1. Decaying Gravitino Dark Matter
Are Raklev
University of Cambridge
In collaboration with Deirdre Black (Cambridge), Nils-Erik Bomark (Bergen), Magda Lola (Patras), Emanuel Malek (Cambridge), Per Osland (Bergen) and Helen Vryonidou (Cambridge)
Based on Lola, Osland, ARR, arXiv:
Lola, Osland, ARR, arXiv:
and various papers in preparation.
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2. Decaying Gravitino Dark Matter
Main Points
Motivation: Dark Matter & SUSY
The necessity of R-parity?
Decaying Dark Matter: The gravitino case
Some calculations on gravitino decays
Cosmological (and other) model constraints
(If time) some LHC phenomenology
Conclusions, hopes & dreams
Decaying Gravitino Dark Matter
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2/20

3. Decaying Gravitino Dark Matter
The WMAP pie
There is more than one ingredient in this pie: CMB, 2dFGRS, Lya-forest, SN1a
LCDM
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3/20

4. Decaying Gravitino Dark Matter
Why do we like SUSY?
SUSY
MSSM
GMSB
CMSSM
NMSSM
Split
SUSY
AMSB
Full of (more or less) good Dark Matter candidates
Decaying Gravitino Dark Matter
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4/20

5. Decaying Gravitino Dark Matter
WIMPs au naturel?
Astrophysics measurements have pinned down the DM density
The relic density of a Weakly Interacting Massive Particle (WIMP) c is suggestive
The lightest neutralino of the MSSM seems to be a good candidate.
Decaying Gravitino Dark Matter
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5/20

6. Decaying Gravitino Dark Matter
WIMPs au naturel?
CMSSM/mSUGRA for generic values of
No EWSB
Tend to overproduce neutralinos, they’re a bit on the heavy side...
Shown is: bulk, stau-coannihilation, higgs-funnel and focus point.
Stau LSP
[Battaglia et al., hep-ph/ ]
Decaying Gravitino Dark Matter
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6/20

7. Decaying Gravitino Dark Matter
WIMPs au naturel?
Astrophysics measurements have pinned down the DM density
However, the WIMPs are just a special case, more generically we get
We may well have DM in a Hidden Valley.
[Feng, Kumar, Phys. Rev. Lett. 101 (2008)]
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7/20

8. The DM needs to stick around
Need mechanism to keep DM (almost) stable!
Need a lifetime of tDMtuniverse13.7£ 109 y
A symmetry is usually introduced:
R-parity in SUSY
T-parity in Little Higgs
KK-parity in UED
... in your own favourite model
What about (super-)weak coupling? Seems to require intolerable fine-tuning.
Decaying Gravitino Dark Matter
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8/20

9. R-parity and all that jazz
Conservation of R-parity
Sparticles decay into sparticles.
Sparticles produced in pairs.
Lightest sparticle (LSP) is a natural DM candidate if weakly interacting.
collider cascade decays
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10. R-parity and all that jazz
Conservation of R-parity
A priori, R-parity violating (RPV) terms
are allowed in the MSSM superpotential.
Allowed, meaning gauge invariant.
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10/20

11. Decaying Gravitino Dark Matter
R-parity violation
The R-parity violating terms
are problematic:
Violate lepton and baryon number.
Can lead to rapid proton decay.
No SUSY Dark Matter candidate?
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11/20

12. Decaying Gravitino Dark Matter
R-parity violation
Conservation of R-parity
Prevents rapid proton decay and other unwanted lepton and baryon number violating processes.
However, dimension-5 operators can still contribute to proton decay.
Saving the proton can be done by introducing a baryon or lepton triality (Z3) instead.
We now look at a possibility for SUSY DM even if there are non-zero RPV couplings!
[Ibanez, Ross, Nucl. Phys. B368, 3-37 (1992)]
Decaying Gravitino Dark Matter
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12/20

13. Decaying Gravitino Dark Matter
Gravity is a natural choice for giving a super-weak coupling.
Since gravitino interactions are suppressed by the Planck mass, Mp~1018 GeV, with a gravitino LSP the DM lifetime goes as easily far above the age of the universe!
[Berezinsky, Phys. Lett. B261, 71-75, 1991]
[Takayama, Yamaguchi, hep-ph/ ]
[Moreau, Chemtob, hep-ph/ ]
Decaying Gravitino Dark Matter
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13/20

14. Decaying Gravitino Dark Matter
The idea has been around for some time – but not recieved much attention until recently:
Most work has centered on bilinear RPV. (neutrino-neutralino mixing decays gravitino)
[W. Buchmuller et al., hep-ph/ ]
[H. Yuksel, M.D. Kistler, arXiv: ]
[Lola, Osland, ARR, arXiv: ]
[M. Taoso et al., arXiv: ]
[G. Bertone et al., arXiv: ]
[A. Ibarra, D. Tran, arXiv: ]
[K. Ishiwata et al., arXiv: ]
[W. Buchmuller et al., arXiv: ]
[L. Covi et al., arXiv: ]
[A. Ibarra, D. Tran, arXiv: ]
[Lola, Osland, ARR, arXiv: ]
[F. Takahashi et al., arXiv: ]
Decaying Gravitino Dark Matter
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14/20

15. Decaying Gravitino Dark Matter
For trilinear RPV the three-body gravitino decays were calculated in
[Moreau, Chemtob, hep-ph/ ]
Decays suppressed by
Planck mass
R-violating coupling
Three-body phase space
Sfermion mass
Fermion final state mass
Decaying Gravitino Dark Matter
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15/20

16. Decaying Gravitino Dark Matter
We have calculated the radiative gravitino decay
[Lola, Osland, ARR, arXiv: ]
Decays suppressed by
Planck mass
R-violating coupling
Loop factors
All three diagrams needed to get gauge invariance.
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16/20

17. Radiative decay calculation
We use the Rarita-Schwinger formalism for spin-3/2 particles with gravitino vertices:
This is a low-energy effective theory.
[See e.g. Moroi, hep-ph/ ]
Decaying Gravitino Dark Matter
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17/20

18. Radiative decay calculation
The resulting total width is
where
Note the fermion mass dependence.
C_0 and B_0 are three and two-point functions of the loop masses.
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18/20

19. Three-body vs. Radiative decay
Radiative decay dominates for low gravitino masses:
[Lola, Osland, ARR, arXiv: ]
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20. Insensitivity to sfermion mass
Gravitino-sfermion-fermion vertex:
depends on loop 4-momentum
[Lola, Osland, ARR, arXiv: ]
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21. An aside on gravitino masses
What is a ”natural” gravitino mass?
Really depends on you favourite method for SUSY breaking.
Gravity mediated
Simplest models (Polonyi, dilaton) suggest
Gauge mediation
Light gravitino masses generic.
Could be down below keV scale.
For gauge mediation the radiative decay may well be the only one.
Decaying Gravitino Dark Matter
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21/20

22. Decaying Gravitino Dark Matter
Constraints on GDM
Dark Matter density
The thermal production of gravitinos after inflation depends on re-heating temperature TR.
Can well be in correct range.
[M. Bolz, W. Buchmüller, M. Plümacher, hep-ph/ ]
Need a number for reheating temperature!
Decaying Gravitino Dark Matter
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22/20

23. Decaying Gravitino Dark Matter
Constraints on GDM
Dark Matter density
Big Bang Nucleosynthesis
Long lived NLSP problem avoided by RPV.
Decaying Gravitino Dark Matter
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23/20

24. Decaying Gravitino Dark Matter
Constraints on GDM
Dark Matter density
Big Bang Nucleosynthesis
Genesis
Baryo-/Leptogenesis may be washed out if RPV strong enough at electroweak phase transition.
Flavour effects may help.
Decaying Gravitino Dark Matter
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24/20

25. Decaying Gravitino Dark Matter
Constraints on GDM
Dark Matter density
Big Bang Nucleosynthesis
Genesis
Neutrino masses
RPV couplings can give rise to neutrino masses.
Gives restrictions on RPV couplings.
May explain measured masses.
Decaying Gravitino Dark Matter
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25/20

26. Decaying Gravitino Dark Matter
Constraints on GDM
Dark Matter density
Big Bang Nucleosynthesis
Genesis
Neutrino masses
Photon flux (!)
Measurement of galactic and diffuse extra-galactic gamma ray flux constrains RPV-couplings.
Perhaps also interesting to look at PAMELAs positrons and/or neutrinos?
Decaying Gravitino Dark Matter
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26/20

27. Decaying Gravitino Dark Matter
Constraints on GDM
Photon flux taken from EGRET data
[P. Sreekumar et al., astro-ph/ ]
Recent re-analysis:
[A.W. Strong et al., astro-ph/ ]
[G. Bertone et al., arXiv: ]
Decaying Gravitino Dark Matter
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27/20

28. Decaying Gravitino Dark Matter
Constraints on GDM
We set limits lmax on RPV coupling vs. gravitino mass, using photon flux taken from EGRET.
Need to take into account redshift.
Assuming one dominant coupling.
[Lola, Osland, ARR, arXiv: ]
[Bomark, Lola, Osland, ARR, in preparation]
Decaying Gravitino Dark Matter
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28/20

29. Decaying Gravitino Dark Matter
Constraints on GDM
Due to loop-decay dependence on fermion mass, lmax is very flavour dependent.
Assuming one dominant coupling.
[Lola, Osland, ARR, arXiv: ]
[Bomark, Lola, Osland, ARR, in preparation]
Decaying Gravitino Dark Matter
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29/20

30. Decaying Gravitino Dark Matter
Low mass gravitino
For light gravitinos hadronization effects are important.
Two-body decays to meson+lepton dominate.
[Black, Malek, ARR, Vryonidou in preparation]
Decaying Gravitino Dark Matter
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30/20

31. Phenomenology at the LHC
Large variety of signatures depending on dominant RPV-coupling.
Gravitino never produced. Great variety of decay signatures for NLSP.
Most NLSP/RPV-coupling combinations not fully reconstructable due to neutrinos.
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31/20

32. Decaying Gravitino Dark Matter
Conclusions
The gravitino is a possible Dark Matter candidate even with large RPV couplings.
For light(ish) gravitinos, radiative loop decays are important and even dominant.
Measurements of photon flux set strict upper bounds on RPV couplings in these scenarios.
We are eagerly awaiting Fermi/GLAST data to set even strickter bounds, or...
Decaying Gravitino Dark Matter
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32/20

33. Decaying Gravitino Dark Matter
Triality?
Lepton triality, allowing bilinear RPV-coupling:
Baryon triality, allowing bilinear
RPV-coupling.
Baryon triality, dis-allowing bilinear RPV-coupling.
Decaying Gravitino Dark Matter
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33/20