gravitino dark matter - startseite
TRANSCRIPT
GRAVITINO DARK MATTER
Wilfried Buchmuller
DESY, Hamburg
LAUNCH09, Nov. 2009, MPK Heidelberg
Why Gravitino Dark Matter?
Supergravity predicts the gravitino, analog of W and Z bosons in electroweaktheory; may be LSP, natural DM candidate:
• m3/2 < 1keV, hot DM, (Pagels, Primack ’81)
• 1keV <∼ m3/2 <∼ 15keV, warm DM, (Gorbunov, Khmelnitsky, Rubakov ’08)
• 100keV <∼ m3/2 <∼ 10MeV, cold DM, gauge mediation and thermalleptogenesis (Fuji, Ibe, Yanagida ’03); recently proven to be correct by F-theory(Heckman, Tavanfar, Vafa ’08)
• 10GeV <∼ m3/2 <∼ 1TeV, cold DM, gaugino/gravity mediation andthermal leptogenesis (Bolz, WB, Plumacher ’98)
Baryogenesis, (gravitino) DM and primordial nucleosynthesis (BBN) stronglycorrelated in cosmological history.
1
Gravitino Problem
Thermally produced gravitino number density grows with reheatingtemperature after inflation (Khlopov, Linde ’83; Ellis, Kim, Nanopoulos ’84;...),
n3/2
nγ∝ α3
M2p
TR.
For unstable gravitinos, nucleosynthesis implies stringent upper bound onreheating temperature TR (Kawasaki, Kohri, Moroi ’05; ...),
TR < O(1) × 105 GeV,
hence standard mSUGRA with neutralino LSP incompatible withbaryogenesis via thermal leptogenesis where TR ∼ 1010 GeV !!
Possible way out: Gravitino LSP, explains dark matter!
2
Gravitino Virtue
Can one understand the amount of dark matter, ΩDM ≃ 0.23, withΩDM = ρDM/ρc, if gravitinos are dominant component, i.e. ΩDM ≃ Ω3/2?
Production mechanisms: (i) WIMP decays, i.e., ‘Super-WIMPs’ (Covi, Kim,
Roszkowski ’99; Feng, Rajaraman, Takayama ’03),
Ω3/2 =m3/2
mNLSPΩNLSP ,
independent of initial temperature TR (!), but inconsistent with BBNconstraints; (ii) Thermal production, from 2 → 2 QCD processes,
Ω3/2h2 ≃ 0.5
(TR
1010GeV
) (100GeV
m3/2
)(mg(µ)
1TeV
).
→ ΩDMh2 for typical parameters of supergravity and leptogenesis!
3
Leptogenesis, GDM and BBN (Bolz, WB, Plumacher ’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 BBNconstraints → τ NLSP ... →... Pospelov ’06 ... review Steffen ’08
4
Reheating: initial RH-neutrino dominance(...Asaka et al ’99; Hahn-Woernle, Plumacher ’08; Erbe ’09)
Reheating process from inflaton decay: φ → N1N1 → (lH)(lH) → . . .;combined system of Boltzmann eqs connects LG and gravitino production
0.05
0.06
0.07
0.08
0.095
0.112
0.14
0.16
0.18
0.2
1 10
ΩG~h2
mG~ [GeV]
M3 = 400 GeV
Dark Matter Region
K=10
K=500
parameters: M1 = 109 GeV ∼ TR, mg = 1 TeV; for K = 10 (strongwashout): m3/2 ≃ 6 GeV (cf. thermal LG: Ωh2 ∼ 1).
5
Decaying GDM (WB, Covi, Hamaguchi, Ibarra, Yanagida ’07)
BBN, leptogenesis and gravitino dark matter are all consistent in case ofa small ‘R-parity’ breaking, which leads to processes τR → τ νµ, µ ντ ,τL → bct, ... and also ψ3/2 → γν. Small R-parity breaking can occurtogether with B-L breaking,
λ ∼ h(e,d)Θ <∼ 10−7 , Θ ∼v2
B−L
MP2 .
The NLSP lifetime becomes sufficiently short (decay before BBN),
cτ lepτ ∼ 30 cm
( mτ
200GeV
)−1(
λ
10−7
)−2
.
BBN, thermal leptogenesis and gravitino dark matter are consistent for10−14 < λ, λ′ < 10−7 (B, L washout) and m3/2 >∼ 5 GeV.
6
At LHC one should see characteristic signal with strongly ionisingmacroscopic charged tracks, followed by a muon track or a jet and missingenergy, corresponding to τ → µντ or τ → τνµ.
The gravitino decay ψ3/2 → γν is suppressed both by the Planck mass andthe small R-parity breaking couplings, so the lifetime is much longer thanthe age of the universe (Takayama, Yamaguchi ’00),
τ3/2 ∼ 1026s
(λ
10−7
)−2 ( m3/2
10 GeV
)−3
;
(Note that this lifetime became very popular after PAMELA). What are thecosmic ray signatures? Gamma-ray flux of the order of EGRET excess !!
Several other mechanisms to generate small R-parity breaking have beenproposed (Mohapatra et al ’08; Endo, Shindou ’09, ...)
7
LAUNCH07, March 2007, MPK Heidelberg:Extragalactic diffuse gamma-ray flux obtained from EGRET data (1998)
energy (MeV) 10 210 310 410 510
MeV
-1 s-1
sr-2
. inten
sity,
cm2 E
-310
V
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 superparticlemasses for unstable gravitinos, i.e. without BBN? GDM: upper bound ongluino mass for given reheating temperature; low energy observables: lowerbound on NLSP.
Connection is model dependent; assume gaugino mass unification (mgluino ≃6mbino). Two typical examples (different ratios mNLSP/mgluino),
(A) χ NLSP : m0 = m1/2 , a0 = 0 , tanβ ;
(B) τ NLSP : m0 = 0 , m1/2 , a0 = 0 , tanβ .
Low energy observables: mh > 114 GeV, BR(Bd → Bsγ), mcharged >100 GeV. Possible hint for supersymmetry (Marciano, Sirlin ’08),
aµ(exp) − aµ(SM) = 302(88) × 10−11 .
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 featuresfrom operator analysis (hierarchy: mSM ≪ m3/2 ≪ msoft):
Leff =iκ√2MP
lγλγνDνφψλ +
i
2lγλ (ξ1g
′Y Bµν + ξ2gWµν)σµνφψλ
+ h.c.
R-parity breaking: κ; further suppression: ξ1.2 = O(1/m3/2)
dim 5 : ψ3/2 → hν, Zν,W±l∓; continuous spectrum ,
i.e., single term correlates antiproton flux, PAMELA and Fermi!
dim 6 : ψ3/2 → γν; gamma line
11
Minimal gravitino lifetime from antiproton flux
10-5
10-4
10-3
10-2
10-1
100
0.1 1 10
Antip
roto
n flu
x [G
eV-1
m-2
s-1
sr-1
]
T [GeV]
Total flux
MED
Lifetime: 7.0E26 s
φF = 500 MV
BESS 95+97BESS 95IMAX 92
CAPRICE 94CAPRICE 98
conservative propagation model (B/C ratio): MED model; require that totalantiproton flux (including gravitino decays) lies below maximal flux fromspallation (including astrophysical uncertainties) → minimal lifetime; form3/2 = 200 GeV one finds τmin
3/2 (200) = 7 × 1026 s.
12
PAMELA & Fermi vs ‘electron dominance’
0.01
0.1
1
1 10 100 1000
Positro
n fra
ction e
+/(
e++
e−)
E [GeV]
PAMELA 08HEAT 94/95/00
10
100
1000
10 100 1000 10000
E3 d
N/d
E [G
eV
2 m
-2 s
-1]
E [GeV]
ATIC 08Fermi LAT 09
HESS 08
Input: m3/2 = 200 GeV, τ3/2 = 3.2 × 1026 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’
0.01
0.1
1
1 10 100 1000
Positro
n fra
ction e
+/(
e++
e−)
E [GeV]
PAMELA 08HEAT 94/95/00
10
100
1000
10 100 1000 10000
E3 d
N/d
E [G
eV
2 m
-2 s
-1]
E [GeV]
ATIC 08Fermi LAT 09
HESS 08
Input: m3/2 = 200 GeV, τ3/2 = 7 × 1026 s, BR(ψ → l±i 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 withincreasing gravitino mass:
0.01
0.1
1
1 10 100 1000
Positro
n fra
ction e
+/(
e++
e−)
E [GeV]
PAMELA 08HEAT 94/95/00
10
100
1000
10 100 1000 10000
E3 d
N/d
E [G
eV
2 m
-2 s
-1]
E [GeV]
ATIC 08Fermi LAT 09
HESS 08
Input: m3/2 = 400 GeV, τ3/2 = 3 × 1026 s, BR(ψ → l±i W∓) universal for
i = e, µ, τ , background: “Model 0”.Conclusion: gravitino contribution to electron/positron fluxes may besizable, has to be complemented by astrophysical sources!
15
Contribution from gravitino decays to positron fraction decreases rapidly forgravitino masses below 200 GeV:
0.01
0.1
1
1 10 100 1000
Positro
n fra
ction e
+/(
e++
e−)
E [GeV]
PAMELA 08HEAT 94/95/00
10
100
1000
10 100 1000 10000
E3 d
N/d
E [G
eV
2 m
-2 s
-1]
E [GeV]
ATIC 08Fermi LAT 09
HESS 08
Input: m3/2 = 100 GeV, τ3/2 = 1 × 1027 s, BR(ψ → l±i W∓) universal for
i = e, µ, τ , background: “Model 0”.Conclusion: gravitino contribution to electron/positron fluxes may benegligable, as for antiproton flux!
16
Predictions for the Gamma-Ray Spectrum
Important contributions form extragalactic DM and DM in the Milky Wayhalo; typical branching ratio for gamma line (cf. operator analysis):
BR(ψ3/2 → νγ) ∼ 0.02
(200 GeV
m3/2
)2
;
Gamma-ray background presently uncertain, two analyses of EGRET data;Sreekumar et al:
[E2dJ
dE
]
bg
= 1.37 × 10−6
(E
GeV
)−0.1
(cm2 str s)−1 GeV ,
and Moskalenko et al:
[E2dJ
dE
]
bg
= 6.8 × 10−7
(E
GeV
)−0.32
(cm2 str s)−1 GeV.
17
Height of gamma line depends on energy resolution (assumed: σ(E)/E =15%) and background; ‘minimal’ lifetime from antiproton flux constraintgive maximal gamma-ray flux:
10-7
10-6
0.1 1 10 100
E2 d
J/d
E [(c
m2 s
tr s
)-1 G
eV
]
E [GeV]
Sreekumar et al.Strong et al.
10-7
10-6
0.1 1 10 100
E2 d
J/d
E [(c
m2 s
tr s
)-1 G
eV
]
E [GeV]
Sreekumar et al.Strong et al.
left: m3/2 = 200 GeV, τ3/2 = 7× 1026 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
γβ0 1 2 3 4 5 6
[G
eV
]1τ∼
m
0
50
100
150
200
250
300
350
400
[GeV]1
τ∼m146 148 150 152 154 156 158 160 162 164
-1E
ven
ts / 0
.2 G
eV
/ 3
0 f
b
0
20
40
60
80
100
120
140
160
180
200 < 0.6γβCut on 0.3 < / ndf 54.1 / 412χ
0.021± 152.485 1τ∼m
0.019± 1.006 1τ∼σ
analysis relevant for sufficiently long lifetimes, such that the τ -lepton leavesthe 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 Eγ ≃ m3/2/2. Gravitino DM can be discovered with
Fermi LAT and/or falsified at the LHC !!
20