Antiproton Limits on Decaying Gravitino Dark Matter

Michael Grefe

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

I Motivation for Decaying Gravitino Dark Matter

I Gravitino Dark Matter with Broken R Parity

I Indirect Detection of Gravitino Dark Matter

I Antiproton Limits on the Lifetime and the Amount of R-Parity Violation

I 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?

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) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford – 13 June 2013 4 / 26 A combination will be necessary to identify the nature of particle dark matter!

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 fur¨ Kernphysik]

[CERN] [Aprile et al. (2012)] [AMS Collaboration]

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 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 fur¨ 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?

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) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford – 13 June 2013 6 / 26 Possible solution: Gravitino is the LSP and thus stable!

Motivation for Decaying Gravitino Dark Matter Why Decaying Gravitino Dark Matter?

I Smallness of observed neutrino masses motivates seesaw mechanism I Explains baryon asymmetry via thermal leptogenesis [Fukugita, Yanagida (1986)] 9 • Needs high reheating temperature: TR & 10 GeV [Davidson, Ibarra (2002)] I Supergravity predicts gravitino as spin-3/2 superpartner of the graviton I Gravitinos are thermally produced after inﬂation in the early universe: 3 2 ! X M ki m3/2 TR ΩTP 2 ' ω 2 + i 3/2h i gi 1 2 ln 10 3 m gi 100 GeV 10 GeV i=1 3/2 [Pradler, Steffen (2006)] I Problem in scenarios with neutralino dark matter: • Gravitino decays suppressed by Planck scale: 2 3 MPl 100 GeV τ3/2 ∼ 3 ≈ 3 years m3/2 m3/2 • 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?

Possible solution: Gravitino is the LSP and thus stable!

I Relation between gravitino mass and reheating temperature: Delahaye & Grefe 2013

1011 H L

Gravitino L by 1010 GeV not H excluded

R searches LSP T gluino

109

GeV Temperature 500 no thermal leptogenesis = m g 8 10 by TeV Reheating 10 = m g disfavouredproblem

107 hierarchy

1 10 100 1000 10 000

Gravitino Mass m3 2 GeV

I With thermal leptogenesis correct relic densityH L possible for O(10) GeV < m3/2 < O(500) GeV ⇒ Gravitino dark matter [Buchmuller¨ et al. (2008))]

Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford – 13 June 2013 8 / 26 Possible solution: R-parity is not exactly conserved!

I Other options: • Choose harmless NLSP like sneutrino [Covi, Kraml (2007)]

• Dilute NLSP density by late entropy production [Buchmuller¨ et al. (2006)]

Motivation for Decaying Gravitino Dark Matter Why Decaying Gravitino Dark Matter?

I Still problematic: • NLSP can only decay to gravitino LSP:

2 2 2 5 48πMPlm3/2 m3/2 150 GeV τNLSP ' 5 ≈ 9 days mNLSP 10 GeV mNLSP

• 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?

I Still problematic: • NLSP can only decay to gravitino LSP:

2 2 2 5 48πMPlm3/2 m3/2 150 GeV τNLSP ' 5 ≈ 9 days mNLSP 10 GeV mNLSP

• Late NLSP decays are in conﬂict with BBN ⇒ Cosmological gravitino problem

Possible solution: R-parity is not exactly conserved!

I Other options: • Choose harmless NLSP like sneutrino [Covi, Kraml (2007)]

• Dilute NLSP density by late entropy production [Buchmuller¨ 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

soft ˜ 2 ∗ ˜ Bilinear R-parity violation: WR/ = µi HuLi , −L = Bi Huì + m H ì + h.c. I p R/ p Hd ì d • Only lepton number violated ⇒ Proton remains stable! hν˜i R-parity violation can be parametrized by sneutrino VEV: ξ = I v

I Bound from contribution to neutrino masses −4–6 • Upper bound: Below limit on sum of neutrino masses: ξ . O(10 )

I Cosmological bounds on R-violating couplings −11–14 • Lower bound: The NLSP must decay before the time of BBN: ξ & O(10 ) −6 • Upper bound: No washout of lepton/baryon asymmetry: ξ . O(10 )

I Tiny bilinear R-parity violation can be related to U(1)B–L breaking [Buchmuller¨ et al. (2007)]

Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford – 13 June 2013 11 / 26 I Rich phenomenology instead of elusive gravitinos: • A long-lived NLSP could be observed at the LHC [Buchmuller¨ et al. (2007), Bobrovskyi et al. (2010, 2011, 2012)]

• Gravitino decays can possibly be observed at indirect detection experiments [Takayama et al. (2000), Buchmuller¨ et al. (2007), Ibarra, Tran (2008), Ishiwata et al. (2008) etc.]

Gravitinos could be observed at colliders and in the spectra of cosmic rays!

Gravitino Dark Matter with Broken R-Parity Gravitino Dark Matter with Bilinear R-Parity Violation

I Gravitino decay suppressed by Planck scale and small R-parity violation 2 3 3 ξ m m 3 2 • Γ ∝ 3/2 = . × −24 −1 3/2 ξ Gravitino decay width: 3/2 2 2 6 10 s 10 GeV 10−7 MPl [Takayama, Yamaguchi (2000)] 17 • The gravitino lifetime by far exceeds the age of the universe (τ3/2 10 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

The unstable gravitino is a well-motivated and viable dark matter candidate!

I Rich phenomenology instead of elusive gravitinos: • A long-lived NLSP could be observed at the LHC [Buchmuller¨ et al. (2007), Bobrovskyi et al. (2010, 2011, 2012)]

• Gravitino decays can possibly be observed at indirect detection experiments [Takayama et al. (2000), Buchmuller¨ 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

I Several two-body decay channels: ψ3/2 → γ νi , Z νi , W `i , h νi

+ ...

ξ2 m3 ξ2 m3 2 • Γ ' i 3/2 |U |2 ∝ i 3/2 M2−M1 γνi π 2 γ˜Z˜ 2 M M 32 MPl MPl 1 2 2 3 ξ m m2 2n m2 o • Γ ' i 3/2 1 − Z U2 f Z + ... Zνi 32 π M2 m2 Z˜Z˜ m2 Pl 3/2 3/2 ξ2 m3 2 2n 2 o i 3/2 mW 2 mW • Γ − ' 1 − U f + ... W +` 16 π M2 m2 W˜ W˜ m2 i Pl 3/2 3/2 2 3 ξ m m2 4 • Γ ' i 3/2 1 − h hνi 192 π M2 m2 Pl 3/2 I 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

L H L 2 Three benchmark models - 10-57 GeV

I H 2 3 3

m -9 • Bino-like NLSP: M1 = 1.1 m3/2 -58 Ξ = 10 2

10 3 G • Wino-like NLSP: M2 = 1.1 m3/2 Bino NLSP Width -59 • Higgsino-like NLSP: µ = 1.1 m3/2 10 Wino NLSP Higgsino NLSP Decay

2 3 Ξ m3 2 -60 10 asymptotic value: G3 2 = Common asymptotic decay width 2

I Gravitino 48 Π MPl

Delahaye & Grefe 2013 10 100 1000 10 000 ΓΝ Gravitino Mass m3 2 GeV 100 % H L W { H L 10 % Bino NLSP I Branching ratios are independent 1 % Wino NLSP Ratio Higgsino NLSP of strength of R-parity violation

0.1 %

Branching I Exact ratio between channels is 0.01 % ZΝ model-dependent, in particular γν

hΝ 0.001 % 100 1000 10 000

Gravitino Mass m3 2 GeV

Michael Grefe (IFT UAM/CSIC) H AntiprotonL Limits on Decaying Gravitino Dark Matter University of Oxford – 13 June 2013 14 / 26 Basis for phenomenology of indirect gravitino dark matter searches!

Gravitino Dark Matter with Broken R-Parity Final State Particle Spectra

I Gravitino decays produce stable cosmic rays: γ, e, p, d, νe/µ/τ • Proton/antiproton spectra from gravitino decay generated with PYTHIA • No protons from γν; Zν and W ` very similar; a bit more protons from hν

Delahaye & Grefe 2013 Delahaye & Grefe 2013 Delahaye & Grefe 2013 1 Ψ ® ZΝ , p p Spectrum 1 Ψ ® W , p p Spectrum 1 Ψ ® hΝ , p p Spectrum 3 2 i 3 2 {i 3 2 i H L H L H L dx dx dx 0.1 0.1 0.1 dN dN dN

x x x 0.01 0.01 0.01

Spectrum 10-3 Spectrum 10-3 Spectrum 10-3

mh = 125 GeV 10-4 10-4 10-4

Antiproton 100 GeV Antiproton 100 GeV Antiproton 150 GeV 10-5 m3 2 = 1 TeV 10-5 m3 2 = 1 TeV 10-5 m3 2 = 1 TeV 10 TeV 10 TeV 10 TeV Proton Proton Proton 10-6 10-6 10-6 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 10-6 10-5 10-4 10-3 0.01 0.1 1

Kinetic Energy x = 2 T m3 2 Kinetic Energy x = 2 T m3 2 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

x x x 0.01 0.01 0.01

Spectrum 10-3 Spectrum 10-3 Spectrum 10-3

mh = 125 GeV 10-4 10-4 10-4

Kinetic Energy x = 2 T m3 2 Kinetic Energy x = 2 T m3 2 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] [PAMELA Collaboration] [IceCube Collaboration]

Michael Grefe (IFT UAM/CSIC) Antiproton Limits on Decaying Gravitino Dark Matter University of Oxford – 13 June 2013 17 / 26 Indirect Detection of Gravitino Dark Matter Cosmic-Ray Propagation

I Diffusion equation for cosmic-ray density ψ: ~ ~ δ ~ ∇ · (Vc ψ − K0 β p ∇ψ) + 2 h δ(z) ∂E (bloss ψ − DEE ∂E ψ) = Qprim + 2 h δ(z) Qsec + Qter − 2 h δ(z)Γann ψ + boundary conditions

~ • Vc : velocity of the convective wind from stars in the Galactic plane δ • K0 β p : spatial diffusion from irregularities of the Galactic magnetic ﬁeld

• bloss: energy losses from interaction with interstellar gas

• DEE : coefﬁcient for diffusion in energy • Qsec: antiprotons from collisions of cosmic-ray protons or α with interstellar gas • Qter: antiprotons from inelastic collisions of antiprotons with interstellar gas • Γann: annihilation of antiprotons with cosmic-ray protons

I Gravitino decays are a primary antiproton source in the Galactic halo: ρ (r) dN Qprim(T , r) = halo m3/2 τ3/2 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

I Two approaches to solve diffusion equation: • Numerical: GALPROP, DRAGON • Semi-analytical: Two-zone diffusion model for the Milky Way (USINE)

I Propagation parameters constrained by secondary-to-primary ratios I Typical approach: 3 parameter sets to estimate uncertainty

2 ~ L (kpc) K0 (kpc /Myr) δ kVck (km/s) Va (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

I 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

0.1 æ PAMELA data Astrophysical BackgroundH L æ L æ æ æ æ æ 1 æ æ ææ

- MAX 100 GeV 0.01 æ sr æ æ MED 1 TeV 1 æ æ - æ s MIN 10 TeV

2 æ - -3 æ

m 10 æ 1

- Bino NLSP æ 28

GeV -4 æ H 10 Τ3 2 = 10 s p F æ -5 Flux 10 æ

10-6 Antiproton

10-7 0.1 1 10 100 1000 Kinetic Energy T GeV I Observed antiproton spectrum well described by astrophysical background • No need for contribution from dark matter H L

I 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

I Lifetime limits derived using chi-squared statistics

2 X (Oi − Ei ) χ2 = σ2 i i

•O i : Observed ﬂux in energy bin i

•E i : Expected ﬂux in energy bin i (DM signal + astrophysical background)

• σi : Data error bar in energy bin i

I Limits at 95 % CL derived from deviation from best ﬁt

2 2 2 χ (τ95 % CL) = χ (τbest ﬁt) + ∆χ

2 • χ (τbest ﬁt)/dof ∼ 0.7 (in general no DM contribution) • ∆χ2 = 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

I Bounds on gravitino lifetime derived from PAMELA antiproton data Delahaye & Grefe 2013 1029

H L L s

H Bino NLSP CL % 95 Τ 1028 Lifetime on

1027 Limit

MAX

Lower MED CL 26 MIN with solar modulation % 10 95 Full range from scan all PAMELA p data

100 1000 10 000

Gravitino Mass m3 2 GeV 28 26 I Gravitino lifetimes below a few times 10 s to 10 s excluded H L • 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 Indirect searches set strong limits on R-parity violation!

Antiproton Limits on the Lifetime and the Amount of R-Parity Violation Limits on the Amount of R-Parity Violation

2 MPl I Gravitino lifetime limits constrain R-parity violation: τ3/2 ∝ 2 3 ξ m3/2

Delahaye & Grefe 2013 10-4 mass -5 excluded by neutrino 10 H L excluded by washout 10-6 Ξ 10-7 MIN Bino NLSP MED Wino NLSP 10-8 MAX Higgsino NLSP Parameter 10-9 Envelope of Antiproton Constraints

-10 excluded 10 by antiprotons Violating 10-11

Parity -12

- 10 R stau NLSP decay 10-13 excluded by Higgsino -14 excluded by 10 Bino Wino NLSP decay 10-15 100 1000 10 000 Gravitino Mass m3 2 GeV

H L

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

2 MPl I Gravitino lifetime limits constrain R-parity violation: τ3/2 ∝ 2 3 ξ m3/2

Delahaye & Grefe 2013 10-4 mass -5 excluded by neutrino 10 H L excluded by washout 10-6 Ξ 10-7 MIN Bino NLSP MED Wino NLSP 10-8 MAX Higgsino NLSP Parameter 10-9 Envelope of Antiproton Constraints

-10 excluded 10 by antiprotons Violating 10-11

Parity -12

- 10 R stau NLSP decay 10-13 excluded by Higgsino -14 excluded by 10 Bino Wino NLSP decay 10-15 100 1000 10 000 Gravitino Mass m3 2 GeV

Indirect searches set strong limits on R-parity violation! H L

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 Thanks for your attention!

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