Boltzmann suppression of interacting heavy particles - art. no. 045026

Matsumoto and Yoshimura have recently argued that the number density of hea vy particles in a thermal bath is not necessarily Boltzmann suppressed for T much less thanM, as power-law corrections may emerge at higher orders in perturbation theory. This fact might have important implications on the det ermination of weakly interacting massive particle relic densities. On the o ther hand, the definition of number densities in an interacting theory is n ot a straightforward procedure. It usually requires renormalization of comp osite operators and operator mixing, which obscure the physical interpretat ion of the computed thermal average. We propose a new definition for the th ermal average of a composite operator, which does not require any new renor malization counterterm and is thus free from such ambiguities. Applying thi s definition to the annihilation model of Matsumoto and Yoshimura we find t hat it gives number densities which are Boltzmann suppressed at any order i n perturbation theory. We also discuss heavy particles which are unstable a lready at T=0, showing that power-law corrections do in general emerge in t his case.