Decaying Gravitino Dark Matter Michael Grefe Werkstattseminar { 28.04.2009 Outline 1 Gravitino Cosmology 2 2 Bilinear R-parity Breaking 2 3 Gravitino Decay Channels 4 4 Fluxes from Gravitino Dark Matter Decay 6 5 Neutrino Observation 7 6 Signals from Gamma Rays and Antimatter 10 References [1] L. Covi, M. Grefe, A. Ibarra and D. Tran, JCAP 0901 (2009) 029 [arXiv:0809.5030 [hep-ph]]. [2] M. Grefe, DESY-THESIS-2008-043 [3] M. Bolz, A. Brandenburg and W. Buchmuller,¨ Nucl. Phys. B 606 (2001) 518 [Erratum-ibid. B 790 (2008) 336] [arXiv:hep-ph/0012052]. [4] R. Barbier et al., Phys. Rept. 420 (2005) 1 [arXiv:hep-ph/0406039]. [5] T. Montaruli, arXiv:0901.2661 [astro-ph]. [6] K. Ishiwata, S. Matsumoto and T. Moroi, arXiv:0903.0242 [hep-ph]. 1 1 Gravitino Cosmology If gravitinos are in thermal equilibrium in the early universe depending ◦ on the gravitino mass their relic density might overclose the universe. An inflationary phase that dilutes any primordial gravitino density ) is needed! Thermal gravitino production during the reheating phase of the uni- ◦ verse can lead to the correct relic density for dark matter [3]: 2 2 TR 100 GeV mg~ Ω3=2h 0:27 10 : ' 10 GeV m3=2 1 TeV Thermal leptogenesis requires a reheating temperature T & 109 GeV. ◦ R A gravitino mass m & (10) GeV is reasonable. ) 3=2 O If the gravitino is not the lightest supersymmetric particle (LSP) it is ◦ very long-lived due to its MPl suppressed couplings and can spoil the successful predictions of big bang nucleosynthesis (BBN). If the gravitino is the LSP it is a natural candidate for cold ) dark matter. Then the next-to-lightest supersymmetric particle (NLSP) is long-lived and can spoil the BBN predictions. One possible solution is the introduction of a tiny R-parity violation. ◦ It must be large enough to make the NLSP decay into standard model particles before BBN and small enough to guarantee that the baryon asymmetry is not washed out by sphaleron processes before the elec- troweak phase transition. These conditions lead to a gravitino lifetime exceeding the age of ) the universe by many orders of magnitude. 2 Bilinear R-parity Breaking The most general MSSM superpotential contains renormalizable lepton ◦ and baryon number violating terms that are usually removed by the introduction of R-parity to avoid rapid proton decay [4]: = 1 1 W Rp = µ H L + λ L L Ec + λ0 L Q Dc + λ00 U cDcDc : MSSM i u i 2 ijk i j k ijk i j k 2 ijk i j k set to zero in the case of bilinear R= p | {z } 2 R-parity breaking introduces a mixing between the Hd and Li fields. ◦ Thus there is an ambiguity in the choice of the basis for these fields: 0 Hd Hd Hd Lα = 0 = U : Li ! Li Li We choose the basis where the bilinear R-parity breaking term vanishes: ◦ µ µ H = H0 i L0 and L = L0 + i H0 : d d − µ i i i µ d In this case trilinear lepton number violating couplings are generated ◦ from the MSSM superpotential: e c d c W = µHuHd + µiHuLi + λjkHdLjEk + λjkHdQjDk + : : : µ µ W 0 = µH H0 i λe L0 L0 Ec i λd L0 Q Dc + : : : : ! u d − µ jk i j k − µ jk i j k No baryon number violating term is generated in this way. Therefore ◦ the proton stability is maintained. There are also R-parity violating terms in the soft scalar potential: ◦ R= p ~ 2 y ~ Vsoft = BiHuLi + m~ diHdLi + h:c: + : : : : The bilinear R-parity breaking term in the superpotential and those in ◦ the soft scalar potential cannot be rotated away simultaneously. One can easily see that there arises a VEV for the sneutrino fields from ◦ the soft R-parity breaking bilinear terms: 2 ~ 2 ~ 2 y ~ V = mL~ Li + BiHuLi + m~ diHdLi + h:c: + : : : i j j = m2 ν~ 2 + B H0ν~ + m~ 2 (H0)∗ν~ + h:c: + : : : ν~i j ij − i u i di d i @Vmin 2 2 0 = ∗ = mν~i ν~i Bivu + m~ divd @ν~i h i − 2 Bi sin β m~ di cos β ν~i = v −2 : ) h i mν~i In fact one has to perform the minimization of the complete scalar ◦ potential for the Higgs and the sneutrino fields. Then one finds for the sneutrino VEV: 2 Bi sin β m~ di cos β ν~i = v 2 1− 2 : h i mν~i + 2 mZ cos 2β 3 With bilinear R-parity breaking we have Higgs{slepton mixing terms ◦ that appear in the soft scalar potential and gaugino{lepton mixing terms that arise from MSSM gauge vertices in the presence of a sneu- trino VEV. 3 Gravitino Decay Channels The gravitino decay channels are determined by the gravitino interac- ◦ tion Lagrangian and the MSSM gauge Lagrangian: i ∗ ∗i µ ν i i i ν µ int = D φ ¯ν γ γ PLχ Dµφ χ¯ PRγ γ ν L − p2 M µ − Pl i ¯ ν ρ µ (α) a (α) a −2 µ [γ ; γ ] γ λ Fνρ + (MPl ) ; − 8MPl O = p2g λ¯(α) aφ∗iT (α) P χj p2g χ¯iP T (α) φjλ(α) a + : : : : Lgauge − α a; ij L − α R a; ij In the presence of bilinear R-parity breaking we find the following tree ◦ level diagrams for gravitino two-body decays: γ; Z0; W Z0; W 3=2 ν~ + 3=2 ν~; h li h li χ~0; χ~∓ ∓ ∓ νl; l νl; l h h ∗ ν~l 3=2 + 3=2 ν~ ; h li χ~0 νl νl The three-body decays from trilinear R-parity breaking terms are ne- ◦ glected in the calculation. 4 0 10 Wl ν Z l 10-1 ν h l 10-2 Branching Ratio γν l 10-3 100 1000 m3/2 (GeV) Figure 1: Gravitino branching ratios for the two-body decays. 0 Then, for instance, the gravitino decay width into Z and νl is given ◦ by: 2 m3 0 ξl 3=2 2 2 8 mZ 1 Γ Z ν β U f U ~ ~ j + h ; 3=2 ! l ' 64π M 2 Z Z~Z~ Z − 3 m ZZ Z 6 Z Pl 3=2 2 4 ∗ ν~l mZ SZ~αSαZ~ ξl = h i ; βZ = 1 ; UZ~Z~ = mZ ; v − m2 m 0 3=2 Xα=1 χ~α 2 4 2 2 4 2 mZ 1 mZ 1 mZ mZ mZ fZ = 1 + 2 + 4 ; jZ = 1 + 2 ; hZ = 1 + 10 2 + 4 : 3 m3=2 3 m3=2 2 m3=2 m3=2 m3=2 The branching ratios are independent of the sneutrino VEV in contrast ◦ to the total decay width. In the phenomenological studies the lifetime (τ = 1=Γ ) and the ◦ 3=2 3=2 mass are unknown parameters. Most of the two-body decay products are unstable. The lepton l sub- ◦ sequently decays (if l = µ, τ) and the Z0, W and h bosons fragment into stable particles: − + γ ; νi ; e ; e ; p ; p¯: The spectra of γ, ν and e∓ (if l = e) contain a peak from the two-body ◦ i decay and all spectra have a continuum contribution from fragmenta- tion. 5 4 Fluxes from Gravitino Dark Matter Decay If the gravitino accounts for the dark matter, its decays produce an ◦ astrophysical flux of decay products. dJ dN dE ≡ dE dA dt dΩ The differential flux from a volume element in the galactic halo is given ◦ by (~l = (s; b; l) are galactic coordinates): ~ ~ dJ(l) n3=2(l) dN 2 = 2 s cos b ds db dl : dE 4π s τ3=2 dE In contrast to charged particles (see Christoph's talk) gamma rays and ◦ neutrinos propagate freely over cosmic distances (neutrino oscillations distribute the signal equally into all flavors). Thus the differential flux is simply given by the line-of-sight integral dJhalo(b; l) 1 dN ~ = %halo(l) ds : dE 4π τ3=2 m3=2 dE Z line of sight There is a second, subdominant contribution from the cosmic dark ◦ matter density: 1 dJ Ω % dN (1 + z)−3=2dz eg = 3=2 c : 1=2 −3 dE 4π τ3=2 m3=2H0Ωm Z d(E (1 + z)) 1 + ΩΛ=Ωm (1 + z) 0 p In the case of WIMP annihilation the halo flux reads ◦ dJhalo(b; l) σv dN 2 ~ = h 2i %halo(l) ds : dE 8π mDM dE Z line of sight 2 Due to the nDM dependence the signal from annihilating dark matter ◦ is much more sensitive to the dark matter distribution in the halo and in particular to the inner slope of the halo profile. In that case one expects a dominant signal from the galactic center and ◦ also neutrino signals from the annihilation of WIMPs that accumulate inside the Sun and the Earth. 6 ) -2 ) -2 -1 10 -1 10 atmospheric neutrinos upper hemisphere sr -3 sr -3 -1 10 -1 10 s νµ s νµ -2 -4 ν -2 -4 ν 10 e 10 e ν τ ν 10-5 10-5 τ 10-6 10-6 10-7 10-7 x dJ/dE (GeV cm -8 m3/2 = 300, 600, 1200 GeV x dJ/dE (GeV cm -8 m3/2 = 300, 600, 1200 GeV 2 10 2 10 E E 0.1 1 10 100 1000 10000 0.1 1 10 100 1000 10000 E (GeV) E (GeV) Figure 2: Neutrino flux from gravitino decay compared to the atmospheric background for the complete sky (left) and for the upper hemisphere (right).