Multiparticle Threshold Amplitudes Exponentiate in Arbitrary Scalar Theories

TL;DR

This paper demonstrates that in arbitrary scalar theories, the leading corrections to tree-level multiparticle amplitudes at threshold exponentiate when summed over all loops, supporting the conjecture of exponential behavior.

Contribution

It extends the exponentiation property of multiparticle threshold amplitudes from $$ theory to arbitrary scalar theories, providing new evidence for the conjecture.

Findings

Leading-$n$ corrections exponentiate when summed over all loops.

Supports the conjecture of exponential behavior of multiparticle amplitudes.

Generalizes previous results from $$ theory to arbitrary scalar theories.

Abstract

Threshold amplitudes are considered for $n$-particle production in arbitrary scalar theory. It is found that, like in $\phi ^4$, 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.