of Higher-Spin Massive Fields

TL;DR

This paper investigates the high-energy behavior of graviton scattering amplitudes involving higher-spin massive particles, revealing unitarity violations for spins > 2 and proposing non-minimal couplings to restore unitarity up to the Planck scale.

Contribution

It provides a detailed analysis of unitarity constraints on gravitational couplings for higher-spin particles and introduces non-minimal couplings to maintain unitarity at high energies.

Findings

Unitarity breaks down for spins > 2 below the Planck scale if mass is much less than M.

Adding curvature-dependent non-minimal couplings restores unitarity up to the Planck scale.

Modifications include particle gravitational quadrupole moments at scales around 1/m.

Abstract

We analyse the high-energy behavior of tree-level graviton Compton amplitudes for particles of mass m and arbitrary spin, concentrating on a combination of forward amplitudes that will be unaffected by eventual cross- couplings to other, higher spins. We first show that for any spin larger than 2, tree-level unitarity is already violated at energies well below the Planck scale M, if m << M. We then restore unitarity to this amplitude up to M by adding non-minimal couplings that depend on the curvature and its derivatives, and modify the minimal description - including particle gravitational quadrupole moments - at scales O(1/m).