Mohamad-Ziad Charif - Antares

dΦ µdE ν= dΦ νdE νP earth ρN A σ CC (E ν )R e f f (E ν ) (5.5)dΦ µdE ν.A E f fµ = dΦ νdE ν.A E f fν (5.6)where, P Earth : Probability of a neutrino not interacting in Earth (Figure 5.28).ρ: Density of matter. σ CC : Charged Current cross-section (Figure 5.29). R e f f :Effective muon range (Figure 5.30).Figure 5.28: Probability of a ¯ν/ν not interacting in Earth as a function of its energy[108] .From eq 5.5 we can use P Earth , σ CC and R e f f as a conversion factor betweenneutrino flux and muon flux and we can transform our neutrino limits into muonlimits as we can see in figure 5.31.As we have seen in chapter 2, we can go from the µ or ν flux to the annihilationrate Γ inside the sun, and if we further assume there is an equilibriumbetween Γ and the capture rate C of WIMPs we can put limits on the σ SD andon σ SI as seen figure 5.32 & 5.33. It is obvious from the last three figures thatwhile we are able probe some of the CMSSM parameter space in Spin-dependentcross-section (Figure 5.32) and just starting to close in on the spin-independentregion (Figure 5.33), but the limits imposed by ANTARES when compared toother experiments are not exactly competitive (Figure 5.31). The limits presentedby the SuperK experiment[109] dominate at WIMP masses below 180 GeV, while104