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Mohamad-Ziad Charif - Antares

Mohamad-Ziad Charif - Antares

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2.2 WIMPs2.2.1 Standard ScenarioThe standard view of WIMPs is that it is an electrically neutral particle that itsexistence can not be inferred by direct electromagnetic radiations, and since wealready established it can not be a baryonic then it should be colorless (no stronginteraction). In addition, this particle has to be stable or at least if it is not then itshalf-life should be extremely long (at least the current age of the Universe). Unfortunatelythese characteristics do not apply to any known particle in the StandardModel of particle physics. Several extensions of this model offer candidates toWIMPs such as the lightest SuperSymmetric particle (LSP) in Supersymmetry(section 2.2.2), in addition to the lightest Kaluza-Klein particle (LKP) in UniversalExtra Dimension[27, 28] models.The main attraction for WIMPs as a candidate for cold dark matter comes fromthe fact that if we try to calculate the WIMPs annihilation cross-section in orderto get the same order of magnitude of the density we have now Ω c (t 0 ) = 0.227we would get a cross section similar to that of the weak force (eq 2.9), the orderof magnitude of a weak cross-section 10 −9 GeV −2 (∼ ( gM W) 4 ) where g couplingconstant of the weak interaction and M W is the W boson mass. M WIMP is the massof the WIMP, N WIMP (t 0 ) is the number of WIMP particles at the present time.Ω WIMP (t 0 ) = M WIMP.N WIMP (t 0 )ρ c (t o )≃10−10 GeV −2< σv >(2.9)(2.10)Equation 2.9 is obtained by first deriving the number of WIMP particles as afunction of time. Standard scenario of WIMPs puts them in thermal equilibriumwith other particles, after their creation in the early Universe. After the Universecools down by expanding, the temperature drops below the WIMP mass haltingtheir creation and resulting in an rapid decrease of their abundance. Eventuallythe thermal equilibrium of WIMPs can not be maintained as the expansion of theUniverse reaches a point where it is larger than the WIMP rate of annihilation,consequently this results in a relic WIMP density that can account for the valuewe have now. This evolution can be described using Boltzmann equation shown inequation 2.11, where H is the Hubble parameter, N WIMP is the number of WIMPsas a function of time and N eqWIMPis the number of WIMPs at thermal equilibrium,and < σv > is the thermally averaged annihilation cross-section of WIMPs multipliedby its velocity.dN WIMPdt+ 3H.N WIMP = < σv > [(N eqWIMP )2 − N 2 WIMP] (2.11)13

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