@article{10272/18371,
year = {2015},
month = {3},
url = {http://hdl.handle.net/10272/18371},
abstract = {We show that the standard theory of thermal production
and chemical decoupling of WIMPs is incomplete.
The hypothesis that WIMPs are produced and decouple from
a thermal bath implies that the rate equation the bath particles
interacting with the WIMPs is an algebraic equation
that constraints the actual WIMPs abundance to have a precise
analytical form down to the temperature x∗ = m  /T∗.
The point x∗, which coincides with the stationary point of the
equation for the quantity  = Y −Y0, is where the maximum
departure of theWIMPs abundance Y from the thermal value
Y0 is reached. For each mass m  and total annihilation cross
section   annvr , the temperature x∗ and the actual WIMPs
abundance Y (x∗) are exactly known. This value provides the
true initial condition for the usual differential equation that
have to be integrated in the interval x ≥ x∗. The matching
of the two abundances at x∗ is continuous and differentiable.
The dependence of the present relic abundance on the abundance
at an intermediate temperature is an exact result. The
exact theory suggests a new analytical approximation that
furnishes the relic abundance accurate at the level of 1–2 %
in the case of S-wave and P-wave scattering cross sections.
We conclude the paper studying the evolution of the WIMPs
chemical potential and the entropy production using methods
of non-equilibrium thermodynamics.},
organization = {Funded by SCOAP3 / License Version CC BY 4.0.},
publisher = {SpringerOpen},
title = {Exact theory of freeze-out},
doi = {10.1140/epjc/s10052-015-3328-6},
author = {Cannoni, Mirco},
}