Universality of low-energy scattering in three-dimensional field theory

TL;DR

This paper proves that in three-dimensional quantum field theories with positive mass, the low-energy scattering behavior near the threshold is universally characterized by a specific logarithmic form, independent of model details.

Contribution

It establishes a non-perturbative, universal low-energy scattering behavior in 3D quantum field theories using an exact Bethe-Salpeter analysis, applicable broadly in relativistic QFT.

Findings

Universal low-energy scattering behavior characterized by logarithmic functions.

The result is independent of specific models and couplings.

Applicable to general relativistic quantum field theories.

Abstract

Universal low-energy behaviour ${2 m c}\over{\ln |s-4m^2|}$ of the scattering function of particles of positive mass m near the threshold $s=4m^2$, and ${\pi} \over {\ln |s-4m^2|}$ for the corresponding S-wave phase-shift, is established for weakly coupled field theory models with a positive mass m in space-time dimension 3; c is a numerical constant independent of the model and couplings. This result is a non-perturbative property based on an exact analysis of the scattering function in terms of a two-particle irreducible (or Bethe-Salpeter) structure function. It also appears as generic by the same analysis in the framework of general relativistic quantum field theory.