Abstract
Abstract There is an increasing interest in accurate dark matter relic density predictions, which requires next-to-leading order (NLO) calculations. The method applied up to now uses zero-temperature NLO calculations of annihilation cross sections in the standard Boltzmann equation for freeze-out, and is conceptually problematic, since it ignores the finite-temperature infrared (IR) divergences from soft and collinear radiation and virtual effects. We address this problem systematically by starting from non-equilibrium quantum field theory, and demonstrate on a realistic model that soft and collinear temperature-dependent divergences cancel in the collision term. Our analysis provides justification for the use of the freeze-out equation in its conventional form and determines the leading finite-temperature correction to the annihilation cross section. This turns out to have a remarkably simple structure.
Highlights
Ii) one can adopt the quasi-particle approximation, one arrives at a semi-classical description
The method applied up to now uses zero-temperature next-to-leading order (NLO) calculations of annihilation cross sections in the standard Boltzmann equation for freeze-out, and is conceptually problematic, since it ignores the finite-temperature infrared (IR) divergences from soft and collinear radiation and virtual effects. We address this problem systematically by starting from non-equilibrium quantum field theory, and demonstrate on a realistic model that soft and collinear temperaturedependent divergences cancel in the collision term
The present work was motivated by the observation that existing approaches to calculating the DM relic density at NLO are based on zero-temperature calculations of the annihilation cross section in the standard freeze-out equation
Summary
Ii) one can adopt the quasi-particle approximation, one arrives at a semi-classical description. It has been noted recently that corrections to the annihilation rate can affect non-negligibly the relic density computation [1,2,3,4,5,6,7,8] With this in mind the first numerical codes including the higher-order corrections are being developed, SloopS [9,10,11] and DM@NLO [12, 13]. What is usually done is to compute the virtual and real radiation corrections to the two-particle processes χχ → ij using standard quantum field theory methods at zero temperature This procedure raises a number of questions, especially for relic density computations, since freeze-out occurs when the temperature of the Universe is small, but non-negligible compared to the DM particle mass. Absorption processes exist, but are neglected in the computation
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