Exponentiation of multiparticle amplitudes in scalar theories

It is argued that the amplitudes of the production of n soft scalar particles by one or a few energetic ones in theories such as λ${\mathit{cphi}}^4$ have the exponential form ${\mathit{A}}_{\mathit{n}}$∝ √n! exp[1/λF(λn,ε)], in the regime λ→0, λn=fixed, ε=fixed, where ε is the typical kinetic energy of outgoing particles. Existing results support this conjecture. Several new analytical and numerical results in favor of the exponential behavior of multiparticle amplitudes are presented.