An Analytic Prescription for $t$-channel Singularities

TL;DR

This paper introduces an analytical method to identify and eliminate $t$-channel singularities in scattering amplitudes, which are divergences occurring when particles go on-shell, applicable in collider and cosmological contexts.

Contribution

The work presents a new fully analytical scheme to handle $t$-channel singularities, filling a gap where no general method previously existed.

Findings

The scheme effectively isolates the divergence source.

It provides a practical tool for collider and cosmological particle studies.

Potential for broad application in scattering amplitude calculations.

Abstract

The $t$-channel singularity is a divergence in the scattering amplitude which occurs when a stable particle propagating in $t$-channel scattering process becomes an on-shell state. Such situations appear either in the system of collider experiments or in the context of the cosmological particle production. No scheme which is generally applicable is known. In this work, we propose a new formulation to identify and remove the source of the divergence. The scheme is fully analytical and various applications can be expected. This work provides a valuable tool in this research field.