Exponentiation of multiparticle amplitudes in scalar theories. II. Universality of the exponent

It has been shown recently that the amplitude of the creation of n real scalar particles by one virtual boson near the n-particle threshold exhibits exponential behavior at n∼1/λ. We extend this result to the processes of multiparticle production at threshold by two virtual bosons. We find that both the tree-level amplitude and leading-n-loop corrections have the same exponential behavior, with the common exponent for 1→n and 2→n processes, for various kinematics. This result strongly indicates that the exponent for multiparticle amplitudes is independent of the initial state and that there may exist a semiclassical approach to the study of multiparticle production.