Antiproton Limits on Decaying Gravitino Dark Matter

Antiproton Limits on Decaying Gravitino Dark Matter Michael Grefe Departamento de Física Teórica Instituto de Física Teórica UAM/CSIC Universidad Autónoma de Madrid Particle Theory Journal Club Rudolf Peierls Centre for Theoretical Physics University of Oxford 13 June 2013 based on T. Delahaye and MG: arxiv:1305.7183 Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 1 / 26

Outline Motivation for Decaying Gravitino Dark Matter Gravitino Dark Matter with Broken R Parity Indirect Detection of Gravitino Dark Matter Antiproton Limits on the Lifetime and the Amount of R-Parity Violation Conclusions Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 2 / 26

Motivation for Decaying Gravitino Dark Matter Motivation for Decaying Gravitino Dark Matter Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 3 / 26

Motivation for Decaying Gravitino Dark Matter What Do We Know about Dark Matter? Observed on various scales through its gravitational interaction Contributes significantly to the energy density of the universe [M. Whittle] [ESA / Planck Collaboration] [NASA / Clowe et al.] 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) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 4 / 26

Motivation for Decaying Gravitino Dark Matter How Can We Unveil the Nature of Dark Matter? I Three search strategies for dark matter Direct detection in the scattering off matter nuclei Production of dark matter particles at colliders Indirect detection in cosmic ray signatures [Max-Planck-Institut fu r Kernphysik] [CERN] Michael Grefe (IFT UAM/CSIC) [Aprile et al. (2012)] Antiproton Limits on Decaying Gravitino Dark Matter [AMS Collaboration] University of Oxford 13 June 2013 5 / 26

Motivation for Decaying Gravitino Dark Matter How Can We Unveil the Nature of Dark Matter? I Three search strategies for dark matter Direct detection in the scattering off matter nuclei Production of dark matter particles at colliders Indirect detection in cosmic ray signatures [Max-Planck-Institut fu r Kernphysik] [CERN] [Aprile et al. (2012)] [AMS Collaboration] A combination will be necessary to identify the nature of particle dark matter! Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 5 / 26

Motivation for Decaying Gravitino Dark Matter Gravitino Dark Matter: Stable or Unstable? Stable Gravitino Dark Matter Typical in gauge mediation with conserved R-parity No direct detection signal expected: σ N M 4 Pl No annihilation signal expected: σ ann M 4 Pl Collider signals from long-lived NLSP expected Long-lived NLSP can be in conflict with BBN Unstable Gravitino Dark Matter [The Particle Zoo] Typical candidate in models with R-parity violation Lifetime larger than the age of the universe No direct detection signal expected: σ N M 4 Pl Decays could lead to observable cosmic-ray signals Collider signals from long-lived NLSP expected Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 6 / 26

Motivation for Decaying Gravitino Dark Matter Why Decaying Gravitino Dark Matter? Smallness of observed neutrino masses motivates seesaw mechanism Explains baryon asymmetry via thermal leptogenesis [Fukugita, Yanagida (1986)] Needs high reheating temperature: T R 10 9 GeV [Davidson, Ibarra (2002)] Supergravity predicts gravitino as spin-3/2 superpartner of the graviton Gravitinos are thermally produced after inflation in the early universe: ( ) 3 ( ) ( ) ( ) Ω TP 3/2 h2 ω i gi 2 1 + M2 i ki m3/2 T R 3 m3/2 2 ln g i 100 GeV 10 10 GeV i=1 Problem in scenarios with neutralino dark matter: Gravitino decays suppressed by Planck scale: ( τ 3/2 M2 Pl 100 GeV 3 years m 3 m 3/2 3/2 ) 3 [Pradler, Steffen (2006)] Decays with τ O(1 1000 s) spoil BBN Cosmological gravitino problem Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 7 / 26

Motivation for Decaying Gravitino Dark Matter Why Decaying Gravitino Dark Matter? Smallness of observed neutrino masses motivates seesaw mechanism Explains baryon asymmetry via thermal leptogenesis [Fukugita, Yanagida (1986)] Needs high reheating temperature: T R 10 9 GeV [Davidson, Ibarra (2002)] Supergravity predicts gravitino as spin-3/2 superpartner of the graviton Gravitinos are thermally produced after inflation in the early universe: ( ) 3 ( ) ( ) ( ) Ω TP 3/2 h2 ω i gi 2 1 + M2 i ki m3/2 T R 3 m3/2 2 ln g i 100 GeV 10 10 GeV i=1 Problem in scenarios with neutralino dark matter: Gravitino decays suppressed by Planck scale: ( τ 3/2 M2 Pl 100 GeV 3 years m 3 m 3/2 3/2 ) 3 [Pradler, Steffen (2006)] Decays with τ O(1 1000 s) spoil BBN Cosmological gravitino problem Possible solution: Gravitino is the LSP and thus stable! Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 7 / 26

Motivation for Decaying Gravitino Dark Matter Why Decaying Gravitino Dark Matter? Relation between gravitino mass and reheating temperature: Delahaye & Grefe 2013 10 11 Reheating Temperature T R GeV 10 10 10 9 10 8 10 7 excluded by gluino searches m g 500 GeV no thermal leptogenesis m g 10 TeV disfavoured by hierarchy problem Gravitino not LSP 1 10 100 1000 10 000 With thermal leptogenesis correct relic density possible for O(10) GeV < m 3/2 < O(500) GeV Gravitino dark matter [Buchmüller et al. (2008))] Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 8 / 26

Motivation for Decaying Gravitino Dark Matter Why Decaying Gravitino Dark Matter? Still problematic: NLSP can only decay to gravitino LSP: τ NLSP 48πM2 Plm 2 3/2 m 5 NLSP ( ) 2 ( m3/2 150 GeV 9 days 10 GeV m NLSP ) 5 Late NLSP decays are in conflict with BBN Cosmological gravitino problem Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 9 / 26

Motivation for Decaying Gravitino Dark Matter Why Decaying Gravitino Dark Matter? Still problematic: NLSP can only decay to gravitino LSP: τ NLSP 48πM2 Plm 2 3/2 m 5 NLSP ( ) 2 ( m3/2 150 GeV 9 days 10 GeV m NLSP ) 5 Late NLSP decays are in conflict with BBN Cosmological gravitino problem Possible solution: R-parity is not exactly conserved! Other options: Choose harmless NLSP like sneutrino [Covi, Kraml (2007)] Dilute NLSP density by late entropy production [Buchmüller et al. (2006)] Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 9 / 26

Gravitino Dark Matter with Broken R-Parity Gravitino Dark Matter with Broken R-Parity Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 10 / 26

Gravitino Dark Matter with Broken R-Parity Gravitino Dark Matter with Bilinear R-Parity Violation Bilinear R-parity violation: W /Rp Only lepton number violated Proton remains stable! = µ i H u L i, L soft /R p = B i H u li + m 2 H d l i H d l i + h.c. R-parity violation can be parametrized by sneutrino VEV: ξ = ν v Bound from contribution to neutrino masses Upper bound: Below limit on sum of neutrino masses: ξ O(10 4 6 ) Cosmological bounds on R-violating couplings Lower bound: The NLSP must decay before the time of BBN: ξ O(10 11 14 ) Upper bound: No washout of lepton/baryon asymmetry: ξ O(10 6 ) Tiny bilinear R-parity violation can be related to U(1) B L breaking [Buchmüller et al. (2007)] Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 11 / 26

Gravitino Dark Matter with Broken R-Parity Gravitino Dark Matter with Bilinear R-Parity Violation Gravitino decay suppressed by Planck scale and small R-parity violation Gravitino decay width: Γ 3/2 ξ2 m 3 3/2 M 2 Pl ( = 2.6 10 24 s 1 m 3 ) 3 3/2 ( ξ ) 2 10 GeV 10 7 [Takayama, Yamaguchi (2000)] The gravitino lifetime by far exceeds the age of the universe (τ 3/2 10 17 s) The unstable gravitino is a well-motivated and viable dark matter candidate! Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 12 / 26

Gravitino Dark Matter with Broken R-Parity Gravitino Dark Matter with Bilinear R-Parity Violation Gravitino decay suppressed by Planck scale and small R-parity violation Gravitino decay width: Γ 3/2 ξ2 m 3 3/2 M 2 Pl ( = 2.6 10 24 s 1 m 3 ) 3 3/2 ( ξ ) 2 10 GeV 10 7 [Takayama, Yamaguchi (2000)] The gravitino lifetime by far exceeds the age of the universe (τ 3/2 10 17 s) The unstable gravitino is a well-motivated and viable dark matter candidate! Rich phenomenology instead of elusive gravitinos: A long-lived NLSP could be observed at the LHC [Buchmüller et al. (2007), Bobrovskyi et al. (2010, 2011, 2012)] Gravitino decays can possibly be observed at indirect detection experiments [Takayama et al. (2000), Buchmüller et al. (2007), Ibarra, Tran (2008), Ishiwata et al. (2008) etc.] Gravitinos could be observed at colliders and in the spectra of cosmic rays! Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 12 / 26

Gravitino Dark Matter with Broken R-Parity Gravitino Decay Channels Several two-body decay channels: ψ 3/2 γ ν i, Z ν i, W l i, h ν i +... Γ γνi ξ2 i m 3/2 3 32 π M Pl 2 U γ Z 2 ξ2 i m 3/2 3 ( ) 2 M2 M 1 M Pl 2 M 1 M 2 Γ Z νi ξ2 i m 3 3/2 32 π M 2 Pl Γ W + l i ξ2 i m 3 3/2 16 π M 2 Pl Γ hνi ξ2 i m 3 3/2 192 π M 2 Pl ( 1 m2 Z m 2 3/2 ( 1 m2 W m 2 3/2 ( 1 m2 h m 2 3/2 ) 2 { U 2 Z Z f ( m 2 Z m 2 3/2 ) 4 ) 2 { U 2 W W f ( m 2 W m 2 3/2 ) } +... ) } +... Dependence on mass mixings dependence on gaugino masses Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 13 / 26

Gravitino Dark Matter with Broken R-Parity Gravitino Decay Width and Branching Ratios Delahaye & Grefe 2013 Three benchmark models Bino-like NLSP: M 1 = 1.1 m 3/2 Wino-like NLSP: M 2 = 1.1 m 3/2 Higgsino-like NLSP: µ = 1.1 m 3/2 Common asymptotic decay width 3 Gravitino Decay Width 3 2 m 3 2 GeV 2 10 57 10 58 10 59 10 60 Bino NLSP Wino NLSP Higgsino NLSP asymptotic value: Ξ 10 9 3 2 Ξ 2 3 m 3 2 2 48 Π M Pl 100 ΓΝ Delahaye & Grefe 2013 W 10 100 1000 Branching Ratio 10 1 0.1 0.01 ZΝ Bino NLSP Wino NLSP Higgsino NLSP Branching ratios are independent of strength of R-parity violation Exact ratio between channels is model-dependent, in particular γν 0.001 hν 100 1000 10 000 Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 14 / 26

Gravitino Dark Matter with Broken R-Parity Final State Particle Spectra Gravitino decays produce stable cosmic rays: γ, e, p, d, ν e/µ/τ Proton Antiproton Spectrum x dn dx Proton/antiproton spectra from gravitino decay generated with PYTHIA No protons from γν; Z ν and W l very similar; a bit more protons from hν 1 0.1 0.01 10 3 10 4 10 5 10 6 Ψ3 2 ZΝi, Delahaye & Grefe 2013 p p Spectrum m3 2 100 GeV 1 TeV 10 TeV 10 6 10 5 10 4 10 3 0.01 0.1 1 Proton Antiproton Spectrum x dn dx 1 0.1 0.01 10 3 10 4 10 5 10 6 Ψ3 2 W i, Delahaye & Grefe 2013 p p Spectrum m3 2 100 GeV 1 TeV 10 TeV 10 6 10 5 10 4 10 3 0.01 0.1 1 Kinetic Energy x 2 T m3 2 Proton Antiproton Spectrum x dn dx 1 0.1 0.01 10 3 10 4 10 5 10 6 Ψ3 2 hνi, Delahaye & Grefe 2013 p p Spectrum mh 125 GeV m3 2 150 GeV 1 TeV 10 TeV 10 6 10 5 10 4 10 3 0.01 0.1 1 Kinetic Energy x 2 T m3 2 Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 15 / 26

Gravitino Dark Matter with Broken R-Parity Final State Particle Spectra Gravitino decays produce stable cosmic rays: γ, e, p, d, ν e/µ/τ Proton Antiproton Spectrum x dn dx Proton/antiproton spectra from gravitino decay generated with PYTHIA No protons from γν; Z ν and W l very similar; a bit more protons from hν 1 0.1 0.01 10 3 10 4 10 5 10 6 Ψ3 2 ZΝi, Delahaye & Grefe 2013 p p Spectrum m3 2 100 GeV 1 TeV 10 TeV 10 6 10 5 10 4 10 3 0.01 0.1 1 Proton Antiproton Spectrum x dn dx 1 0.1 0.01 10 3 10 4 10 5 10 6 Ψ3 2 W i, Delahaye & Grefe 2013 p p Spectrum m3 2 100 GeV 1 TeV 10 TeV 10 6 10 5 10 4 10 3 0.01 0.1 1 Kinetic Energy x 2 T m3 2 Proton Antiproton Spectrum x dn dx 1 0.1 0.01 10 3 10 4 10 5 10 6 Ψ3 2 hνi, Delahaye & Grefe 2013 p p Spectrum mh 125 GeV m3 2 150 GeV 1 TeV 10 TeV 10 6 10 5 10 4 10 3 0.01 0.1 1 Kinetic Energy x 2 T m3 2 Basis for phenomenology of indirect gravitino dark matter searches! Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 15 / 26

Indirect Detection of Gravitino Dark Matter Indirect Detection of Gravitino Dark Matter Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 16 / 26

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] Michael Grefe (IFT UAM/CSIC) [PAMELA Collaboration] Antiproton Limits on Decaying Gravitino Dark Matter [IceCube Collaboration] University of Oxford 13 June 2013 17 / 26

Indirect Detection of Gravitino Dark Matter Cosmic-Ray Propagation Diffusion equation for cosmic-ray density ψ: ( V c ψ K 0 β p δ ψ) + 2 h δ(z) E (b loss ψ D EE E ψ) V c: + boundary conditions = Q prim + 2 h δ(z) ( Q sec + Q ter) 2 h δ(z) Γ ann ψ velocity of the convective wind from stars in the Galactic plane K 0 β p δ : spatial diffusion from irregularities of the Galactic magnetic field b loss : D EE : Q sec : Q ter : Γ ann : energy losses from interaction with interstellar gas coefficient for diffusion in energy antiprotons from collisions of cosmic-ray protons or α with interstellar gas antiprotons from inelastic collisions of antiprotons with interstellar gas annihilation of antiprotons with cosmic-ray protons Gravitino decays are a primary antiproton source in the Galactic halo: Q prim (T, r) = ρ halo(r) dn m 3/2 τ 3/2 dt Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 18 / 26

Indirect Detection of Gravitino Dark Matter Cosmic-Ray Propagation Two approaches to solve diffusion equation: Numerical: Semi-analytical: GALPROP, DRAGON Two-zone diffusion model for the Milky Way (USINE) Propagation parameters constrained by secondary-to-primary ratios Typical approach: 3 parameter sets to estimate uncertainty L (kpc) K 0 (kpc 2 /Myr) δ V c (km/s) V a (km/s) MIN 1 0.0016 0.85 13.5 22.4 MED 4 0.0112 0.70 12 52.9 MAX 15 0.0765 0.46 5 117.6 Our approach: Scan over all allowed propagation parameters Roughly 1600 parameter sets [Maurin et al. (2001))] Allows to reliably estimate the uncertainty from cosmic-ray propagation Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 19 / 26

Indirect Detection of Gravitino Dark Matter Gravitino Decay Signals in Antiproton Spectra Delahaye & Grefe 2013 Antiproton Flux p GeV 1 m 2 s 1 sr 1 0.1 0.01 10 3 10 4 10 5 10 6 PAMELA data Astrophysical Background MAX MED MIN Bino NLSP Τ 3 2 10 28 s 100 GeV 1 TeV 10 TeV 10 7 0.1 1 10 100 1000 Observed antiproton spectrum well described by astrophysical background No need for contribution from dark matter Propagation uncertainty roughly one order of magnitude Expected to be improved by forthcoming AMS-02 cosmic-ray data Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 20 / 26

Antiproton Limits on the Lifetime and the Amount of R-Parity Violation Antiproton Limits on the Lifetime and the Amount of R-Parity Violation Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 21 / 26

Antiproton Limits on the Lifetime and the Amount of R-Parity Violation Limits on the Gravitino Lifetime Lifetime limits derived using chi-squared statistics χ 2 = i (O i E i ) 2 σ 2 i O i : Observed flux in energy bin i E i : Expected flux in energy bin i (DM signal + astrophysical background) σ i : Data error bar in energy bin i Limits at 95 % CL derived from deviation from best fit χ 2 (τ 95 % CL ) = χ 2 (τ best fit ) + χ 2 χ 2 (τ best fit )/dof 0.7 (in general no DM contribution) χ 2 = 4 (corresponding to 2σ exclusion for 1 fit parameter) Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 22 / 26

Antiproton Limits on the Lifetime and the Amount of R-Parity Violation Limits on the Gravitino Lifetime Bounds on gravitino lifetime derived from PAMELA antiproton data 95 CL Lower Limit on Lifetime Τ95 CL s 10 29 10 28 10 27 10 26 MAX MED MIN Full range from scan Delahaye & Grefe 2013 Bino NLSP with solar modulation all PAMELA p data 100 1000 10 000 Gravitino lifetimes below a few times 10 28 s to 10 26 s excluded Scan over propagation parameters can change highest/lowest limits by 40 % Gravitino decay cannot explain rise in positron fraction (PAMELA, AMS-02) Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 23 / 26

Antiproton Limits on the Lifetime and the Amount of R-Parity Violation Limits on the Amount of R-Parity Violation Gravitino lifetime limits constrain R-parity violation: τ 3/2 M2 Pl ξ 2 m 3 3/2 10 4 10 5 10 6 excluded by neutrino mass excluded by washout Delahaye & Grefe 2013 R Parity Violating Parameter Ξ 10 7 10 8 10 9 10 10 10 11 10 12 10 13 MIN MED MAX excluded by antiprotons Bino NLSP Wino NLSP Higgsino NLSP Envelope of Antiproton Constraints excluded by Higgsino stau NLSP decay 10 14 excluded by Bino Wino NLSP decay 10 15 100 1000 10 000 Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 24 / 26

Antiproton Limits on the Lifetime and the Amount of R-Parity Violation Limits on the Amount of R-Parity Violation Gravitino lifetime limits constrain R-parity violation: τ 3/2 M2 Pl ξ 2 m 3 3/2 10 4 10 5 10 6 excluded by neutrino mass excluded by washout Delahaye & Grefe 2013 R Parity Violating Parameter Ξ 10 7 10 8 10 9 10 10 10 11 10 12 10 13 MIN MED MAX excluded by antiprotons Bino NLSP Wino NLSP Higgsino NLSP Envelope of Antiproton Constraints excluded by Higgsino stau NLSP decay 10 14 excluded by Bino Wino NLSP decay 10 15 100 1000 10 000 Indirect searches set strong limits on R-parity violation! Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 24 / 26

Conclusions Conclusions Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 25 / 26

Conclusions Conclusions Both, stable and unstable gravitinos, are viable dark matter candidates Gravitino DM with broken R-parity is well motivated from cosmology Decaying gravitino DM can be probed in colliders and cosmic rays Strong constraints on the lifetime from PAMELA antiproton data Antiproton limits constrain the strength of R-parity violation Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 26 / 26

Conclusions Conclusions Both, stable and unstable gravitinos, are viable dark matter candidates Gravitino DM with broken R-parity is well motivated from cosmology Decaying gravitino DM can be probed in colliders and cosmic rays Strong constraints on the lifetime from PAMELA antiproton data Antiproton limits constrain the strength of R-parity violation Thanks for your attention! Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford 13 June 2013 26 / 26