Gravitino Problem
Introduction Supersymmetry (SUSY) Fermion Boson Hierarchy Problem Keep electroweak scale against radiative correction Coupling Constant Unification in GUT quark squarks lepton slepton photon photino Gravitino Superpartner of graviton ψ 3 / 2
SUSY Breaking Scheme Low Energy SUSY ( m ˜ � ∼ 1TeV � m q , m � ) q , m ˜ (A) Gravity Mediated SUSY Breaking Observable SUSY sector sector (s)quark,(s)lepton gravity M SUSY Squark, slepton masses � ∼ M 2 ∼ 10 2 − 3 GeV SUSY m ˜ q , m ˜ M p Gravitino M SUSY ∼ 10 11 − 13 GeV m 3 / 2 ∼ 10 2 − 3 GeV
Gravitino Problem Gravitino only gravitationally suppressed int. long lifetime � m 3 / 2 � − 3 γ + γ ) � 4 × 10 8 sec τ ( ψ 3 / 2 → ˜ 100GeV Standard Big Bang Cosmology n 3 / 2 ∼ n γ if gravitino decays after BBN ( m 3 / 2 < 100TeV) Too Large Entropy Production Gravitino Problem (Weinberg 1982)
Gravitino in Inflationary Universe Primordial gravitinos are diluted However, gravitinos are produced during reheating ˜ e.g. g q g q → ψ 3 / 2 + ˜ q + ¯ g ¯ ψ 3 / 2 q � � n 3 / 2 T R ≃ 10 − 11 Bolz, Brandenburg, Buchmüller 10 10 GeV n γ (2001); MK, Moroi (1995) n 3 / 2 /n γ ∼ σ n q t ∼ (1 /M 2 p ) T 3 R ( M p /T 2 R )
Gravitino Decay and BBN ˜ γ Gravitino in Gravity Med. ψ 3 / 2 SUSY Breaking γ m 3 / 2 ∼ 10 2 − 3 GeV Unstable Radiative Decay ψ 3 / 2 → ˜ γ + γ � m 3 / 2 � − 3 γ + γ ) � 4 × 10 8 sec τ ( ψ 3 / 2 → ˜ 100GeV ψ 3 / 2 → ˜ g + g Hadronic Decay � m 3 / 2 � − 3 g + g ) � 6 × 10 7 sec τ ( ψ 3 / 2 → ˜ 100GeV
Decay Products (photons, hadrons) Disastrous Effect on Big Bang Nucleosynthesis Stringent Ellis, Nanopoulos,Sarkar (1985) Constraint on T R Reno, Seckel (1988) Dimopoulos et al (1989) MK, Moroi (1995) . . . . .
Big Bang Nucleosynthesis In the early universe (T=1 - 0.01MeV) 2 p + 2 n → 4 He + small 3 He 7 Li D Abundances of Light Elements Baryon-Photon ratio η = n B n γ
Observational Abundances of Light Elements He4 Y p = 0 . 238 ± 0 . 002 ± 0 . 005 Fields,Olive (1998) Y p = 0 . 242 ± 0 . 002( ± 0 . 005) Izotov et al. (2003) D/H D/H = (2 . 8 ± 0 . 4) × 10 − 5 Kirkman et al. (2003) Li7/H log 10 ( 7 Li/H ) = − 9 . 66 ± 0 . 056 ( ± 0 . 3) Bonifacio et al. (2002) Li6/H 6 Li/H < 6 × 10 − 11 (2 σ ) Smith et al. (1993) He3/D 3 He/D < 1 . 13 (2 σ ) Geiss (1993)
Gravitino Decay and BBN ˜ γ Gravitino in Gravity Med. ψ 3 / 2 SUSY Breaking γ m 3 / 2 ∼ 10 2 − 3 GeV Unstable Radiative Decay ψ 3 / 2 → ˜ γ + γ � m 3 / 2 � − 3 γ + γ ) � 4 × 10 8 sec τ ( ψ 3 / 2 → ˜ 100GeV ψ 3 / 2 → ˜ g + g Hadronic Decay � m 3 / 2 � − 3 g + g ) � 6 × 10 7 sec τ ( ψ 3 / 2 → ˜ 100GeV
Radiative Decay
Radiative Decay ˜ γ ψ 3 / 2 γ High Energy Photons Electromagnetic Cascade 1) Photon-photon pair creation � γ > m 2 e / 22 T γ + γ BG → e + + e − 2) Inverse Compton e + γ BG → e + γ 3) Photon-photon scattering � γ > m 2 e / 80 T γ + γ BG → γ + γ 4) Thomson scattering γ + e BG → γ + e
Photon Spectrum MK, Moroi (1995) 40 ε γ 0 =100GeV γ + γ BG → γ + γ γ + γ BG → e + + e − 30 2 )] log 10 [f/(GeV 10eV 20 1keV T=100keV 10 -3 -2 -1 0 1 2 3 4 10 10 10 10 10 10 10 10 Energy (GeV)
Many Soft Photons � γ > 2 . 2MeV ( T < 10keV) � γ > 20MeV ( T < 1keV) Destroy Light Elements D + γ → n + p [2 . 22 MeV] T + γ → D + n [6 . 2 MeV] 3 He + γ → D + p [5 . 5 MeV] 4 He + γ → T + n [19 . 8 MeV] 4 He + γ → 3 He + n [20 . 5 MeV] 4 He + γ → D + n + p [26 . 1 MeV] etc
Non-thermal Production of D and He3 Non-thermal Production of Li6 � n + 3 He 4 He + γ → p + T T + 4 He → 6 Li + n [4 . 03MeV] 3 He + 4 He → 6 Li + p [4 . 8MeV]
Constraint
He3/D Constraint Chemical Evolution of He3 and D Whenever He3 is destroyed, D is also destroyed 3 He Increasing Function of time D Observation Gives Upper Limit 3 He / D < 1 . 13 (2 σ ) Geiss (1993) ∼ 10 6 sec Destruction of D t < ∼ 10 6 sec Overproduction of He3 t >
Application to Gravitino Problem � � �� � m 2 � T R g ˜ 1 . 9 × 10 − 12 Y 3 / 2 = 1 + 3 m 2 10 10 GeV 3 / 2 � � �� � � �� T R T R 1 + 0 . 045 ln 1 − 0 . 028 ln × 10 10 GeV 10 10 GeV � m 3 / 2 � − 3 γ + γ ) ≃ 4 × 10 8 sec τ ( ψ 3 / 2 → ˜ 100GeV
7 Li / H Y p D / H 6 Li / 7 Li 3 He / D
Hadronic Decay
Hadronic Decay Reno, Seckel (1988) Dimopoulos et al (1989) ˜ g ψ 3 / 2 B h ∼ 1 Two hadron jets with E = m/2 g Even if gravitino only decay into photino ˜ γ B h ∼ α / 4 π ∼ 0 . 001 ψ 3 / 2 γ ¯ Two hadron jets q with E = m/3 q
� DECAY radiative hadronic Overview partons q g e hadronization hadronization hadron K electromagnetic jets p n � shower energy energy loss loss photo- hadron hadron dissociation decay shower int. p n hadro- dissociation 3 7 4 He D He Li destruction destruction 3 7 6 D He Li Li production
Spectrum of hadron jets JETSET 7.4 Kohri 2001
Effect of hadron injection on BBN Reno, Seckel (1988) (I) Early stage of BBN Kohri (2001) � p + π 0 Pion π + + n → p + γ τ π ± = 2 . 6 × 10 − 8 sec � n + π 0 π − + p → n + γ Kaon K − + p → Σ − + π 0 , · · · τ K ± = 1 . 2 × 10 − 8 sec K L + N → N � + . . . N, N � = p, n τ K L = 5 . 2 × 10 − 8 sec Hadron-Nucleon interaction rate Γ N → N � ∼ 10 8 sec − 1 ( σ v/ 10mb)( T/ 2MeV) 3
� DECAY radiative hadronic Overview partons q g e hadronization hadronization hadron K electromagnetic jets p n � shower energy energy loss loss photo- hadron hadron dissociation decay shower int. p n hadro- dissociation 3 7 4 He D He Li destruction destruction 3 7 6 D He Li Li production
p-n interchange interaction rate N → N � + Γ π , K Γ N → N � = Γ std N → N � n-p ratio increases (std: n/p ~ 1/7) More He4 n + ν e ↔ p + e −
� DECAY radiative hadronic Overview partons q g e hadronization hadronization hadron K electromagnetic jets p n � shower energy energy loss loss photo- hadron hadron dissociation decay shower int. p n hadro- dissociation 3 7 4 He D He Li destruction destruction 3 7 6 D He Li Li production
Effect of hadron injection on BBN (II) Late stage of BBN Dimopoulos et al (1989) Hadron Shower n + n + π ( p + n + π ) inelastic np ( pp ) n + p + π ( p + p + π ) elastic n + p ( p + p ) n ( p ) T + D ( 3 He + D) E = E f 3 He + 2 n ( 3 He + pn ) inelastic T + pn (T + 2 n ) n 4 He ( p 4 He) 2D + n (2D + p ) . . . elastic 4 He + n ( 4 He + p )
Energy Loss High energy hadrons lose their energy by Coulomb and Compton scatterings off background photons and electrons before they interacts with nuclei Non-relativistic Nucleus v N > v e dt = − 4 πα 2 Λ Z 2 n e dE Λ ∼ O (1) m e v N
Final Energy of Proton
Final Energy of Neutron
Hadron Shower n + n + π ( p + n + π ) inelastic n + p + π ( p + p + π ) np ( pp ) elastic n + p ( p + p ) n ( p ) T + D ( 3 He + D) 3 He + 2 n ( 3 He + pn ) inelastic T + pn (T + 2 n ) n 4 He ( p 4 He) 2D + n (2D + p ) . . . elastic 4 He + n ( 4 He + p )
ξ i : number of nuclei “i” produced per one massive particle decay
Non-thermal Production of Li6 4 He + N → N � + 3 He , N � + T T + 4 He → 6 Li + n [4 . 03MeV] 3 He + 4 He → 6 Li + p [4 . 8MeV] T,He3 enegy loss He4
ξ i : number of nuclei “i” produced per one massive particle decay
Estimate non-thermal production and destruction rates for D, T, He3, He4, Li6, Li7 Run BBN code Compare theoretical and observational abundances of light elements Constraint on abundance and lifetime of gravitino
Constraint on Abundance and Lifetime
Constraint on Abundance and Lifetime (3)
Application to Gravitino Problem � � �� � m 2 � T R g ˜ 1 . 9 × 10 − 12 Y 3 / 2 = 1 + 3 m 2 10 10 GeV 3 / 2 � � �� � � �� T R T R 1 + 0 . 045 ln 1 − 0 . 028 ln × 10 10 GeV 10 10 GeV � m 3 / 2 � − 3 g + γ ) ≃ 6 × 10 7 sec τ ( ψ 3 / 2 → ˜ 100GeV � m 3 / 2 � − 3 γ + γ ) ≃ 4 × 10 8 sec τ ( ψ 3 / 2 → ˜ 100GeV
Constraint on Reheating Temperature
Constraint on Reheating Temperature (2)
Conclusion Decay products destroy He4, which leads to overproduction of D, He3, Li6 In particular, for hadronic decay, the constraint on reheating temperature is very stringent ∼ 10 5 − 10 7 GeV T R < for m 3 / 2 = 100 GeV − 3 TeV
Recommend
More recommend
