Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds

TL;DR

This paper develops crossing symmetric dispersion relations for spinning particle scattering, enabling bounds on low energy Wilson coefficients and connecting to weak low spin dominance, with applications to photons, gravitons, and Majorana fermions.

Contribution

It introduces crossing symmetric dispersion relations for spinning particles and applies geometric function theory to derive bounds and locality constraints in EFTs.

Findings

Derived general locality/null constraints for spinning particles.

Connected positivity of absorptive parts with weak low spin dominance.

Constructed crossing symmetric amplitudes for various particle theories.

Abstract

We develop crossing symmetric dispersion relations for describing 2-2 scattering of identical external particles carrying spin. This enables us to import techniques from Geometric Function Theory and study two sided bounds on low energy Wilson coefficients. We consider scattering of photons, gravitons in weakly coupled effective field theories. We provide general expressions for the locality/null constraints. Consideration of the positivity of the absorptive part leads to an interesting connection with the recently conjectured weak low spin dominance. We also construct the crossing symmetric amplitudes and locality constraints for the massive neutral Majorana fermions and parity violating photon and graviton theories. The techniques developed in this paper will be useful for considering numerical S-matrix bootstrap in the future.