Exact theory of freeze-out
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 ac...
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| Format: | article |
| Publication Date: | 2015 |
| Country: | España |
| Institution: | Universidad de Huelva (UHU) |
| Repository: | Arias Montano. Repositorio Institucional de la Universidad de Huelva |
| Language: | English |
| OAI Identifier: | oai:ariasmontano.uhu.es:10272/18371 |
| Online Access: | http://hdl.handle.net/10272/18371 |
| Access Level: | Open access |
| Keyword: | Freeze-out Thermal production WIMPs |
| Summary: | 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. |
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