Gravitino Dark Matter

GRAVITINO DARK MATTER

Wilfried Buchm¨uller DESY, Hamburg

LAUNCH09, Nov. 2009, MPK Heidelberg Why Gravitino Dark Matter? Supergravity predicts the gravitino, analog of W and Z bosons in electroweak theory; may be LSP, natural DM candidate:

m < 1keV, hot DM, (Pagels, Primack ’81) • 3/2

1keV < m3/2 < 15keV, warm DM, (Gorbunov, Khmelnitsky, Rubakov ’08) • ∼ ∼ 100keV < m < 10MeV, cold DM, gauge mediation and thermal • 3/2 leptogenesis∼ (Fuji, Ibe,∼ Yanagida ’03); recently proven to be correct by F-theory (Heckman, Tavanfar, Vafa ’08)

10GeV < m < 1TeV, cold DM, gaugino/gravity mediation and • 3/2 thermal leptogenesis∼ ∼ (Bolz, WB, Pl¨umacher ’98)

Baryogenesis, (gravitino) DM and primordial nucleosynthesis (BBN) strongly correlated in cosmological history.

1 Gravitino Problem

Thermally produced gravitino number density grows with reheating temperature after inﬂation (Khlopov, Linde ’83; Ellis, Kim, Nanopoulos ’84;...),

n3/2 α3 2 TR. nγ ∝ Mp

For unstable gravitinos, nucleosynthesis implies stringent upper bound on reheating temperature TR (Kawasaki, Kohri, Moroi ’05; ...),

T < (1) 105 GeV, R O × hence standard mSUGRA with neutralino LSP incompatible with baryogenesis via thermal leptogenesis where T 1010 GeV !! R ∼ Possible way out: Gravitino LSP, explains dark matter!

2 Gravitino Virtue

Can one understand the amount of dark matter, ΩDM 0.23, with Ω = ρ /ρ , if gravitinos are dominant component, i.e. Ω≃ Ω ? DM DM c DM ≃ 3/2 Production mechanisms: (i) WIMP decays, i.e., ‘Super-WIMPs’ (Covi, Kim, Roszkowski ’99; Feng, Rajaraman, Takayama ’03),

m3/2 Ω3/2 = ΩNLSP , mNLSP independent of initial temperature TR (!), but inconsistent with BBN constraints; (ii) Thermal production, from 2 2 QCD processes, →

2 TR 100GeV mg˜(µ) Ω3/2h 0.5 10 . ≃ 10 GeV m3/2 1TeV

Ω h2 for typical parameters of supergravity and leptogenesis! → DM

3 Leptogenesis, GDM and BBN (Bolz, WB, Pl¨umacher ’98)

Left: Gravitino abundance as function of reheating temperature. Right: Upper bound on gluino mass, lower bound on higgsino NLSP; shaded area: BBN ok. Note: gaugino mass uniﬁcation not possible. Improved BBN constraints τ˜ NLSP ...... Pospelov ’06 ... review Steﬀen ’08 → →

4 Reheating: initial RH-neutrino dominance (...Asaka et al ’99; Hahn-Woernle, Pl¨umacher ’08; Erbe ’09)

Reheating process from inﬂaton decay: φ N1N1 (lH)(lH) ...; combined system of Boltzmann eqs connects→ LG and gravitino→ production→

M 3 = 400 GeV

0.2 Dark Matter Region 0.18 K=10 0.16 K=500 0.14

0.112 Ω ~ 2 Gh 0.095 0.08 0.07 0.06 0.05

1 10 ~ m G [GeV]

9 parameters: M1 = 10 GeV TR, mg˜ = 1 TeV; for K = 10 (strong washout): m 6 GeV (cf. thermal∼ LG: Ωh2 1). 3/2 ≃ ∼

5 Decaying GDM (WB, Covi, Hamaguchi, Ibarra, Yanagida ’07) BBN, leptogenesis and gravitino dark matter are all consistent in case of a small ‘R-parity’ breaking, which leads to processes τR τ νµ, µ ντ , c → τL b t, ... and also ψ3/2 γν. Small R-parity breaking can occur together→ with B-L breaking, → e e v2 (e,d) < −7 B−L λ h Θ 10 , Θ 2 . ∼ ∼ ∼ MP

The NLSP lifetime becomes suﬃciently short (decay before BBN),

−1 −2 lep mτ˜ λ cττ˜ 30 cm −7 . ∼ 200GeV 10

BBN, thermal leptogenesis and gravitino dark matter are consistent for −14 ′ −7 10 < λ, λ < 10 (B, L washout) and m3/2 > 5 GeV. ∼ 6 At LHC one should see characteristic signal with strongly ionising macroscopic charged tracks, followed by a muon track or a jet and missing energy, corresponding to τ µν or τ τν . → τ → µ

The gravitino decay ψ3/2e γν is suppressede both by the Planck mass and the small R-parity breaking→ couplings, so the lifetime is much longer than the age of the universe (Takayama, Yamaguchi ’00),

−2 −3 26 λ m3/2 τ3/2 10 s −7 ; ∼ 10 10 GeV

(Note that this lifetime became very popular after PAMELA). What are the cosmic ray signatures? Gamma-ray ﬂux of the order of EGRET excess !!

Several other mechanisms to generate small R-parity breaking have been proposed (Mohapatra et al ’08; Endo, Shindou ’09, ...)

7 LAUNCH07, March 2007, MPK Heidelberg: Extragalactic diﬀuse gamma-ray ﬂux obtained from EGRET data (1998) MeV -1 s -1 sr -2

10 -3 . intensity, cm 2 E

2 3 4 5 10 10 10 10energy (MeV) 10 analysis of Strong, Moskalenko and Reimer, astro-ph/0406254 (2004), astro-ph/0506359 (2005); subtraction of galactic component diﬃcult astro-ph/0609768; extragalactic gravitino signal consistent with data for m3/2 ∼ 10 GeV; halo component may partly be hidden in anisotropic galactic gamma-ray ﬂux → wait for GLAST !!

8 Superparticle Mass Window (WB, Endo, Shindou ’08)

What are the constraints from leptogenesis and GDM on superparticle masses for unstable gravitinos, i.e. without BBN? GDM: upper bound on gluino mass for given reheating temperature; low energy observables: lower bound on NLSP.

Connection is model dependent; assume gaugino mass uniﬁcation (m gluino ≃ 6mbino). Two typical examples (diﬀerent ratios mNLSP/mgluino),

(A)χ ˜ NLSP : m0 = m1/2 , a0 = 0 , tan β ;

(B)τ ˜ NLSP : m0 = 0 , m1/2 , a0 = 0 , tan β .

Low energy observables: m > 114 GeV, BR(B B γ), m > h d → s charged 100 GeV. Possible hint for supersymmetry (Marciano, Sirlin ’08),

a (exp) a (SM) = 302(88) 10−11 . µ − µ ×

9 Stau and gravitino masses

Left: (A) gravitino: m3/2 < 490 GeV. Right: (B) stau: 100 GeV < mstau < 490 GeV. Red: mass range favoured by aµ.

10 Cosmic-Ray Signatures from Decaying Gravitinos (WB, Ibarra, Shindou, Takayama, Tran ’09)

± ∓ Gravitino decays: ψ3/2 γν; hν,Zν,W l , leads to continuous gamma- → ± ray and antimatter spectrum: ψ3/2 γX, pX,e¯ X; qualitative features from operator analysis (hierarchy: m → m m ): SM ≪ 3/2 ≪ soft

iκ λ ν i λ ′ µν eﬀ = ¯lγ γ Dνφψλ + ¯lγ (ξ1g YBµν + ξ2gWµν) σ φψλ +h.c. L √2MP 2 R-parity breaking: κ; further suppression: ξ = (1/m ) 1.2 O 3/2 dim 5 : ψ hν,Zν,W ±l∓; continuous spectrum , 3/2 → i.e., single term correlates antiproton ﬂux, PAMELA and Fermi!

dim 6 : ψ γν; gamma line 3/2 →

11 Minimal gravitino lifetime from antiproton ﬂux

10 0 BESS 95 BESSIMAX 95+97 92 CAPRICE 94 ] 10 -1 CAPRICE 98 -1 sr -1 s -2 -2 m 10 Total flux -1

10 -3 MED

-4 Antiproton flux [GeV 10 Lifetime: 7.0E26 s

-5 φ 10 F = 500 MV 0.1 1 10 T [GeV] conservative propagation model (B/C ratio): MED model; require that total antiproton flux (including gravitino decays) lies below maximal flux from spallation (including astrophysical uncertainties) minimal lifetime; for m = 200 GeV one finds τ min(200) = 7 1026 s→. 3/2 3/2 ×

12 PAMELA & Fermi vs ‘electron dominance’

1 1000 PAMELA 08 ATIC 08 HEAT 94/95/00 Fermi LAT 09 HESS 08 ) − ] -1 + e s + -2 /(e + m 2

0.1 100 dN/dE [GeV 3 E Positron fraction e

0.01 10 1 10 100 1000 10 100 1000 10000 E [GeV] E [GeV]

26 ± ∓ ± ∓ Input: m3/2 = 200 GeV, τ3/2 = 3.2 10 s, BR(ψ µ W , τ W ) ± ∓ × → ≪ BR(ψ e W ) (why?); background: “Model 0” (Grasso et al, Fermi LAT ’09) Conclusion:→ GALPROP & gravitino incompatible with PAMELA & Fermi !! [PAMELA & Fermi make CR signature for dark matter UNLIKELY !!]

13 PAMELA & Fermi vs ‘ﬂavour democracy’

1 1000 PAMELA 08 ATIC 08 HEAT 94/95/00 Fermi LAT 09 HESS 08 ) − ] -1 + e s + -2 /(e + m 2

0.1 100 dN/dE [GeV 3 E Positron fraction e

0.01 10 1 10 100 1000 10 100 1000 10000 E [GeV] E [GeV]

26 ± ∓ Input: m3/2 = 200 GeV, τ3/2 = 7 10 s, BR(ψ li W ) universal for i = e, µ, τ (theoretical model exists),× background: “Model→ 0”. Conclusion: astrophysical sources needed to explain PAMELA & FERMI!!

14 Contribution from gravitino decays to positron fraction increases with increasing gravitino mass:

1 1000 PAMELA 08 ATIC 08 HEAT 94/95/00 Fermi LAT 09 HESS 08 ) − ] -1 + e s + -2 /(e + m 2

0.1 100 dN/dE [GeV 3 E Positron fraction e

0.01 10 1 10 100 1000 10 100 1000 10000 E [GeV] E [GeV]

26 ± ∓ Input: m3/2 = 400 GeV, τ3/2 = 3 10 s, BR(ψ li W ) universal for i = e, µ, τ, background: “Model 0”.× → Conclusion: gravitino contribution to electron/positron ﬂuxes may be sizable, has to be complemented by astrophysical sources!

15 Contribution from gravitino decays to positron fraction decreases rapidly for gravitino masses below 200 GeV:

1 1000 PAMELA 08 ATIC 08 HEAT 94/95/00 Fermi LAT 09 HESS 08 ) − ] -1 + e s + -2 /(e + m 2

0.1 100 dN/dE [GeV 3 E Positron fraction e

0.01 10 1 10 100 1000 10 100 1000 10000 E [GeV] E [GeV]

27 ± ∓ Input: m3/2 = 100 GeV, τ3/2 = 1 10 s, BR(ψ li W ) universal for i = e, µ, τ, background: “Model 0”.× → Conclusion: gravitino contribution to electron/positron ﬂuxes may be negligable, as for antiproton ﬂux!

16 Predictions for the Gamma-Ray Spectrum Important contributions form extragalactic DM and DM in the Milky Way halo; typical branching ratio for gamma line (cf. operator analysis):

200 GeV 2 BR(ψ3/2 νγ) 0.02 ; → ∼ m3/2

Gamma-ray background presently uncertain, two analyses of EGRET data; Sreekumar et al:

dJ E −0.1 E2 = 1.37 10−6 (cm2 str s)−1 GeV , dEbg × GeV and Moskalenko et al:

dJ E −0.32 E2 = 6.8 10−7 (cm2 str s)−1 GeV. dEbg × GeV

17 Height of gamma line depends on energy resolution (assumed: σ(E)/E = 15%) and background; ‘minimal’ lifetime from antiproton ﬂux constraint give maximal gamma-ray ﬂux:

Sreekumar et al. Sreekumar et al. Strong et al. Strong et al.

-6 -6 10 10 GeV] GeV] -1 -1 str s) str s) 2 2

-7 -7 10 10 dJ/dE [(cm dJ/dE [(cm 2 2 E E

0.1 1 10 100 0.1 1 10 100 E [GeV] E [GeV]

26 left: m3/2 = 200 GeV, τ3/2 = 7 10 s; right: m3/2 = 100 GeV, τ3/2 = 1 1027 s; improvement of energy× resolution? ×

18 Hope for the LHC: τ˜-mass measurement (Ellis, Raklev, Oye ’06)

τ˜-mass can be measured from mτ˜ = pmeas/βγmeas, slow τ˜’s important! Background from muon tracks, accurate measurement of τ˜-mass possible

400 -1 γβ 200 Cut on 0.3 << 0.6 2

[GeV] χ

1 350 / ndf 54.1 / 41 ∼ τ 180

m ∼ ± mτ 152.485 0.021 1 300 σ∼ ± 160 τ 1.006 0.019 1

140 250

120 200 Events / 0.2 GeV / 30 fb 100

150 80

60 100

40 50 20

0 0 0 1 2 3 4 5146 6 148 150 152 154 156 158 160 162 164 ∼ γβ mτ [GeV] 1 analysis relevant for suﬃciently long lifetimes, such that the τ˜-lepton leaves the detector; more work in progress ...

19 SUMMARY

Gravitino DM is viable possibility • Gravitino DM is theoretically motivated: leptogenesis and/or • gauge mediation ...

Decaying gravitino DM consistent with leptogenesis and BBN • GALPROP & gravitino DM incompatible with PAMELA & • Fermi, astrophysical sources needed !!

Sizable excess in gamma-ray spectrum possible, in particular • line at E m /2. Gravitino DM can be discovered with γ ≃ 3/2 Fermi LAT and/or falsiﬁed at the LHC !!