Softness and Amplitudes' Positivity for Spinning Particles

TL;DR

This paper establishes positivity bounds for scattering amplitudes involving particles with arbitrary spin, linking low-energy effective action coefficients to fundamental principles like unitarity and analyticity, and constraining the energy growth of such amplitudes.

Contribution

It derives new positivity bounds for spinning particles and shows that amplitudes softer than $O(p^4)$ cannot have unitary UV completions unless free, imposing limits on effective theory behavior.

Findings

Low-energy amplitudes softer than $O(p^4)$ lack unitary UV completions.

Positivity bounds relate low-energy coefficients to fundamental principles.

Explicit examples include Goldstino and spin-1/2 fermion theories.

Abstract

We derive positivity bounds for scattering amplitudes of particles with arbitrary spin using unitarity, analyticity and crossing symmetry. The bounds imply the positivity of certain low-energy coefficients of the effective action that controls the dynamics of the light degrees of freedom. We show that low-energy amplitudes strictly softer than $O(p^4)$ do not admit unitary ultraviolet completions unless the theory is free. This enforces a bound on the energy growth of scattering amplitudes in the region of validity of the effective theory. We discuss explicit examples including the Goldstino from spontaneous supersymmetry breaking, and the theory of a spin-1/2 fermion with a shift symmetry.