Antiproton Limits on Decaying Gravitino Dark Mattermgrefe/files/Grefe_Oxford2013.pdf · 2014. 7. 2. · Outline I Motivation for Decaying Gravitino Dark Matter I Gravitino Dark Matter

Antiproton Limits on Decaying Gravitino Dark Matter

Michael GrefeDepartamento de Fı́sica TeóricaInstituto de Fı́sica Teórica UAM/CSICUniversidad Autónoma de Madrid

Particle Theory Journal ClubRudolf 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


Motivation for Decaying Gravitino Dark Matter

Motivation forDecaying Gravitino Dark Matter



What Do We Know about Dark Matter?

I Observed on various scales through its gravitational interactionI 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]



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 für Kernphysik]

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

A combination will be necessary to identify the nature of particle dark matter!



Gravitino Dark Matter: Stable or Unstable?

I Stable Gravitino Dark Matter• Typical in gauge mediation with conserved R-parity• No direct detection signal expected: σN ∼ M−4Pl• No annihilation signal expected: σann ∼ M−4Pl• 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• No direct detection signal expected: σN ∼ M−4Pl• Decays could lead to observable cosmic-ray signals• Collider signals from long-lived NLSP expected



Why Decaying Gravitino Dark Matter?I Smallness of observed neutrino masses motivates seesaw mechanism

I Explains baryon asymmetry via thermal leptogenesis [Fukugita, Yanagida (1986)]• Needs high reheating temperature: TR & 109 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:

ΩTP3/2h2 '

3∑i=1

ωi g2i

(1 +

M2i3 m23/2

)ln(

kigi

)(m3/2

100 GeV

)(TR

1010 GeV

)[Pradler, Steffen (2006)]

I Problem in scenarios with neutralino dark matter:• Gravitino decays suppressed by Planck scale:

τ3/2 ∼M2Pl

m33/2≈ 3 years

(100 GeV

m3/2

)3• Decays with τ & O(1–1000 s) spoil BBN ⇒ Cosmological gravitino problem

Possible solution: Gravitino is the LSP and thus stable!



Why Decaying Gravitino Dark Matter?I Relation between gravitino mass and reheating temperature:

m g =

500Ge

V

m g =

10Te

V

no thermal leptogenesis

Gravitino not LSPexc

luded

by

gluino

search

es

disfav

oured

by

hierar

chypro

blem

Delahaye & Grefe H2013L

1 10 100 1000 10 000

107

108

109

1010

1011

Gravitino Mass m32 HGeVL

Reh

eatin

gT

empe

ratu

reT

RHG

eVL

I With thermal leptogenesis correct relic density possible forO(10) GeV < m3/2 < O(500) GeV ⇒ Gravitino dark matter

[Buchmüller et al. (2008))]



Why Decaying Gravitino Dark Matter?

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

τNLSP '48πM2Plm

23/2

m5NLSP≈ 9 days

(m3/2

10 GeV

)2(150 GeVmNLSP

)5• 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 [Buchmüller et al. (2006)]


Gravitino Dark Matter with Broken R-Parity

Gravitino Dark Matterwith Broken R-Parity



Gravitino Dark Matter with Bilinear R-Parity Violation

I Bilinear R-parity violation: W/Rp = µiHuLi , −Lsoft/Rp

= BiHu ˜̀i + m2Hd`i H∗d

˜̀i + h.c.

• Only lepton number violated ⇒ Proton remains stable!

I R-parity violation can be parametrized by sneutrino VEV: ξ =〈ν̃〉v

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

I 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)

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



Gravitino Dark Matter with Bilinear R-Parity Violation

I Gravitino decay suppressed by Planck scale and small R-parity violation

• Gravitino decay width: Γ3/2 ∝ξ2 m33/2

M2Pl= 2.6× 10−24 s−1

( m33/210 GeV

)3 (ξ

10−7)2

[Takayama, Yamaguchi (2000)]

• The gravitino lifetime by far exceeds the age of the universe (τ3/2 � 1017 s)

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[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!



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

+ ...

• Γγνi 'ξ2i m

33/2

32πM2Pl|Uγ̃Z̃ |

2 ∝ξ2i m

33/2

M2Pl

(M2−M1M1 M2

)2• ΓZνi '

ξ2i m33/2

32πM2Pl

(1− m

2Z

m23/2

)2{U2Z̃ Z̃ f

(m2Z

m23/2

)+ ...

}• ΓW+`−i '

ξ2i m33/2

16πM2Pl

(1− m

2W

m23/2

)2{U2W̃W̃ f

(m2W

m23/2

)+ ...

}• Γhνi '

ξ2i m33/2

192πM2Pl

(1− m

2h

m23/2

)4I Dependence on mass mixings → dependence on gaugino masses



Gravitino Decay Width and Branching Ratios

I Three benchmark models• Bino-like NLSP: M1 = 1.1 m3/2• Wino-like NLSP: M2 = 1.1 m3/2• Higgsino-like NLSP: µ = 1.1 m3/2

I Common asymptotic decay width

Ξ = 10-9

Bino NLSP

Wino NLSP

Higgsino NLSP

asymptotic value: G32 =Ξ

2 m323

48 Π MPl2


10 100 1000 10 000

10-60

10-59

10-58

10-57


Gra

vitin

oD

ecay

Wid

thG

32

m3

23

HGeV

-2 L

Bino NLSP

Wino NLSP

Higgsino NLSP

ΓΝ

W{

ZΝ

hΝ


100 1000 10 000

0.001 %

0.01 %

0.1 %

1 %

10 %

100 %


Bra

nchi

ngR

atio I Branching ratios are independent

of strength of R-parity violation

I Exact ratio between channels ismodel-dependent, in particular γν



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

Ψ32 ® ZΝi , pp Spectrum

m32 =100 GeV

1 TeV10 TeV


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 Tm32

Prot

onA

ntip

roto

nSp

ectr

umx

dNd

x

Ψ32 ® W {i , pp Spectrum

m32 =100 GeV

1 TeV10 TeV


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


Prot

onA

ntip

roto

nSp

ectr

umx

dNd

x

Ψ32 ® hΝi , pp Spectrum

mh = 125 GeV

m32 =150 GeV

1 TeV10 TeV


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


Prot

onA

ntip

roto

nSp

ectr

umx

dNd

x

Basis for phenomenology of indirect gravitino dark matter searches!


Indirect Detection of Gravitino Dark Matter

Indirect Detection ofGravitino Dark Matter



Cosmic-Ray PropagationI 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]



Cosmic-Ray PropagationI Diffusion equation for cosmic-ray density ψ:

~∇ · (~Vc ψ − K0 β pδ ~∇ψ) + 2 h δ(z) ∂E (bloss ψ − DEE ∂Eψ)= 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• K0 β pδ: 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:

Qprim(T , r) =ρhalo(r)

m3/2 τ3/2dNdT



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

L (kpc) K0 (kpc2/Myr) δ ‖~Vc‖ (km/s) Va (km/s)

MIN 1 0.0016 0.85 13.5 22.4MED 4 0.0112 0.70 12 52.9MAX 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



Gravitino Decay Signals in Antiproton Spectra

æ

æ ææ æ æ

ææ æ

æ ææ

æ

æ ææ

æ

æ

æ

æ

æ

æ

æ

ææ PAMELA dataAstrophysical Background

MAXMEDMIN

100 GeV1 TeV10 TeV

Bino NLSP

Τ32 = 1028 s


0.1 1 10 100 1000

10-7

10-6

10-5

10-4

10-3

0.01

0.1

Kinetic Energy T HGeVL

Ant

ipro

ton

Flux

Fp

HGeV

-1

m-

2s-

1sr

-1

L

I Observed antiproton spectrum well described by astrophysical background• No need for contribution from dark matter

I Propagation uncertainty roughly one order of magnitude• Expected to be improved by forthcoming AMS-02 cosmic-ray data


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

Antiproton Limits on the Lifetimeand the Amount of R-Parity Violation



Limits on the Gravitino Lifetime

I Lifetime limits derived using chi-squared statistics

χ2 =∑

i

(Oi − Ei )2

σ2i

• Oi : Observed flux in energy bin i• Ei : 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

χ2(τ95 % CL) = χ2(τbest fit) + ∆χ

2

• χ2(τbest fit)/dof ∼ 0.7 (in general no DM contribution)• ∆χ2 = 4 (corresponding to 2σ exclusion for 1 fit parameter)



Limits on the Gravitino Lifetime

I Bounds on gravitino lifetime derived from PAMELA antiproton data

MAX

MED

MIN

Full range from scan

Bino NLSP

with solar modulation

all PAMELA p data


100 1000 10 000

1026

1027

1028

1029


95%

CL

Low

erL

imit

onL

ifet

ime

Τ95

%C

LHsL

I Gravitino lifetimes below a few times 1028 s to 1026 s excluded• Scan over propagation parameters can change highest/lowest limits by ∼ 40 %• Gravitino decay cannot explain rise in positron fraction (PAMELA, AMS-02)



Limits on the Amount of R-Parity Violation

I Gravitino lifetime limits constrain R-parity violation: τ3/2 ∝M2Pl

ξ2 m33/2

MAX

MED

MIN Bino NLSP

Wino NLSP

Higgsino NLSP

Envelope of Antiproton Constraints

excluded by washout

excluded by BinoWino NLSP decay

excluded by Higgsinostau NLSP decay

excluded by neutrinomass

excluded by antiprotons


100 1000 10 00010-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4


R-

Par

ity

Vio

lati

ngP

aram

eter

Ξ

Indirect searches set strong limits on R-parity violation!


Conclusions

Conclusions


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!


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!


Motivation for Decaying Gravitino Dark MatterGravitino Dark Matter with Broken R-ParityIndirect Detection of Gravitino Dark MatterAntiproton Limits on the Lifetime and the Amount of R-Parity ViolationConclusions

Documents

Antiproton Limits on Decaying Gravitino Dark Mattermgrefe/files/Grefe_Oxford2013.pdf · 2014. 7. 2. · Outline I Motivation for Decaying Gravitino Dark Matter I Gravitino Dark Matter