Accurate Neutralino Relic Density. Paolo Gondolo

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1 Accurate Neutralino Relic Density Paolo Gondolo

2 The concordance cosmology Adapted from L. Verde

3 The best matter density WMAP (Bennett et al., 2003) of which Ω m h 2 = Ω ν h 2 < (95%CL) Ω b h 2 = ± Ω CDM h 2 = (Units are g/cm 3 = 18.79yg/m 3 )

4 Smaller error bars on Ω m WMAP: first year data Ω cdm h 2 = error is 7% Planck: Ω m to 1%

5 Cosmology and msugra Cosmological data on Ω χ h 2 : expect 1% WMAP first year data: Ω CDM h 2 = (7%) Compute Ω χ h 2 to 1%

6 Cosmology and msugra Cosmological data on Ω χ h 2 : expect 1% WMAP first year data: Ω CDM h 2 = (7%) Compute Ω χ h 2 to 1% From e.w. scale to relic density: 1% Edsjö, Schelke, Ullio, Gondolo 2003

7 Cosmology and msugra Cosmological data on Ω χ h 2 : expect 1% WMAP first year data: Ω CDM h 2 = (7%) Compute Ω χ h 2 to 1% From e.w. scale to relic density: 1% Edsjö, Schelke, Ullio, Gondolo 2003 From GUT parameters to e.w. scale: 50% See Allanach, Kraml, Porod 2003

8 . From e.w. scale to relic density

9 Relic density to 1% Gondolo,Gelmini 1991 Edsjö,Gondolo 1997 Edsjö,Schelke,Ullio,Gondolo 2003 Ω χ to cosmology precision (1%) relativistic corrections resonances, thresholds coannihilations

10 . Accelerator bounds Relic density Scattering off nucleons Signals in neutrino telescopes Gamma-ray signals Cosmic-ray positrons Cosmic-ray antiprotons Signals from galactic center Gondolo, Edsjö, Ullio, Bergström, Schelke, Baltz

11 Relic density - the basics Decoupling when Γ ann H where Γ ann = σv n χ = Ω χ cm 3 /s σv

12 Relic Density Density equation ṅ + 3Hn = σv (n 2 n 2 eq ) Stiff equation: requires special numerical method Relativistic thermal average (v c/3) σv = 0 dp p 2 W(p) K 1 ( s/t) m 4 T [K 2 (m/t)] 2 W(p) = annihilation rate per unit volume and unit time Gondolo, Gelmini 1991

13 What not to do... σv = a + bv 2 + σv = a b T m + Problems near resonances and thresholds (negative σv, e.g.) resonances σv threshold thermal distr. momentum

14 Coannihilations Depletion through chain of reactions χ 0 1 e χ 2 ν e χ 2 χ0 2 du χ 0 2 χ0 1 W + W χ 0 1 τ τγ τ χ + 1 τw + Possible if m T Binetruy,Girardi,Salati 1984; Griest,Seckel 1991

15 Effective σv σ eff v = 1 n 2 tot ij θ(v ij )n i n j v ij σ(ij all) Coannihilations appear as thresholds in σ eff v. Edsjö,Gondolo 1997

16 Example σ eff v as function of p cm W eff / (4E eff 2) [cm 3 s -1 ] With coannihilations 0 χ 1 t ẽ/µ t 0 χ 1 ẽ/µ ẽ/µ ẽ/µ t t τ t < σ eff v > τ ẽ/µ κ [GeV -1 ] τ τ χ 1 0 τ T = m χ /24.3 Ω χ h 2 = m χ = GeV m τ = GeV m µ = GeV m ẽ = GeV m t = GeV p eff [GeV] κ m 0 = 387GeV, m 1/2 = 950GeV, tan β = 10, A 0 = 3770GeV, µ > 0

17 (Co)annihilation processes Several thousands! Diagrams Process s t u p χ 0 i χ0 j B0 m B0 n H 0 1,2,3, Z χ0 k χ 0 l χ 0 i χ0 j B m B+ n H 0 1,2,3, Z χ+ k χ + l χ 0 i χ0 j f f H 0 1,2,3, Z f1,2 f1,2 χ + i χ0 j B+ m B0 n H +, W + χ 0 k χ + l χ + i χ0 j f u f d H +, W + f d1,2 f u1,2 χ + i χ j B0 m B0 n H 0 1,2,3, Z χ+ k χ + l χ + i χ j B+ m B n H 0 1,2,3, Z, γ χ0 k χ + i χ j f u f u H 0 1,2,3, Z, γ f d1,2 χ + i χ j f d f d H 0 1,2,3, Z, γ f u1,2 χ + i χ+ j B+ m B+ n χ 0 k χ 0 l f i χ 0 j B0 f f f1,2 χ 0 l f di χ 0 j B f u f d fu1,2 χ + l f ui χ 0 j B+ f d f u fd1,2 χ + l Diagrams Process s t u p f di χ + j B0 f u f u fd1,2 χ + l f ui χ + j B+ f u fd1,2 χ 0 l f di χ + j B+ f d f u χ 0 l f ui χ j B0 f d f d fu1,2 χ + l f ui χ j B f u f d χ 0 l f di χ j B f d fu1,2 χ 0 l f di f dj B 0 m B0 n H 0 1,2,3, Z, g fd1,2 fd1,2 p f di f dj B m B+ n H 0 1,2,3, Z, γ fu1,2 p f f di dj f d f d f u H 0 1,2,3, Z, γ, g χ0 k, g f f di dj f u H1,2,3 0, Z, γ, g χ+ k f di f dj f d f d χ 0 k, g χ0 l, g f ui f dj B + m B0 n H +, W + fd1,2 fu1,2 p f f ui dj f u f d H +, W + χ 0 k, g f ui f dj f u f d χ 0 k, g χ+ l

18 Annihilation amplitudes W(p) = d LIPS A(χχ all) 2 spin Spin amplitudes in covariant formalism Analytic expressions (REDUCE)

19 WMAP and msugra m 0 [GeV] tan β = 30, A 0 = 0 GeV, µ < 0 With coannihilations Excluded [WMAP added by P.G., 2003] J. Edsjö, M. Schelke, P. Ullio and P. Gondolo, 2003 WMAP m χ + = 104 GeV m χ 0 = 80 GeV Ω χ h 2 = 0.3 m χ 0 = 175 GeV WMAP m 1/2 [GeV]

20 From GUT to e.w. scale.

21 LC/LHC/mSUGRA/DM 1600 msugra with tanβ = 45, A 0 = 0, µ < 0 Ωh 2 < LEP2 excluded m 1/2 (GeV) LHC 600 LC LC 500 Tevatron m 0 (GeV) Baer,Belyaev,Krupovnickas,Tata 2003

22 msugra spectra kraml.home.cern.ch/kraml/comparison/compare.html m 0 = 565, m 1/2 = 1000, A 0 = 0, tan β = 45, µ < 0 Calculating... Isajet Softsusy [ Tachyon ] Spheno Suspect Warning: RGE problems (non-pert and/or Landau poles) Done. Status code: 0 Sparticle Isajet Softsusy Spheno Suspect % w/o Suspect nt ch h % H % A % H %...

23 Conclusions cosmological considerations are important now accurate neutralino relic density (1%) is essential from e.w. scale to relic density under control from GUT to e.w. scale needs more work