t-channel singularities in cosmology and particle physics

Abstract

The t-channel singularity of a cross section for a binary 2→2 scattering occurs when the 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→2 and an inverse decay 2→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−→Ze−. After critically reviewing regularization methods proposed in literature, we discuss singular processes that occur in a medium composed of particles in thermal equilibrium. The medium is shown to regulate the singularities naturally as particles acquire a non-zero width. We demonstrate a possible cosmological application by calculating thermally averaged cross section for an elastic scattering within a simple scalar model. The transition probability, which is divergent in vacuum, becomes finite when the process occurs in a thermal bath due to the imaginary part of the t-channel mediator's self-energy computed within the Keldysh-Schwinger formalism.