Gravitino Dark Matter

Michael Grefe

Departamento de F´ısica Teorica´ Instituto de F´ısica Teorica´ UAM/CSIC Universidad Autonoma´ de Madrid

Exotic Physics with Neutrino Telescopes 2013

Centre de Physique des Particules de Marseille 3 April 2013

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 1 / 15 Motivation for Unstable Gravitino Dark Matter What Do We Know about Dark Matter?

I Observed on various scales through its gravitational interaction I Contributes significantly to the energy density of the universe

[M. Whittle] [ESA / Planck Collaboration] [NASA / Clowe et al.]

I Dark matter properties known from observations: • No electromagnetic and strong interactions • At least gravitational and at most weak-scale interactions • Non-baryonic • Cold (maybe warm) • Extremely long-lived but can be unstable! [ESA / Planck Collaboration]

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 2 / 15 Motivation for Unstable Gravitino Dark Matter Gravitino Dark Matter: Stable or Unstable?

I Stable Gravitino Dark Matter • Typical in gauge mediation with conserved R-parity −4 • No direct detection signal expected: σN ∼ MPl −4 • No annihilation signal expected: σann ∼ MPl • Collider signals from long-lived NLSP expected • Long-lived NLSP can be in conflict with BBN [The Particle Zoo] I Unstable Gravitino Dark Matter • Typical candidate in models with R-parity violation • Lifetime larger than the age of the universe −4 • No direct detection signal expected: σN ∼ MPl • Decays could lead to observable cosmic-ray signals • Collider signals from long-lived NLSP expected

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 3 / 15 Gravitino Dark Matter with Broken R Parity Models with Gravitino DM and R-Parity Violation

I Bilinear R-parity violation (BRpV) [Takayama, Yamaguchi (2000), Restrepo et al. (2011)] • R-parity violation is source of neutrino masses and mixings • Predictive model: gravitino mass constrained to be below few GeV

I ”µ from ν” Supersymmetric SM (µνSSM) [Lopez-Fogliani,´ Munoz˜ (2005)] • Electroweak see-saw mechanism for neutrino masses • Solves the µ-problem similar to the NMSSM • Predictive model: gravitino mass constrained to be below few GeV

I Bilinear R-parity violation from B–L breaking [Buchmuller¨ et al. (2007)] • Consistent gravitino cosmology with thermal leptogenesis and BBN

•O (10) GeV < m3/2 < O(500) GeV, gluino mass below a few TeV I Trilinear R-parity violation [Moreau et al. (2001), Lola et al. (2007)] • Phenemenological study, trilinear terms generically expected without R-parity

I PeV neutrino events from gravitino decay? [Feldstein et al. (2013)] • Gravitino mass and lifetime: 2.4 PeV, 1028 s. Continuum neutrinos observable?

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 4 / 15 Gravitino Dark Matter with Broken R Parity Gravitino Decay Channels

I Bilinear R-parity violation • Several two-body decay channels: ψ3/2 → γν i , Z νi , W `i , h νi • Neutrino line + continuous spectrum • Flavour of the monochromatic neutrino depends on the flavour structure of RpV [MG (2011)]

f I Trilinear R-parity violation • Several three-body decay channels: G ¯ ¯ ¯ pf f˜ ψ3/2 → νi `j `k ,ν i dj dk , `i uj dk , ui dj dk

R • Depends on flavour structure of RpV • 6 (c) γ k • Continuous neutrino spectrum ℓ G ν pf • p k • Two-body decay only possible via loops: R − ℓ˜ 6 ψ3/2 → γν i [Lola et al. (2007)]

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 5 / 15 Gravitino Dark Matter with Broken R Parity Final State Particle Spectra

I Gravitino decays produce stable cosmic rays: γ, e, p, d,ν e/µ/τ • Spectra can be simulated with PYTHIA

• Soft part dominated by pion decay: νµ ∼ 2 × νe , ντ much lower • Spectral features close to high-energy cut-off from Z, W , h decay

• In addition neutrino line at E ∼ m3/2/2

1 10 Ψ3 2 ® Z Νi , Νe Νe Spectrum 10 Ψ3 2 ® Z Νi , ΝΜ ΝΜ Spectrum Ψ3 2 ® Z Νi , ΝΤ ΝΤ Spectrum dx  dx  dx  dN  

dN  x dN  x  0.1  x 1 1

Spectrum 0.01 Spectrum Spectrum

0.1 0.1

Neutrino -3 Neutrino 10 100 GeV 100 GeV Neutrino 100 GeV m3 2 = 1 TeV m3 2 = 1 TeV m3 2 = 1 TeV Tau Muon

Electron 10 TeV 10 TeV 10 TeV 0.01 0.01 -4   10  10-6 10-5 10-4 10-3 0.01 0.1 1 10-6 10-5 10-4 10-3 0.01 0.1 1 10-4 10-3 0.01 0.1 1 Energy x = 2 E m Energy x = 2 E m Energy x = 2 E m 3 2 3 2 [MG et al. (2013)] 3 2

     

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 6 / 15 Indirect Detection of Gravitino Dark Matter Cosmic-Ray Propagation

I Cosmic rays from gravitino decays propagate through the Milky Way

I Experiments observe spectra of cosmic rays at Earth

[NASA E/PO, SSU, Aurore Simonnet] [AMS-02 Collaboration] [IceCube Collaboration]

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 7 / 15 Directional detection can distinguish unstable gravitino from WIMPs!

Indirect Detection of Gravitino Dark Matter Difference of Dark Matter Annihilations and Decays

I Angular distribution of the gamma-ray/neutrino flux from the galactic halo: Dark Matter Annihilation Dark Matter Decay dJ σv dN dJ 1 dN halo DM 2 ~ ~ halo = ρ (~) ~ = h i 2 ρhalo(l) dl halo l dl dE 8π mDM dE dE 4π τDM mDM dE l.o.s.Z l.o.s.Z particle physics astrophysics particle physics astrophysics Annihilation (e.g. WIMP dark matter)

NFW Anticenter • Annihilation cross section related to relic density 100

to Einasto Isothermal • Strong signal from peaked structures annihilation • Uncertainties from choice of halo profile Normalized 10 Decay (e.g. unstable gravitino dark matter) Integral

decay

Sight • Lifetime unrelated to production in early universe - 1 value at galactic anticenter of - • Less anisotropic signal

Line -180 ° -90 ° 0 ° 90 ° 180 ° Galactic Longitude [MG (2011)] • Less sensitive to the halo model

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 8 / 15 Indirect Detection of Gravitino Dark Matter Difference of Dark Matter Annihilations and Decays

I Angular distribution of the gamma-ray/neutrino flux from the galactic halo: Dark Matter Annihilation Dark Matter Decay dJ σv dN dJ 1 dN halo DM 2 ~ ~ halo = ρ (~) ~ = h i 2 ρhalo(l) dl halo l dl dE 8π mDM dE dE 4π τDM mDM dE l.o.s.Z l.o.s.Z particle physics astrophysics particle physics astrophysics Annihilation (e.g. WIMP dark matter)

NFW Anticenter • Annihilation cross section related to relic density 100

to Einasto Isothermal • Strong signal from peaked structures annihilation • Uncertainties from choice of halo profile Normalized 10 Decay (e.g. unstable gravitino dark matter) Integral

decay

Sight • Lifetime unrelated to production in early universe - 1 value at galactic anticenter of - • Less anisotropic signal

Line -180 ° -90 ° 0 ° 90 ° 180 ° Galactic Longitude [MG (2011)] • Less sensitive to the halo model Directional detection can distinguish unstable gravitino from WIMPs!

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 8 / 15 Indirect Detection of Gravitino Dark Matter Neutrino Signals from Gravitino Decays

I Atmospheric neutrinos are dominant background for gravitino decay signal • Discrimination of neutrino flavours allows to reduce the background • Sensitivity best for large gravitino masses

3 ç æ - Ν 10 ò ò IceCube-79 Νe IceCube 40 Unfolding Μ ò ò ó ó ó Fréjus Νe IceCube-40 Forward Folding ΝΜ ó ò ò ì - Ν L ò AMANDA II Unfolding Μ 1 100 ó - ó ó AMANDA-II Forward Folding ΝΜ sr

1 ò Super-Kamiokande ΝΜ - ò s 10 2 ó ò Fréjus ΝΜ - æ Ν

m atm. Μ æ ò atm. Νe 1 ç æ GeV

H atm. ΝΤ æ preliminary ç ì

Flux æ 0.1 ò ì 26 ç æ ì Τ3 2 = 10 s ì æ 0.01 ì Neutrino  ç æ ì

´ ì 2 æ Ν - ì E 10 3 æ ì 100 GeV 1 TeV 10 TeV æ 10-4 1 10 100 1000 10 000 100 000 Neutrino Energy EΝ GeV [MG et al. (2013)] I Neutrinos from models like BRpV and µνSSMH L most likely not observable • Sensitivity to lifetimes beyond 1028 s needed at energies around 1 GeV

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 9 / 15 Indirect Detection of Gravitino Dark Matter Neutrino Detection – Upward Through-Going Muons

I Muon tracks from charged current DIS of muon neutrinos off nuclei Advantages • Muon track reconstruction is well-understood at neutrino telescopes Disadvantages • Neutrino–nucleon DIS and propagation energy losses shift muon spectrum to lower energies

• Bad energy resolution (∼ 0.3 in log10 E) smears out cut-off energy

Upward Through-Going Muons Upward Through-Going Muons 105 10 4 atmospheric background

L 10 1 - yr

2 3

- 10 1 km H 100 0.1 10 Statistical Significance Muon Flux 26 Τ32 = 10 s 1 m32 = 100 GeV 1 TeV 10 TeV 0.01 m32 = 100 GeV 1 TeV 10 TeV 26 Τ32 = 10 s 0.1 1 10 100 1000 10 000 100 000 1 10 100 1000 10 000 100 000 Energy HGeVL Energy HGeVL [MG (2011)]

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 10 / 15 Indirect Detection of Gravitino Dark Matter Neutrino Detection – Improvements With Cascades

I Hadronic and electromagnetic cascades from charged current DIS of electron and tau neutrinos and neutral current interactions of all neutrino flavours Disadvantages • TeV-scale cascades are difficult to discriminate from short muon tracks Advantages • 3× larger signal and 3× lower background compared to other channels

• Better energy resolution (0.18 in log10 E) helps to distinguish spectral features

Shower Events 106 Shower Events 100

5 L

1 10 -

yr atmospheric background 10 3 4 - 10 km H 1 103

100 0.1 Statistical Significance Shower Rate Τ = 1026 s 26 10 32 Τ32 = 10 s = 0.01 m32 100 GeV 1 TeV 10 TeV m32 = 100 GeV 1 TeV 10 TeV 1 1 10 100 1000 10 000 100 000 1 10 100 1000 10 000 100 000 Energy HGeVL Energy HGeVL [MG (2011)]

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 11 / 15 Indirect Detection of Gravitino Dark Matter Gravitino Decay Signals in Cosmic-Ray Spectra

Antiproton Flux 0.1 preliminary æ PAMELA data Astrophysical Background æ æ æ æ æ æ æ L æ æ æ 1 æ MAX 150 GeV - 0.01 æ æ sr æ æ MED 1 TeV 1 æ - MIN 5 TeV s æ 2 æ - 10-3 m æ 28 1 Τ = - 3 2 10 s æ

GeV æ H 10-4 

Flux æ 10-5 æ Antiproton 10-6

10-7 0.1 1 10 100 1000 Kinetic Energy GeV [MG et al. (2013)]

I Observed antiproton spectrum well describedH L by astrophysical background • No need for contribution from dark matter Lifetimes below (1026–1028) s excluded I O • Gravitino decay cannot explain PAMELA and Fermi LAT cosmic-ray anomalies

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 12 / 15 Indirect Detection of Gravitino Dark Matter Limits on the Gravitino Lifetime

Antiproton Limits Neutrino Limits

1028 preliminary 26 L L

s s 10 preliminary H H

1027 Lifetime Lifetime 1025 on on Limit Limit

1024 1026 Upper Upper MAX Bino NLSP Bino NLSP CL CL ΝΜ limits Wino NLSP

% MED Wino NLSP % 23 95 95 Ν limits Higgsino NLSP MIN Higgsino NLSP 10 e

1025 100 103 104 100 103 104 Gravitino Mass GeV Dark Matter Mass GeV [MG et al. (2013)] Cosmic-ray data give bounds on gravitino lifetime I H L H L • Uncertainties from charged cosmic-ray propagation through the Milky Way

I Estimated bounds on gravitino lifetime from atmospheric neutrino data • Neutrino sensitivity could be competitive for heavy gravitinos • Bounds from cascade events are already stronger than bounds from track events • Improvement with a dedicated analysis using angular and spectral information?

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 13 / 15 Thanks for your attention!

Summary Summary

Both, stable and unstable gravitinos, are viable dark matter candidates • Gravitino DM models with broken R-parity are well motivated: • could explain neutrino masses / solve cosmological gravitino problem

Decaying gravitino DM can be probed in colliders and cosmic rays • Gravitino decays from bilinear RpV produce neutrino line • Neutrino telescopes have best sensitivity for heavy gravitino DM • Cascade events appear to be the most valuable channel • A dedicated search for gravitino signals could improve the sensitivity •

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 14 / 15 Summary Summary

Both, stable and unstable gravitinos, are viable dark matter candidates • Gravitino DM models with broken R-parity are well motivated: • could explain neutrino masses / solve cosmological gravitino problem

Decaying gravitino DM can be probed in colliders and cosmic rays • Gravitino decays from bilinear RpV produce neutrino line • Neutrino telescopes have best sensitivity for heavy gravitino DM • Cascade events appear to be the most valuable channel • A dedicated search for gravitino signals could improve the sensitivity •

Thanks for your attention!

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 14 / 15 Further Reading Further Reading ...

I Models with decaying gravitino dark matter • Takayama et al., Phys. Lett. B 485 (2000) 388 [hep-ph/0005214] • Lopez-Fogliani´ et al., Phys. Rev. Lett. 97 (2006) 041801 [hep-ph/0508297] • Buchmuller¨ et al., JHEP 0703 (2007) 037 [hep-ph/0702184] • Lola et al., Phys. Lett. B 656 (2007) 83 [arXiv:0707.2510 [hep-ph]] • Bajc et al., JHEP 1005 (2010) 048 [arXiv:1002.3631 [hep-ph]] • D´ıaz et al., Phys. Rev. D 84 (2011) 055007 [arXiv:1106.0308 [hep-ph]] • Restrepo et al., Phys. Rev. D 85 (2012) 023523 [arXiv:1109.0512 [hep-ph]] • ...

I Neutrino signals from gravitino decays • Covi et al., JCAP 0901 (2009) 029 [arXiv:0809.5030 [hep-ph]] • Bomark et al., Phys. Lett. B 686 (2010) 152 [arXiv:0911.3376 [hep-ph]] • Erkoca et al., Phys. Rev. D 82 (2010) 113006 [arXiv:1009.2068 [hep-ph]] • MG, DESY-THESIS-2011-039 [arXiv:1111.6779 [hep-ph]] • Feldstein et al., arXiv:1303.7320 [hep-ph] • ...

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter EPNT 2013 – 3 April 2013 15 / 15