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:0707.2510 Lola, Osland, ARR, arXiv:0811.2969 and various papers in preparation. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAA
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 IPPP Seminar Durham 2/20
Decaying Gravitino Dark Matter The WMAP pie There is more than one ingredient in this pie: CMB, 2dFGRS, Lya-forest, SN1a LCDM Decaying Gravitino Dark Matter IPPP Seminar Durham 3/20
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 IPPP Seminar Durham 4/20
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 IPPP Seminar Durham 5/20
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/0106204] Decaying Gravitino Dark Matter IPPP Seminar Durham 6/20
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)] Decaying Gravitino Dark Matter IPPP Seminar Durham 7/20
The DM needs to stick around Need mechanism to keep DM (almost) stable! Need a lifetime of tDMtuniverse13.7£ 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 IPPP Seminar Durham 8/20
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 Decaying Gravitino Dark Matter IPPP Seminar Durham 9/20
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. Decaying Gravitino Dark Matter IPPP Seminar Durham 10/20
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? Decaying Gravitino Dark Matter IPPP Seminar Durham 11/20
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 IPPP Seminar Durham 12/20
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/0005214] [Moreau, Chemtob, hep-ph/0107286] Decaying Gravitino Dark Matter IPPP Seminar Durham 13/20
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/0702184] [H. Yuksel, M.D. Kistler, arXiv:0711.2906] [Lola, Osland, ARR, arXiv:0707.2510] [M. Taoso et al., arXiv:0711.4996] [G. Bertone et al., arXiv:0709.2299] [A. Ibarra, D. Tran, arXiv:0804.4596] [K. Ishiwata et al., arXiv:0805.1133] [W. Buchmuller et al., arXiv:0809.4667] [L. Covi et al., arXiv:0809.5030] [A. Ibarra, D. Tran, arXiv:0811.1555] [Lola, Osland, ARR, arXiv:0811.2969] [F. Takahashi et al., arXiv:0901.21.68] Decaying Gravitino Dark Matter IPPP Seminar Durham 14/20
Decaying Gravitino Dark Matter For trilinear RPV the three-body gravitino decays were calculated in [Moreau, Chemtob, hep-ph/0107286] Decays suppressed by Planck mass R-violating coupling Three-body phase space Sfermion mass Fermion final state mass Decaying Gravitino Dark Matter IPPP Seminar Durham 15/20
Decaying Gravitino Dark Matter We have calculated the radiative gravitino decay [Lola, Osland, ARR, arXiv:0707.2510] Decays suppressed by Planck mass R-violating coupling Loop factors All three diagrams needed to get gauge invariance. Decaying Gravitino Dark Matter IPPP Seminar Durham 16/20
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/9503210] Decaying Gravitino Dark Matter IPPP Seminar Durham 17/20
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. Decaying Gravitino Dark Matter IPPP Seminar Durham 18/20
Three-body vs. Radiative decay Radiative decay dominates for low gravitino masses: [Lola, Osland, ARR, arXiv:0803.0547] Decaying Gravitino Dark Matter IPPP Seminar Durham 19/20
Insensitivity to sfermion mass Gravitino-sfermion-fermion vertex: depends on loop 4-momentum [Lola, Osland, ARR, arXiv:0707.2510] Decaying Gravitino Dark Matter IPPP Seminar Durham 20/20
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 IPPP Seminar Durham 21/20
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/0012052] Need a number for reheating temperature! Decaying Gravitino Dark Matter IPPP Seminar Durham 22/20
Decaying Gravitino Dark Matter Constraints on GDM Dark Matter density Big Bang Nucleosynthesis Long lived NLSP problem avoided by RPV. Decaying Gravitino Dark Matter IPPP Seminar Durham 23/20
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 IPPP Seminar Durham 24/20
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 IPPP Seminar Durham 25/20
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 IPPP Seminar Durham 26/20
Decaying Gravitino Dark Matter Constraints on GDM Photon flux taken from EGRET data [P. Sreekumar et al., astro-ph/9709257] Recent re-analysis: [A.W. Strong et al., astro-ph/0406254] [G. Bertone et al., arXiv:0709.2299] Decaying Gravitino Dark Matter IPPP Seminar Durham 27/20
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:0811.2969] [Bomark, Lola, Osland, ARR, in preparation] Decaying Gravitino Dark Matter IPPP Seminar Durham 28/20
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:0811.2969] [Bomark, Lola, Osland, ARR, in preparation] Decaying Gravitino Dark Matter IPPP Seminar Durham 29/20
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 IPPP Seminar Durham 30/20
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. Decaying Gravitino Dark Matter IPPP Seminar Durham 31/20
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 IPPP Seminar Durham 32/20
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 IPPP Seminar Durham 33/20