  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.
