Multiparticle Threshold Amplitudes Exponentiate in Arbitrary Scalar Theories

Abstract

Threshold amplitudes are considered for $n$-particle production in arbitrary scalar theory. It is found that, like in $ϕ^4$, leading-$n$ corrections to the tree level amplitudes, being summed over all loops, exponentiate. This result provides more evidence in favor of the conjecture on the exponential behavior of the multiparticle amplitudes.