$t$-channel singularities in cosmology and particle physics

TL;DR

This paper investigates the conditions and implications of $t$-channel singularities in particle scattering processes, demonstrating how a thermal medium can naturally regulate these divergences with applications to cosmology.

Contribution

It derives conditions for $t$-channel singularities, identifies divergent Standard Model processes, and shows how thermal effects regulate these divergences in cosmological contexts.

Findings

Identified conditions for $t$-channel singularities in binary processes.

Demonstrated divergence in vacuum and regularization in thermal medium.

Applied the formalism to a cosmological scalar scattering model.

Abstract

The $t$-channel singularity of a cross-section for a binary $2 \to 2$ scattering process occurs when a particle exchanged in the $t$ channel is kinematically allowed to be on its mass-shell, that is when the process can be viewed as a sequence of two physical subprocesses: a two-body decay $1\to 2$ and an inverse decay $2 \to 1$. We derive conditions for the singularity to be present in a binary process. A class of divergent cross sections for Standard Model processes has been determined and illustrated by the weak analog of the Compton scattering $Ze^{-}\to Ze^{-}$. After critically reviewing regularization methods proposed in literature, we discuss singular processes which occur in a medium composed of particles in thermal equilibrium. The medium is shown to regulate the singularities naturally as particles acquire a finite width. We demonstrate a possible cosmological application by calculating thermally averaged cross section for an elastic scattering within a simple scalar model. The cross section, which is divergent in vacuum, becomes finite when the process occurs in a thermal bath due to the imaginary self-energy of the $t$-channel mediator computed within the Keldysh-Schwinger formalism.