Bounds on Crossing Symmetry

TL;DR

This paper advances the understanding of crossing symmetry in quantum field theory by deriving bounds on internal masses that ensure crossing symmetry of scattering amplitudes at all loop orders.

Contribution

It provides the first bounds on internal masses guaranteeing crossing symmetry in perturbative quantum field theory for multiple particles and loop orders.

Findings

Derived mass bounds for crossing symmetry validity.

Established crossing symmetry for four- and five-point processes.

Extended crossing symmetry results to higher multiplicities with momentum deformations.

Abstract

Proposed in 1954 by Gell-Mann, Goldberger, and Thirring, crossing symmetry postulates that particles are indistinguishable from anti-particles traveling back in time. Its elusive proof amounts to demonstrating that scattering matrices in different crossing channels are boundary values of the same analytic function, as a consequence of physical axioms such as causality, locality, or unitarity. In this work we report on the progress in proving crossing symmetry on-shell within the framework of perturbative quantum field theory. We derive bounds on internal masses above which scattering amplitudes are crossing-symmetric to all loop orders. They are valid for four- and five-point processes, or to all multiplicity if one allows deformations of momenta into higher dimensions at intermediate steps.