Tran - DESY Theory workshop 2008

Indirect Signatures of Gravitino Dark Matter 

with Broken R-Parity 

David Tran 

Physik-Department T30d 

Technische Universität München 

Dark Matter at the Crossroads 

DESY, Hamburg 

October 1, 2008 


Indirect Signatures of Gravitino Dark Matter with Broken R-Parity

Outline 

Based on 

A. Ibarra and D. Tran, Phys.Rev.Lett.100:061301,2008 [arXiv:0709:4593 [astro-ph]] 

A. Ibarra and D. Tran, JCAP 0807:002,2008 [arXiv:0804.4596 [astro-ph]] 

1 Gravitino Dark Matter 

2 Gamma Rays 

3 Positrons 

4 Antiprotons 

5 Antideuterons 

6 Conclusions 



Outline 

Based on 

A. Ibarra and D. Tran, Phys.Rev.Lett.100:061301,2008 [arXiv:0709:4593 [astro-ph]] 

A. Ibarra and D. Tran, JCAP 0807:002,2008 [arXiv:0804.4596 [astro-ph]] 


2 Gamma Rays 

3 Positrons 

4 Antiprotons 


6 Conclusions 



Gravitino Dark Matter with Broken R-Parity 

Our scenario: The gravitino is the lightest supersymmetric particle, 

small violation of R-parity 

Detailed motivation → See Michael Grefe’s talk 

Reconciles clash between supersymmetric dark matter, leptogenesis 

and Big Bang nucleosynthesis 

The gravitino is an excellent dark matter candidate, but is usually 

assumed to be experimentally undetectable 

That is not necessarily true! 

R-parity violation can make gravitino dark matter accessible to indirect 

detection! 



Indirect Detection 

Even for gravitino lifetimes far in excess of the age of the Universe, 

the decay products may be observable due to the huge amount of 

dark matter 

Look for anomalous signatures in rare, low background cosmic-ray 

species and spectra of freely propagating particles: 

Gamma rays 

Positrons 

Antiprotons 

Antideuterons 

Neutrinos → Talk by Michael Grefe 



Outline 


2 Gamma Rays 

3 Positrons 

4 Antiprotons 


6 Conclusions 



The Gamma-Ray Spectrum 

The diffuse extragalactic gamma-ray spectrum was measured by 

EGRET 

A first analysis of the extragalactic spectrum gave a power law 

spectrum [P. Sreekumar et al. 1998] 

A more recent re-analysis revealed a clear excess over the power law 

behavior at energies above ∼ 1 GeV [A.W. Strong, I.V. Moskalenko, O. Reimer 

2004] 

E 2 dJ/dE [GeV cm -2 s -1 sr -1 ] 

10 -6 

10 -7 

0.1 1 10 100 

E [GeV] 

Interpretation of this excess in terms of dark matter annihilation or 

decay? 




Two contributions to the gamma-ray spectrum from gravitino decay: 

The signal from gravitino decays in the Milky Way halo 

A redshifted signal from extragalactic sources 

The halo contribution has an angular dependence on the line of sight 

The extragalactic contribution gives an isotropic signal 

The intensity of the two contributions is of the same order, with the 

halocomponent being slightly dominant 




Calculate decay rates from supergravity Lagrangian 

The model is highly constrained: gravitino interactions are 

completely fixed by symmetries 

b 

µ 

p 

ρ, a 

= − i δ ab γ µ [/p, γ ρ ] 

4M P 

→ Very predictive scenario from the particle physics point of view 




Light gravitino: m 3/2 < m W 

Injection spectrum is a monochromatic line from ψ 3/2 → γν at 

E = 1 2 m 3/2 

ν 

ψ 3/2 

˜γ 

γ 




Spectrum for light gravitino, m 3/2 = 10GeV: 

E 2 dJ/dE [GeV (cm 2 s str) -1 ] 

10 -6 

10 -7 

0.1 1 10 

E [GeV] 

[G. Bertone, W. Buchmüller, L. Covi, A. Ibarra 2007] 




Heavier gravitino: m 3/2 > m W , m Z 

ν 

˜Z 0 

ψ 3/2 

Z 0 

l ∓ 

˜W ∓ 

ψ 3/2 

W ± 




Heavier gravitino: m 3/2 > m W , m Z 

ψ 3/2 → Z 0 ν 

ψ 3/2 → W ± l ∓ 

ψ 3/2 → hν 

are kinematically allowed 

Only two free parameters: m 3/2 , τ 3/2 (under assumption of gaugino 

mass universality at the GUT scale, neglecting Higgs channel) 

10 0 Wτ 

100 1000 

Branching Ratio 

10 -1 

10 -2 

Zν τ 

hν τ 

γν τ 

10 -3 

m 3/2 [GeV] 




Fragmentation of the gauge bosons produces photons in the 

gamma-ray energy range, primarily from pion decay 

ν 

˜Z 0 

ψ 3/2 

˜W ∓ 

Z 0 

l ∓ 

ψ 3/2 

W ± 




Fragmentation of the gauge bosons produces photons in the 

gamma-ray energy range, primarily from pion decay 

ν 

˜Z 0 

ψ 3/2 

˜W ∓ 

Z 0 

l ∓ 

ψ 3/2 

W ± 

Determining the energy spectrum is a very complicated problem → 

use Monte Carlo simulation 




Spectrum for heavier gravitino: 


10 -7 

10 -6 0.1 1 10 100 

E [GeV] 






10 -7 

10 -6 0.1 1 10 100 

[A. Ibarra, DT 2007] 

E [GeV] 

m 3/2 = 150 GeV, τ 3/2 = 1.3 × 10 26 s. 






10 -7 

10 -6 0.1 1 10 100 


E [GeV] 

m 3/2 = 150 GeV, τ 3/2 = 1.3 × 10 26 s. 






10 -7 

10 -6 0.1 1 10 100 


E [GeV] 

m 3/2 = 150 GeV, τ 3/2 = 1.3 × 10 26 s. 






10 -7 

10 -6 0.1 1 10 100 


E [GeV] 

m 3/2 = 150 GeV, τ 3/2 = 1.3 × 10 26 s. 






10 -7 

10 -6 0.1 1 10 100 


E [GeV] 

m 3/2 = 150 GeV, τ 3/2 = 1.3 × 10 26 s. 

The monochromatic line is very characteristic and more strongly 

suppressed in the case of neutralino dark matter 




Together with the assumed power law background, the angular 

dependence of the predicted spectrum is mild enough to be easily 

compatible with the EGRET results 

The predicted anisotropy and the presence of the line may be tested 

by GLAST 

The line may also be detectable by Cerenkov telescopes in galaxies 

such as M31 



Outline 


2 Gamma Rays 

3 Positrons 

4 Antiprotons 


6 Conclusions 



The Positron Fraction 

Fragmentation of the gauge bosons also produces positrons and 

antiprotons → Important consistency check, but may also produce 

interesting signatures 

Complicated antimatter propagation due to diffusion and energy loss 

→ loss of directional and spectral information 

The astrophysics of propagation involves many uncertainties about 

properties of the interstellar medium 




Propagation is modeled using a cylindrical two-layer diffusion zone 

Diffusion-loss equation can be solved semi-analytically 

10 

5 

V c 

z [kpc] 

0 

Earth 

-5 

-10 

-20 -15 -10 -5 0 5 10 15 20 

r [kpc] 




Experiments usually measure the positron fraction 

HEAT measured an excess in the positron fraction that cannot be 

explained by standard production and propagation models 

HEAT 94/95/00 

Positron fraction e + /(e + + e − ) 

0.1 

Background only 

0.01 

1 10 100 1000 

T [GeV] 




Experiments usually measure the positron fraction 

HEAT measured an excess in the positron fraction that cannot be 

explained by standard production and propagation models 


0.1 

HEAT 94/95/00 

AMS-01 98 

CAPRICE 94 

MASS 91 


0.01 

1 10 100 1000 

T [GeV] 

Preliminary results from PAMELA seem to support an excess of 

positrons at higher energies! 




Using the EGRET excess to fix m 3/2 , τ 3/2 predicts a bump in the 

positron fraction in just the right energy range 


0.1 

HEAT 94/95/00 

AMS-01 98 

CAPRICE 94 

MASS 91 


0.01 

1 10 100 1000 

T [GeV] 

[A. Ibarra, DT 2008] 

m 3/2 = 150 GeV, τ 3/2 = 1.3 × 10 26 s, M2 propagation model. 




Using the EGRET excess to fix m 3/2 , τ 3/2 predicts a bump in the 

positron fraction in just the right energy range 

HEAT 94/95/00 

AMS-01 98 

CAPRICE 94 

MASS 91 

0.1 


Isothermal 

Moore et al. 

NFW 


0.01 

1 10 100 1000 

T [GeV] 


m 3/2 = 150 GeV, τ 3/2 = 1.3 × 10 26 s, M2 propagation model. 

Excellent agreement with the positron fraction measured by HEAT! 




The presence of the bump is not very sensitive to the astrophysical 

parameters 


0.1 

M2 

HEAT 94/95/00 

AMS-01 98 

CAPRICE 94 

MASS 91 


M1, MED 

0.01 

1 10 100 1000 

T [GeV] 


m 3/2 = 150 GeV, τ 3/2 = 1.3 × 10 26 s, NFW profile. 




The coincidence of parameters is very intriguing... 

The anomalies in gamma-rays and positrons are related in this 

model – interpreting one of them in terms of decaying gravitinos 

“predicts” the existence of the other 

HEAT 94/95/00 

AMS-01 98 

CAPRICE 94 

MASS 91 

0.1 


M2 



10 -6 

10 -7 

0.1 1 10 100 

M1, MED 

0.01 

1 10 100 1000 

T [GeV] 

E [GeV] 



Outline 


2 Gamma Rays 

3 Positrons 

4 Antiprotons 


6 Conclusions 



The Antiproton Spectrum 

Theoretical calculations describe the measured antiproton spectrum 

quite well 

→ No need for new physics in the antiproton spectrum (?) 

p – flux (m -2 sr -1 sec -1 GeV -1 ) 

10 -2 

2 

3 

4 

1 

5 

1 

2 

3 

4 

5 

10 -1 10 -1 1 10 

Cosmic Ray P – David Tran Indirect Signatures of Gravitino Dark Matter with Broken R-Parity 

BESS(95+97) 

BESS(93) 

IMAX 

CAPRICE 

Bottino 

Bergstrom 

Biebar 

Mitsui λ(R,β) 

Mitsui λ(R) 

10 -3 

Kinetic Energy (GeV)


Similar propagation mechanism as in the case of positrons 

We neglect effects of reacceleration and tertiary contributions 

Huge uncertainties due to degeneracies in the determination of the 

propagation parameters 

Primary antiproton flux can vary by two orders of magnitude for 

parameters compatible with the Boron-to-Carbon ratio 




Primary top-of-atmosphere antiproton spectrum: 

10 1 0.1 1 10 100 

Antiproton flux [GeV -1 m -2 s -1 sr -1 ] 

10 0 

10 -1 

10 -2 

10 -3 

MAX 

MED 

MIN 

BESS 95+97 

BESS 95 

IMAX 92 

CAPRICE 94 

CAPRICE 98 

Φ = 500 MV 

10 -4 


T [GeV] 

m 3/2 = 150 GeV, τ 3/2 = 1.3 × 10 26 s, different sets of propagation 

parameters. 

Dangerous overproduction of antiprotons → for MED, MAX 

parameters, the model is probably not phenomenologically viable 




The minimal case: 


10 -1 

10 -2 

10 0 0.1 1 10 

Background 

BESS 95+97 

BESS 95 

IMAX 92 

CAPRICE 94 

CAPRICE 98 

Signal 

Total 

10 -3 

Φ = 500 MV 


T [GeV] 

Together with the background, the flux is a factor ∼ 2 too large 

Is that enough to rule out the model? 



Outline 


2 Gamma Rays 

3 Positrons 

4 Antiprotons 


6 Conclusions 



The Antideuteron Spectrum 

No cosmic-ray antideuterons have been detected yet, only upper 

limits exist 

Antideuterons may form by coalescence of an antineutron-antiproton 

pair that lies very closely together in momentum space 

Spectral shape of background and dark matter signal are different at 

low energies 

Detection of a single antideuteron at low energies could provide 

important clue 



Outline 


2 Gamma Rays 

3 Positrons 

4 Antiprotons 


6 Conclusions 



Nice Features of Decaying Gravitino Dark Matter 

The gravitino is theoretically very well motivated 

Gravitino dark matter with broken R-parity reconciles thermal 

leptogenesis, primordial nucleosynthesis and supersymmetric dark 

matter 

Very few free parameters → predictive scenario that can “easily” be 

falsified experimentally 

May explain two anomalies simultaneously in a natural way, although 

the model was not invented for this purpose 



Overview of the Indirect Signatures 

For the MIN propagation model, we get these possible signatures of 

gravitino decay 

EGRET 

HEAT 94/95/00 

E 2 dJ/dE [(cm 2 str s) -1 GeV] 


0.1 

10 -6 

10 -7 

0.1 1 10 100 

E [GeV] 

0.01 

1 10 100 1000 

T [GeV] 

10 -1 BESS 95+97 

0.1 1 10 


10 -2 

φ F = 500 MV 

10 -3 

T [GeV] 



Conclusions 

Gravitino dark matter with broken R-parity is an attractive scenario 

The antiproton flux is an important constraint and potentially 

dangerous for the model 

It will be interesting to refine the analysis using a more realistic 

propagation model 

GLAST and PAMELA (AMS-02?) will soon provide clarification on 

the existence of the anomalies and their interpretation in terms of 

new physics 

Collider searches at the LHC for low-energy supersymmetry and 

direct detection experiments will provide complementary information 

We will soon be able to test this scenario!

Tran - DESY Theory workshop 2008

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