Finite-temperature modification of heavy particle decay and dark matter annihilation

TL;DR

This paper uses the operator product expansion to analyze how finite temperature affects heavy particle decay and dark matter annihilation, revealing simplified, model-independent corrections at low temperatures.

Contribution

It introduces a novel application of the operator product expansion to compute thermal corrections for heavy particle processes, simplifying calculations and clarifying correction orders.

Findings

Thermal correction to charged particle decay width is a multiplicative factor of the zero-temperature width.

Leading thermal correction to fermionic dark matter annihilation appears only at order T^4/m_hi^4.

The method separates model-independent thermal matrix elements from short-distance coefficients.

Abstract

We apply the operator product expansion (OPE) technique to the decay and annihilation of heavy particles in a thermal medium with temperature below the heavy particle mass, m_chi. This allows us to explain two interesting observations made before: a) that the leading thermal correction to the decay width of a charged particle is the same multiplicative factor of the zero-temperature width for a two-body decay and muon decay, and b) that the leading thermal correction to fermionic dark matter annihilation arises only at order T^4/m_chi^4. The OPE further considerably simplifies the computation and factorizes it into model-independent matrix elements in the thermal background, and short-distance coefficients to be computed in zero-temperature field theory.