Wilfried Buchmuller- Gravitino Dark Matter

8/3/2019 Wilfried Buchmuller- Gravitino Dark Matter

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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 thermal

leptogenesis (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

M 2p T R.

For unstable gravitinos, nucleosynthesis implies stringent upper bound onreheating temperature T R (Kawasaki, Kohri, Moroi ’05; ...),

T R < O(1)× 105 GeV,

hence standard mSUGRA with neutralino LSP incompatible withbaryogenesis via thermal leptogenesis where T R ∼ 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 T R (!), but inconsistent with BBNconstraints; (ii) Thermal production, from 2 → 2 QCD processes,

Ω3/2h2

≃ 0.5 T R1010GeV100GeV

m3/2 mg(µ)

1TeV .

→ ΩDM h2 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 → N 1N 1 → (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~h

2

mG~

[GeV]

M 3 = 400 GeV

Dark Matter Region

K=10

K=500

parameters: M 1 = 109 GeV ∼ T R, 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 of a small ‘R-parity’ breaking, which leads to processes τ R → τ ν µ, µ ν τ ,

τ L → bct, ... and also ψ3/2 → γν . Small R-parity breaking can occurtogether with B-L breaking,

λ ∼ h(e,d)Θ <∼ 10−7 , Θ ∼ v2B−L

M P2 .

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 ionising

macroscopic charged tracks, followed by a muon track or a jet and missingenergy, corresponding to τ → µν τ or τ → τ ν µ.

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 than

the age of the universe (Takayama, Yamaguchi ’00),

τ 3/2 ∼ 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

M e V

- 1

s - 1

s r

- 2

. i n t e n s i t y ,

c m

2 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 , tan β ;

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

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√2M P

lγ λγ νDνφψλ +

i

2lγ λ (ξ1g′Y Bµν + ξ2gW µν) 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

A n t i p r o t o n f l u x [ G e V - 1 m

- 2 s

- 1 s

r - 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 total

antiproton flux (including gravitino decays) lies below maximal flux fromspallation (including astrophysical uncertainties) → minimal lifetime; form3/2 = 200 GeV one finds τ min

3/2 (200) = 7× 1026 s.

12





PAMELA & Fermi vs ‘flavour democracy’

0.01

0.1

1

1 10 100 1000

P o s i t r o n f r a c t i o n e + / (

e + + e − )

E [GeV]

PAMELA 08HEAT 94/95/00

10

100

1000

10 100 1000 10000

E 3

d N / d E [ G e V 2

m

- 2 s

- 1 ]

E [GeV]

ATIC 08Fermi LAT 09

HESS 08

Input: m3/2 = 200 GeV, τ 3/2 = 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 with

increasing gravitino mass:

0.01

0.1

1

1 10 100 1000

P o s i t r o n f r a c t i o n e + / ( e +

+ e − )

E [GeV]


10

100

1000

10 100 1000 10000

E 3

d N / d E [ G e V 2

m - 2

s - 1 ]

E [GeV]

ATIC 08Fermi LAT 09

HESS 08

Input: m3/2

= 400 GeV, τ 3/2

= 3×

1026 s, BR(ψ→

l±

iW ∓) 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 for

gravitino masses below 200 GeV:

0.01

0.1

1

1 10 100 1000

P o s i t r o n f r a c t i o n e + / ( e +

+ e − )

E [GeV]


10

100

1000

10 100 1000 10000

E 3

d N / d E [ G e V 2

m - 2 s

- 1 ]

E [GeV]

ATIC 08Fermi LAT 09

HESS 08

Input: m3/2

= 100 GeV, τ 3/2

= 1×

1027 s, BR(ψ→

l±

iW ∓) 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:

E 2 dJ dE

bg

= 1.37× 10−6 E GeV

−0.1

(cm2 str s)−1 GeV ,

and Moskalenko et al:

E 2 dJ 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

E 2

d J / d E [ ( c m

2 s

t r s ) - 1 G

e V ]

E [GeV]

Sreekumar et al.Strong et al.

10-7

10-6

0.1 1 10 100

E 2

d J / d E [ ( c m

2 s

t r s ) - 1 G

e V ]

E [GeV]

Sreekumar et al.Strong et al.

left: m3/2 = 200 GeV, τ 3/2 = 7× 1026 s; right: m3/2 = 100 GeV, τ 3/2 =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/βγ meas, slow τ ’s important!Background from muon tracks, accurate measurement of τ -mass possible

γ β0 1 2 3 4 5 6

[ G e V ]

1 τ ∼

m

0

50

100

150

200

250

300

350

400

[GeV]1τ∼

m146 148 150 152 154 156 158 160 162 164

- 1

E v e n t s / 0 . 2

G e V /

3 0 f b

0

20

40

60

80

100

120

140

160

180

200 < 0.6γ βCut on 0.3 <

/ ndf 54.1 / 412

χ 0.021±152.4851τ∼m

0.019±1.0061τ∼

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 particularline at E γ ≃ m3/2/2. Gravitino DM can be discovered with

Fermi LAT and/or falsified at the LHC !!

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Wilfried Buchmuller- Gravitino Dark Matter