Gravitino Dark Matter p.1/42. with broken R-parity

Transcription

1 Gravitino Dark Matter with broken R-parity In collaboration with Alejandro Ibarra DESY W. Buchmüller, L. Covi, K. Hamaguchi and T. Yanagida (JHEP 0703:037, 2007) G. Bertone, W. Buchmüller, L. Covi (JCAP11(2007)003) D. Tran (arxiv: To appear in PRL) Bonn 24th January 2008 Gravitino Dark Matter p.1/42

2 Outline Introduction: thermal history of the Universe. Supersymmetric dark matter. Constraints. Gravitino cosmology/next-to-lsp cosmology. Gravitino dark matter with broken R-parity. A model for small R-parity breaking. Experimental signatures from gamma ray observatories and colliders Conclusions. Gravitino Dark Matter p.2/42

3 Introduction Standard thermal history of the Universe Temperature time 1eV s decoupling of photons/cmb 1MeV 1s decoupling of neutrinos 0.1MeV-10MeV s BBN 100MeV 10 4 s QCD phase transition 100GeV s EW phase transition GeV s leptogenesis??? reheating?? inflation? 0 Big Bang Gravitino Dark Matter p.3/42

4 New elements have to be incorporated into the thermal history of the Universe: Dark matter Dark energy Cosmic pie determined by WMAP Gravitino Dark Matter p.4/42

5 New elements have to be incorporated into the thermal history of the Universe: Dark matter Dark energy Cosmic pie determined by WMAP Gravitino Dark Matter p.4/42

6 More evidences for dark matter Gravitino Dark Matter p.5/42

7 Clowe et al. astro-ph/ Composite image from NASA of the Bullet Cluster (1E ). Superposition of an optical image by the Hubble Space Telescope, an X-ray image from Chandra (red), and a weak lensing map (blue). The X-ray image shows the distribution of hot gas (baryonic matter) and the weak lensing map, the distribution of matter. There is more matter apart from the baryonic matter = direct evidence for dark matter? Gravitino Dark Matter p.6/42

8 Candidates for dark matter Many! Some interesting candidates are: Massive SM neutrinos (now excluded) Axions Heavy sterile neutrinos Gravitino Dark Matter p.7/42

9 Candidates for dark matter Many! Some interesting candidates are: Massive SM neutrinos (now excluded) Axions Heavy sterile neutrinos Neutralinos (requires R-parity) Gravitinos Gravitino Dark Matter p.7/42

10 Candidates for dark matter Many! Some interesting candidates are: Massive SM neutrinos (now excluded) Axions Heavy sterile neutrinos Neutralinos (requires R-parity) Gravitinos Axinos Gravitino Dark Matter p.7/42

11 Candidates for dark matter Many! Some interesting candidates are: Massive SM neutrinos (now excluded) Axions Heavy sterile neutrinos Neutralinos (requires R-parity) Gravitinos Axinos Lightest Kaluza-Klein particle... Gravitino Dark Matter p.7/42

12 Candidates for dark matter Many! Some interesting candidates are: Massive SM neutrinos (now excluded) Axions Heavy sterile neutrinos Neutralinos (requires R-parity) Gravitinos Axinos Lightest Kaluza-Klein particle... Gravitino Dark Matter p.7/42

13 Goal: construct a consistent thermal history of a Universe with supersymmetric dark matter (neutralino/gravitino) Constraints: leptogenesis ((T > 10 9 GeV, t < s) BBN (T MeV, t s) CMB (T 1eV, t s) And of course, the relic dark matter abundance should be the observed one Ω DM Gravitino Dark Matter p.8/42

14 Goal: construct a consistent thermal history of a Universe with supersymmetric dark matter (neutralino/gravitino) Constraints: leptogenesis ((T > 10 9 GeV, t < s) BBN (T MeV, t s) CMB (T 1eV, t s) And of course, the relic dark matter abundance should be the observed one Ω DM Gravitino Dark Matter p.8/42

15 Leptogenesis After the discovery of neutrino oscillations, leptogenesis stands as one of the most appealing explanations for the observed baryon asymmetry of the Universe. Simplest realization: the lightest right-handed neutrino decays out of equilibrium, producing a lepton asymmetry. Sphaleron processes partially convert the lepton asymmetry into a baryon asymmetry. η B = n B nγ 0.01ǫ 1 κ f Fukugita, Yanagida Buchmüller, di Bari, Plümacher ǫ 1 CP asymmetry M 1 m 3 H 0 2 ǫ 1 3 Davidson, A.I. 8π = Lower bound on M 1 κ f efficiency factor, that can be parametrized by em 1 = Y Y M 1 H 0 2 M1 (GeV) m 1 (ev) Gravitino Dark Matter p.9/42

16 Leptogenesis After the discovery of neutrino oscillations, leptogenesis stands as one of the most appealing explanations for the observed baryon asymmetry of the Universe. Simplest realization: the lightest right-handed neutrino decays out of equilibrium, producing a lepton asymmetry. Sphaleron processes partially convert the lepton asymmetry into a baryon asymmetry. η B = n B nγ 0.01ǫ 1 κ f Fukugita, Yanagida Buchmüller, di Bari, Plümacher ǫ 1 CP asymmetry M 1 m 3 H 0 2 ǫ 1 3 Davidson, A.I. 8π = Lower bound on M 1 κ f efficiency factor, that can be parametrized by em 1 = Y Y M 1 H 0 2 M1 (GeV) T R > 10 9 GeV m 1 (ev) Gravitino Dark Matter p.9/42

17 ???? Big Bang Nucleosynthesis Baryon density Ω B h He Y p D H 3 He/H p The Standard Model prediction for the abundances of primordial elements are in good overall agreement with the observations D/H p?@ Fields, Sarkar, for PDG BBN CMB Li/H p Baryon-to-photon ratio η Gravitino Dark Matter p.10/42

18 If the gravitino is NOT the lightest supersymmetric particle (i.e. the neutralino is the LSP), it decays into the lightest neutralino and a photon: ψ 3/2 χ 0 1γ. Potentially problematic for BBN! The photons can dissociate the light-elements if the photon energy is above a certain threshold. For example D +γ n + p, E th = 2.225MeV Kawasaki, Moroi Gravitino Dark Matter p.11/42

19 Even worst, if m 3/2 > m g the gravitino could decay into gluon and gluino, that hadronize producing energetic hadrons hadro-dissociation of the primordial elements. Other hadronic channels are also dangerous. Kawasaki, Kohri, Moroi Gravitino Dark Matter p.12/42

20 Even worst, if m 3/2 > m g the gravitino could decay into gluon and gluino, that hadronize producing energetic hadrons hadro-dissociation of the primordial elements. Other hadronic channels are also dangerous. Kawasaki, Kohri, Moroi Difficult to reconcile with the leptogenesis requirement T R > 10 9 GeV. Hadronic decays of the gravitino are an important constraint for the scenario with thermal leptogenesis and neutralino dark matter. Gravitino Dark Matter p.12/42

21 Solutions: Very heavy gravitino (anomaly mediation) Ibe, Kitano, Murayama, Yanagida late-time entropy production Kohri, Yamaguchi, Yokoyama The standard (thermal) leptogenesis scenario is not valid. Alternative mechanisms have to be advocated working at lower T : resonant leptogenesis, Affleck-Dine baryo/leptogenesis, electroweak baryogenesis... The gravitino IS the LSP gravitino dark matter Pagels, Primack 81 Gravitino Dark Matter p.13/42

22 Solutions: Very heavy gravitino (anomaly mediation) Ibe, Kitano, Murayama, Yanagida late-time entropy production Kohri, Yamaguchi, Yokoyama The standard (thermal) leptogenesis scenario is not valid. Alternative mechanisms have to be advocated working at lower T : resonant leptogenesis, Affleck-Dine baryo/leptogenesis, electroweak baryogenesis... The gravitino IS the LSP gravitino dark matter Pagels, Primack 81 Gravitino Dark Matter p.13/42

23 Gravitino dark matter Gravitinos are thermally produced in the early Universe by QCD processes. For example: g a G g a G g a G g a G g c + g a + g b + g b g c g b g c g b g c g b g c Also produced by non-thermal processes (inflaton decay, NLSP decay) Gravitino Dark Matter p.14/42

24 Gravitino dark matter Gravitinos are thermally produced in the early Universe by QCD processes. For example: g a G g a G g a G g a G g c + g a + g b + g b g c g b g c g b g c g b g c Also produced by non-thermal processes (inflaton decay, NLSP decay) The relic abundance is proportional to T R Bolz, Brandemburg, Buchmüller Gravitino Dark Matter p.14/42

25 Gravitino dark matter Gravitinos are thermally produced in the early Universe by QCD processes. For example: g a G g a G g a G g a G g c + g a + g b + g b g c g b g c g b g c g b g c Also produced by non-thermal processes (inflaton decay, NLSP decay) The relic abundance is proportional to T R Ω 3/2 h TR 5 GeV ` m eg 10 9 GeV m 3/2 500 GeV 2 Bolz, Brandemburg, Buchmüller Gravitino Dark Matter p.14/42

26 Gravitino dark matter Gravitinos are thermally produced in the early Universe by QCD processes. For example: g a G g a G g a G g a G g c + g a + g b + g b g c g b g c g b g c g b g c Also produced by non-thermal processes (inflaton decay, NLSP decay) The relic abundance is proportional to T R Ω 3/2 h TR 5 GeV ` m eg 10 9 GeV m 3/2 500 GeV Very interesting candidate for dark matter. Theoretically very attractive: all interactions are fixed by symmetries. And also, it is nicely compatible with leptogenesis! (But it is undetectable with direct searches) 2 Bolz, Brandemburg, Buchmüller Gravitino Dark Matter p.14/42

27 The next-to-lightest SUSY particle Most likely candidates: lightest neutralino, lightest charged slepton (right-handed stau). (In some speciphic models, the NLSP could also be a sneutrino or a stop.) If the gravitino is the LSP and R-parity is conserved, the NLSP can only decay gravitationally into gravitinos and SM particles, with a decay rate suppressed by M P : Stau: eτ R τψ 3/2, Γ eτ Neutralino: χ 0 1 γψ 3/2, m 5 eτ 48πm 2 3/2 M2 P τ eτ 9 days = very long lifetimes. m3/2 10GeV τ eχ days 2 m3/2 10GeV 5 150GeV m eτ 2 150GeV m eχ 0 1 «5 (for χ 0 1 = eγ). The NLSP is present during and after BBN. The decays could jeopardize the abundances of primordial elements. Gravitino Dark Matter p.15/42

28 Neutralino NLSP The photons from χ 0 1 γψ 3/2 can dissociate primordial elements. Also, χ 0 1 Zψ 3/2 could be kinematically allowed, and the hadronic decays of the Z could be disastreous. For χ 0 1 = B, e Feng, Su, Takayama Gravitino Dark Matter p.16/42

29 Neutralino NLSP The photons from χ 0 1 γψ 3/2 can dissociate primordial elements. Also, χ 0 1 Zψ 3/2 could be kinematically allowed, and the hadronic decays of the Z could be disastreous. For χ 0 1 = B, e Incompatible with leptogenesis (m 3/ GeV). Feng, Su, Takayama Gravitino Dark Matter p.16/42

30 Right-handed stau NLSP The two body decay eτ R τψ 3/2 only releases electromagnetic energy. Hadronic decays only arise in three body decay processes: eτ R τzψ 3/2 or eτ R ν τ Wψ 3/2, with suppressed branching ratio. Feng, Su, Takayama Gravitino Dark Matter p.17/42

31 Right-handed stau NLSP The two body decay eτ R τψ 3/2 only releases electromagnetic energy. Hadronic decays only arise in three body decay processes: eτ R τzψ 3/2 or eτ R ν τ Wψ 3/2, with suppressed branching ratio. Feng, Su, Takayama Compatible with leptogenesis (m 3/ GeV)! The revised thermal history of the Universe seems to point to gravitino LSP, with m 3/ GeV, and stau NLSP. Gravitino Dark Matter p.17/42

32 A new turn of the screw Recently another effect of stau NLSP during BBN has been realized: stau catalysis of lithium 6. Pospelov D γ D 6 Li 4 He 6 Li ( 4 HeX ) X 4 He + D 6 Li + γ ( 4 HeX ) + D 6 Li + X Gravitino Dark Matter p.18/42

33 A new turn of the screw Recently another effect of stau NLSP during BBN has been realized: stau catalysis of lithium 6. Pospelov D γ D 6 Li 4 He 6 Li ( 4 HeX ) X 4 He + D 6 Li + γ ( 4 HeX ) + D 6 Li + X The cross section for the catalyzed channel is around eight orders of magnitude larger than the standard channel! This leads to an overproduction of 6 Li of a factor Gravitino Dark Matter p.18/42

34 Summary of the implications of a high reheat temperature (T R > 10 9 GeV) for SUSY dark matter: neutralino LSP gravitino LSP neutralino NLSP RH stau NLSP other candidates ψ 3/2 χ 0 1 hadrons χ 0 1 ψ 3/2 hadrons Catalytic production stop Hadrodissociation of Hadrodissociation of of 6 Li LH sneutrino primordial elements primordial elements RH sneutrino Conflict with BBN Conflict with BBN Conflict with BBN Gravitino Dark Matter p.19/42

35 Summary of the implications of a high reheat temperature (T R > 10 9 GeV) for SUSY dark matter: neutralino LSP gravitino LSP neutralino NLSP RH stau NLSP other candidates ψ 3/2 χ 0 1 hadrons χ 0 1 ψ 3/2 hadrons Catalytic production stop Hadrodissociation of Hadrodissociation of of 6 Li LH sneutrino primordial elements primordial elements RH sneutrino Conflict with BBN Conflict with BBN Conflict with BBN BBN is the Achilles heel of SUSY dark matter Root of all the problems: the NLSP is very long lived. Simple solution: get rid of the NLSP before BBN R-parity violation Gravitino Dark Matter p.19/42

36 Gravitino DM with broken R-parity When R-parity is broken, the superpotential reads: W = W MSSM + µ i (H u L i ) λ ijk(l i L j )e c k + λ ijk(q i L j )d c k + λ ijk(u c id c jd c k) The coupling λ ijk induces the decay of the right-handed stau. For example, eτ R µ ν τ with lifetime: τ eτ 10 3 s ` λ 2 ` m eτ GeV Even with a tiny amount of R-parity violation (λ > ) the stau will decay before the time of BBN. Gravitino Dark Matter p.20/42

37 Gravitino DM with broken R-parity When R-parity is broken, the superpotential reads: W = W MSSM + µ i (H u L i ) λ ijk(l i L j )e c k + λ ijk(q i L j )d c k + λ ijk(u c id c jd c k) The coupling λ ijk induces the decay of the right-handed stau. For example, eτ R µ ν τ with lifetime: τ eτ 10 3 s ` λ 2 ` m eτ GeV Even with a tiny amount of R-parity violation (λ > ) the stau will decay before the time of BBN. The lepton/baryon number violating couplings λ, λ, λ can erase the lepton/baryon asymmetry. The requirement that an existing baryon asymmetry is not erased before the electroweak transition implies: λ, λ < 10 7 Campbell, Davidson, Ellis, Olive Fischler, Giudice, Leigh, Paban Dreiner, Ross Plenty of room! < λ, λ < In this range leptogenesis is unaffected. Gravitino Dark Matter p.20/42

38 Interestingly, even though the gravitino is not stable anymore, it still constitutes a viable dark matter candidate. It decays for example ψ 3/2 νγ, with lifetime: τ 3/ s ` 3 (Remember: age of the Universe s) λ 2 m3/ GeV Stable enough to constitute the dark matter of the Universe. Takayama, Yamaguchi Gravitino Dark Matter p.21/42

39 Interestingly, even though the gravitino is not stable anymore, it still constitutes a viable dark matter candidate. It decays for example ψ 3/2 νγ, with lifetime: τ 3/ s ` 3 (Remember: age of the Universe s) λ 2 m3/ GeV Stable enough to constitute the dark matter of the Universe. Takayama, Yamaguchi In summary: The existence of a gravitino LSP with a mass in the range GeV, and a small amount of R-parity violation < λ, λ < 10 7, is consistent with the standard thermal history of the Universe + SUSY dark matter (allows leptogenesis, and does not spoil BBN or CMB observations). Gravitino Dark Matter p.21/42

40 Interestingly, even though the gravitino is not stable anymore, it still constitutes a viable dark matter candidate. It decays for example ψ 3/2 νγ, with lifetime: τ 3/ s ` 3 (Remember: age of the Universe s) λ 2 m3/ GeV Stable enough to constitute the dark matter of the Universe. Takayama, Yamaguchi In summary: The existence of a gravitino LSP with a mass in the range GeV, and a small amount of R-parity violation < λ, λ < 10 7, is consistent with the standard thermal history of the Universe + SUSY dark matter (allows leptogenesis, and does not spoil BBN or CMB observations). Question 1: is < λ, λ < 10 7 reasonable? Question 2: which are the experimental signatures for this scenario? Gravitino Dark Matter p.21/42

41 A model for small (and peculiar) R-parity breaking Buchmüller, Covi, Hamaguchi AI, Yanagida We want to construct a model with small lepton number violation (10 14 < λ,λ < 10 7 ) and tiny baryon number violation ( λ λ < ) Some insights to construct such a model: For convenience, we use SO(10) notation (but no GUT in our model!). Quarks and leptons in 16 i, Higgses in 10 H. To give Majorana masses to neutrinos, B L has to be broken, either by a 16, 16 (with B L = ±1), or by 126 (with B L = 2). To have just small representations, we use 16 and 16 R-parity is necessarily broken when = v B L. Gravitino Dark Matter p.22/42

42 There are two type of terms in the superpotential: 16 i 16 j 10 H. Good term. Produces Dirac masses. 16 i 16 j Good term. Produces right-handed neutrino masses. 16 i 1610 H. Bad term. Produces v B L LH u. Too large neutrino masses. 16 i 16 j 16 k 16. Bad term. Produces v B L M P u c d c d c, v B L M P QLd c. Too fast p decay. Gravitino Dark Matter p.23/42

43 There are two type of terms in the superpotential: 16 i 16 j 10 H. Good term. Produces Dirac masses. 16 i 16 j Good term. Produces right-handed neutrino masses. 16 i 1610 H. Bad term. Produces v B L LH u. Too large neutrino masses. 16 i 16 j 16 k 16. Bad term. Produces v B L M P u c d c d c, v B L M P QLd c. Too fast p decay. Key point: the bad terms always involve the 16. We cannot get rid of 16, but we can try to suppress/forbid the couplings. Gravitino Dark Matter p.23/42

44 There are two type of terms in the superpotential: 16 i 16 j 10 H. Good term. Produces Dirac masses. 16 i 16 j Good term. Produces right-handed neutrino masses. 16 i 1610 H. Bad term. Produces v B L LH u. Too large neutrino masses. 16 i 16 j 16 k 16. Bad term. Produces v B L M P u c d c d c, v B L M P QLd c. Too fast p decay. Key point: the bad terms always involve the 16. We cannot get rid of 16, but we can try to suppress/forbid the couplings. We will forbid the bad terms by means of a U(1) R symmetry: 16 i 10 H R (the SO(10) singlet has been introduced to break the R-symmetry). With this assignment, holomorphicity guarantees that there is no R-parity violation in the superpotential. Gravitino Dark Matter p.23/42

45 There are two type of terms in the superpotential: 16 i 16 j 10 H. Good term. Produces Dirac masses. 16 i 16 j Good term. Produces right-handed neutrino masses. 16 i 1610 H. Bad term. Produces v B L LH u. Too large neutrino masses. 16 i 16 j 16 k 16. Bad term. Produces v B L M P u c d c d c, v B L M P QLd c. Too fast p decay. Key point: the bad terms always involve the 16. We cannot get rid of 16, but we can try to suppress/forbid the couplings. We will forbid the bad terms by means of a U(1) R symmetry: 16 i 10 H R (the SO(10) singlet has been introduced to break the R-symmetry). With this assignment, holomorphicity guarantees that there is no R-parity violation in the superpotential. Key point 2: the Kähler potential is not protected by holomorphicity. Terms line i 10 H, i 10 H can appear in the Kähler potential, producing eventually bilinear R-parity violation. Gravitino Dark Matter p.23/42

46 The model Particle content: 16 i 10 H R Gravitino Dark Matter p.24/42

47 The model Particle content: Q, u c, e c, d c, L, ν c H u, H d N N c Φ X Z B L ±1/3, ± R Φ and Z are spectator fields, Φ = v B L and Z = F Z θθ. The effective theory is described by W W MSSM + W ν c + W Rp : W MSSM = h e LH d e c + h d QH d d c + h u QH u u c + µh u H d W ν c = h ν LH u ν c + Mν c ν c, with M 3 v2 B L M P W Rp = 1 2 λ LLec + λ QLd c + λ u c d c d c λ C v2 B L M 2 P λ C v2 B L M 2 P λ m 3/2 v 4 B L M 5 P h e C M 3 M P h e h d C M 3 M P h d m 3/2 M P M3 M P 2 Gravitino Dark Matter p.24/42

48 The model Particle content: Q, u c, e c, d c, L, ν c H u, H d N N c Φ X Z B L ±1/3, ± R Φ and Z are spectator fields, Φ = v B L and Z = F Z θθ. The effective theory is described by W W MSSM + W ν c + W Rp : W MSSM = h e LH d e c + h d QH d d c + h u QH u u c + µh u H d W ν c = h ν LH u ν c + Mν c ν c, with M 3 v2 B L M P = W Rp 1 λ 2 LLec + λ QLd c + λ u c d c d c λ C v2 B L M 2 P λ C v2 B L M 2 P λ m 3/2 v 4 B L M 5 P h e C M 3 M P h e h d C M 3 M P h d m 3/2 M P M3 M P 2 In a particular flavour model λ 10 7 h e Buchmüller, Yanagida λ 10 7 h d λ Then, λ 3ij, λ 3ij 10 8, within < λ, λ < 10 7 Gravitino Dark Matter p.24/42

49 I- Signatures at gamma ray observatories The gravitino lifetime is much longer than the age of the Universe, but a few decays are happening NOW, and the decay products could be observed. In particular, the photon flux could be observable as an extragalactic diffuse gamma-ray flux with a characteristic spectrum. Shining dark matter Gravitino Dark Matter p.25/42

50 I- Signatures at gamma ray observatories The gravitino lifetime is much longer than the age of the Universe, but a few decays are happening NOW, and the decay products could be observed. In particular, the photon flux could be observable as an extragalactic diffuse gamma-ray flux with a characteristic spectrum. Shining dark matter DATA! First analysis of Sreekumar et al. from the EGRET data gave an extragalactic flux described by the power law. ` E 2 dj E 0.1 = de 1 GeV (cm 2 str s) 1 GeV, for 50 MeV< E < 10 GeV This flux is close to the predictions of models. This scenario might be tested soon!! Gravitino Dark Matter p.25/42

51 The more recent analysis by Strong, Moskalenko and Reimer ( 04) shows a power law behaviour between 50 MeV and 2 GeV, but a clear excess between 2 GeV and 50GeV!! HEAO A2,A4(LED) ASCA HEAO-A4 (MED) E 2 dj/de (kev 2 /(cm 2 -s-kev-sr) COMPTEL EGRET v Photon Energy (kev) The extragalactic gamma ray flux from the decay of gravitinos may be hidden in this excess. Still, many open questions: Extraction of the signal from the galactic background Is the signal isotropic/anisotropic? Precise shape of the energy spectrum? Is the excess really there? Stecker, Hunter & Kniffen GLAST will clarify these issues. Gravitino Dark Matter p.26/42

52 Gravitino decay channels Light gravitino m 3/2 < M W ψ 3/2 γν Γ(ψ 3/2 γν) = 1 32π U γν 2 m3 3/2 M 2 P ψ 3/2 γ γ ν Gravitino Dark Matter p.27/42

53 Gravitino decay channels Light gravitino m 3/2 < M W ψ 3/2 γν Γ(ψ 3/2 γν) = 1 32π U γν 2 m3 3/2 M 2 P ψ 3/2 γ γ ν not-so-light gravitino 100 GeV < m 3/2 < 300 GeV Z ψ 3/2 Z 0 ν ψ 3/2 Γ(ψ 3/2 Z 0 ν) = 1 32π U Zν 2 m3 3/2 MP 2 f MZ 2 m 2 3/2! Z ν f(x) ψ 3/2 W ± l ψ 3/2 W x Γ(ψ 3/2 W ± l ) = 2 32π U Wl 2 m3 3/2 MP 2 f MW 2 m 2 3/2! W l Gravitino Dark Matter p.27/42

54 Gravitino decay channels Light gravitino m 3/2 < M W ψ 3/2 γν Γ(ψ 3/2 γν) = 1 32π U γν 2 m3 3/2 M 2 P ψ 3/2 γ γ ν γ s not-so-light gravitino 100 GeV < m 3/2 < 300 GeV Z ψ 3/2 Z 0 ν ψ 3/2 Γ(ψ 3/2 Z 0 ν) = 1 32π U Zν 2 m3 3/2 MP 2 f MZ 2 m 2 3/2! Z ν γ s f(x) ψ 3/2 W ± l ψ 3/2 W x Γ(ψ 3/2 W ± l ) = 2 32π U Wl 2 m3 3/2 MP 2 f MW 2 m 2 3/2! W l Gravitino Dark Matter p.27/42

55 The energy spectrum of photons from gravitino decay is dn γ de BR(ψ 3/2 γν)δ E m 3/2 + BR(ψ 3/2 Wl) dnw γ 2 de + BR(ψ 3/2 Z 0 ν) dnz γ de m 3/2 =10 GeV m 3/2 =150 GeV E 2 dn/de γ E 2 dn/de Z W γ E (GeV) E (GeV) Gravitino Dark Matter p.28/42

56 What are typical values for U γν, U Zν, U Wl? When R-parity is broken neutralinos mix with neutrinos, through the sneutrino vev <ν> B ν <ν> W 0 ν Gravitino Dark Matter p.29/42

57 What are typical values for U γν, U Zν, U Wl? When R-parity is broken neutralinos mix with neutrinos, through the sneutrino vev B <ν> ν Z 0 <ν> ν U Zν g eν 2c W M ez <ν> <ν> W 0 ν γ ν Gravitino Dark Matter p.29/42

58 What are typical values for U γν, U Zν, U Wl? When R-parity is broken neutralinos mix with neutrinos, through the sneutrino vev B <ν> ν Z 0 <ν> ν U Zν g eν 2c W M ez W 0 <ν> ν γ <ν> ν Gravitino Dark Matter p.29/42

59 What are typical values for U γν, U Zν, U Wl? When R-parity is broken neutralinos mix with neutrinos, through the sneutrino vev B <ν> ν Z 0 <ν> ν U Zν g eν 2c W M ez W 0 <ν> ν <ν> <ν> γ ν 0 γ Z ν M γ Z «(M2 M 1 )s W c W U eγν M 1 c 2 W + M 2s 2 U ezν W U γν Assuming universality at the GUT scale, U eγν 0.32 U ezν Gravitino Dark Matter p.29/42

60 Also, the charginos mix with the charged leptons W <ν> l U Wl g 2 eν M fw U fwl 2c W M 1 s 2 W + M 2 c 2 W M 2 U ezν Assuming universality at the GUT scale, U fwl 1.09 U ezν Gravitino Dark Matter p.30/42

61 The branching ratios are determined by the size of the mixing parameters U γν, U Zν, U Wl. This is very model dependent, however, their relative size is fairly model independent: U eγν» (M2 M 1 )s W c W M 1 c 2 W + M 2s 2 W U ezν U fwl 2c W M 1 s 2 W + M 2 c 2 W M 2 U ezν Assuming gaugino mass universality at the Grand Unified Scale, U eγν : U ezν : U fwl 1 : 3.2 : 3.5 m 3/2 BR(ψ 3/2 γν) BR(ψ 3/2 Wl) BR(ψ 3/2 Z 0 ν) 10 GeV GeV GeV GeV GeV Gravitino Dark Matter p.31/42

62 The energy spectrum of photons from gravitino decay is dn γ de BR(ψ 3/2 γν)δ E m 3/2 + BR(ψ 3/2 Wl) dnw γ 2 de + BR(ψ 3/2 Z 0 ν) dnz γ de m 3/2 =10 GeV m 3/2 =150 GeV E 2 dn/de γ E 2 dn/de Z W γ E (GeV) E (GeV) Gravitino Dark Matter p.32/42

63 Gamma ray spectrum If gravitinos decay, we expect a diffuse background of gamma rays with two different sources. The decay at cosmological distances gives rise to a perfectly isotropic extragalactic diffuse gamma-ray flux.» E 2 dj de extgal = 2E2 m 3/2 C γ Z 1 dy dn γ d(ey) y 3/2 1 + Ω «1/2 Λ y 3 Ω M where y = 1 + z, C γ = Ω 3/2 ρ c 8πτ 3/2 H 0 Ω 1/2 M = 10 7 (cm 2 str s) 1 GeV τ3/ s and dn γ de is the spectrum of photons from gravitino decay Gravitino Dark Matter p.33/42

64 The decay of the gravitinos in the Milky Way halo gives rise to an anisotropic γ ray flux where D γ = 1 8πτ 3/2 Z los» E 2 dj de halo ρ halo ( l)d l = 2E2 dn γ D γ m 3/2 de The precise value of D γ (b, l) depends on the halo profile. Averaging over all sky, one finds typically D γ /C γ O(1) the halo contribution dominates Gravitino Dark Matter p.34/42

65 The decay of the gravitinos in the Milky Way halo gives rise to an anisotropic γ ray flux where D γ = 1 8πτ 3/2 Z los» E 2 dj de halo ρ halo ( l)d l = 2E2 dn γ D γ m 3/2 de The precise value of D γ (b, l) depends on the halo profile. Averaging over all sky, one finds typically D γ /C γ O(1) the halo contribution dominates Gravitino Dark Matter p.34/42

66 γ ray spectrum for light gravitinos m 3/2 < M W The energy spectrum from gravitino decay is just a delta function: dn γ de = δ E m 3/2 2» E 2 dj de extgal» E 2 dj de halo = C γ " 1 + Ω Λ Ω M = D γ δ 1 2E m 3/2 2E m 3/2!! 3 # 1/2 2E m 3/2! 5/2 θ 1 2E m 3/2! Bertone, Buchmüller, Covi, AI E 2 dj/de (GeV (cm 2 s str) -1 ) extgal halo energy resolution of EGRET: 15% E (GeV) Gravitino Dark Matter p.35/42

67 γ ray spectrum for not-so-light gravitinos 100 GeV < m 3/2 < 300 GeV The total flux receives contribution from different sources. U eγν : U ezν : U fwl 1 : 3.2 : 3.5 Gamma-ray spectrum for m 3/2 = 150 GeV AI, Tran 10-6 E 2 dj/de [GeV cm -2 s -1 sr -1 ] E [GeV] Gravitino Dark Matter p.36/42

68 γ ray spectrum for not-so-light gravitinos 100 GeV < m 3/2 < 300 GeV The total flux receives contribution from different sources. U eγν : U ezν : U fwl 1 : 3.2 : 3.5 Gamma-ray spectrum for m 3/2 = 150 GeV AI, Tran 10-6 E 2 dj/de [GeV cm -2 s -1 sr -1 ] 10-7 W -halo W -extgal E [GeV] Gravitino Dark Matter p.36/42

69 γ ray spectrum for not-so-light gravitinos 100 GeV < m 3/2 < 300 GeV The total flux receives contribution from different sources. U eγν : U ezν : U fwl 1 : 3.2 : 3.5 Gamma-ray spectrum for m 3/2 = 150 GeV AI, Tran 10-6 E 2 dj/de [GeV cm -2 s -1 sr -1 ] 10-7 Z-halo Z-extgal E [GeV] Gravitino Dark Matter p.36/42

70 γ ray spectrum for not-so-light gravitinos 100 GeV < m 3/2 < 300 GeV The total flux receives contribution from different sources. U eγν : U ezν : U fwl 1 : 3.2 : 3.5 Gamma-ray spectrum for m 3/2 = 150 GeV AI, Tran 10-6 E 2 dj/de [GeV cm -2 s -1 sr -1 ] 10-7 γ-halo γ-extgal E [GeV] Gravitino Dark Matter p.36/42

71 γ ray spectrum for not-so-light gravitinos 100 GeV < m 3/2 < 300 GeV The total flux receives contribution from different sources. U eγν : U ezν : U fwl 1 : 3.2 : 3.5 Gamma-ray spectrum for m 3/2 = 150 GeV AI, Tran 10-6 E 2 dj/de [GeV cm -2 s -1 sr -1 ] 10-7 background E [GeV] Gravitino Dark Matter p.36/42

72 γ ray spectrum for not-so-light gravitinos 100 GeV < m 3/2 < 300 GeV The total flux receives contribution from different sources. U eγν : U ezν : U fwl 1 : 3.2 : 3.5 Gamma-ray spectrum for m 3/2 = 150 GeV total AI, Tran 10-6 E 2 dj/de [GeV cm -2 s -1 sr -1 ] E [GeV] τ 3/2 = s = U eγν Gravitino Dark Matter p.36/42

73 Gamma-ray spectrum for m 3/2 = 100 GeV E 2 dj/de [GeV cm -2 s -1 sr -1 ] E [GeV] Gravitino Dark Matter p.37/42

74 Gamma-ray spectrum for m 3/2 = 250 GeV E 2 dj/de [GeV cm -2 s -1 sr -1 ] E [GeV] Gravitino Dark Matter p.38/42

75 II- Signatures for colliders The signatures depend on the nature of the NLSP (stau/neutralino) If the NLSP is a (mainly right-handed) stau Main decay: eτ R τ ν µ,µ ν τ (through λlle c ) 1 ` ǫ2 2 `tan β cτ lep τ 30 cm ` m τ 200GeV Long heavily ionizing charged track followed by a muon track or a jet. 2 Gravitino Dark Matter p.39/42

76 II- Signatures for colliders The signatures depend on the nature of the NLSP (stau/neutralino) If the NLSP is a (mainly right-handed) stau Main decay: eτ R τ ν µ,µ ν τ (through λlle c ) 1 ` ǫ2 2 `tan β cτ lep τ 30 cm ` m τ 200GeV Long heavily ionizing charged track followed by a muon track or a jet. Also, the small left-handed component induces eτ L b c t (through λ QLd c ) cτ τ had 1.4 m ` m τ 1 ` ǫ GeV 10 7 Long heavily ionizing charged track, followed by jets. 2 Gravitino Dark Matter p.39/42

77 II- Signatures for colliders The signatures depend on the nature of the NLSP (stau/neutralino) If the NLSP is a (mainly right-handed) stau Main decay: eτ R τ ν µ,µ ν τ (through λlle c ) 1 ` ǫ2 2 `tan β cτ lep τ 30 cm ` m τ 200GeV Long heavily ionizing charged track followed by a muon track or a jet. Also, the small left-handed component induces eτ L b c t (through λ QLd c ) cτ τ had 1.4 m ` m τ 1 ` ǫ GeV 10 7 Long heavily ionizing charged track, followed by jets. If the NLSP is a neutralino Main decays: χ 0 1 τ ± W, or χ 0 1 b b c ν cτ 2 body mχ cm 1 ` ǫ3 χ GeV m meνl 300 GeV 4 mχ GeV 2 2 `tan β ` ǫ3 2 `tan β cτ 3 body χ 0 1 If the neutralino decays inside the detector, jets will be observed. Gravitino Dark Matter p.39/42

78 Conclusions During the 20th century, a consistent thermal history of the Universe was outlined. The recent discoveries of dark matter and dark energy require a revision of the thermal history. We have concentrated on incorporating the supersymmetric dark matter into the thermal history of the Universe. The requirements of succesful thermal leptogenesis and Big Bang Nucleosynthesis essentially lead to a scenario with gravitino dark matter and tiny R-parity violation. The photons from the gravitino decay contribute to the diffuse gamma background. They may have already been observed by EGRET. Future experiments, such as GLAST, AMS-02 or Cherenkov telescopes, will provide unique oportunities to test this scenario. A flux of positrons, antiprotons and neutrinos is also expected in preparation This scenario predicts striking signatures at the LHC, in particular a vertex of the NLSP significantly displaced from the beam axis. Gravitino Dark Matter p.40/42

79 Isotropy of the signal MeV -1 s -1 sr -2. intensity, cm 2 E V Strong, Moskalenko, Reimer energy (MeV) 5 10 Gravitino Dark Matter p.41/42

80 l b Intensity GeV Description < 10, > ± 0.12 N+S hemispheres < ± 0.15 N hemisphere > ± 0.21 S hemisphere < 10, > ± 0.17 Inner Galaxy N+S < 10, > ± 0.17 Outer Galaxy N+S < 10, > ± 0.17 Positive longitudes N+S < 10, > ± 0.16 Negative longitude N+S > ± 0.22 Inner Galaxy N < ± 0.32 Inner Galaxy S > ± 0.22 Outer Galaxy N < ± 0.34 Outer Galaxy S Gravitino Dark Matter p.42/42