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

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_χ. 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 T⁴/m_χ 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.