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

The universal low-energy behavior, 2mc/ln \|s-4m²\| of the scattering function of particles of positive mass m near the threshold s=4m², and π/ln \|s-4m²\| for the corresponding S-wave phase shift, is established for weakly coupled field theory models with a mass m>0 in space-time dimension 3; c is a numerical constant independent of the model and couplings. This result is a nonperturbative 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.