Gravitino Dark Matter with Broken R-Paritymgrefe/files/Grefe_IFIC2012.pdfMichael Grefe (IFT UAM/CSIC) Gravitino Dark Matter with Broken R-Parity IFIC Valencia – 21 June 2012 10

Gravitino Dark Matter with Broken R-Parity

Michael Grefe

Departamento de Fı́sica TeóricaInstituto de Fı́sica Teórica UAM/CSICUniversidad Autónoma de Madrid

Instituto de Fı́sica Corpuscular – CSIC/Universitat de València

València – 21 June 2012

Based on JCAP 0901 (2009) 029, JCAP 1004 (2010) 017,arXiv:1111.6779 [hep-ph] and ongoing work.

Collaborators: L. Covi, T. Delahaye, A. Ibarra, D. Tran, G. Vertongen

Michael Grefe (IFT UAM/CSIC) Gravitino Dark Matter with Broken R-Parity IFIC València – 21 June 2012 1 / 32

Outline

I Motivation for Unstable Gravitino Dark Matter

I Gravitino Dark Matter with Broken R Parity

I Indirect Detection of Gravitino Dark Matter

I Implications for the LHC

I Limits on the Amount of R-Parity Violation

I Conclusions and Outlook


Motivation for Unstable Gravitino Dark Matter




What Do We Know about Dark Matter?

I Dark matter is observed on various scales through its gravitational interaction

I Dark matter contributes significantly to the energy density of the universe

[van Albada et al. (1985)] [Clowe et al. (2006)] [NASA / WMAP Science Team]

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)• Long-lived on cosmological time scales but not necessarily stable! [NASA / WMAP Science Team]

Particle dark matter could be a (super)WIMP with lifetime� age of the universe!



How Can We Unveil the Nature of Dark Matter?

I There are three main search strategies for dark matter:

• Direct detection of dark matter in the scattering off matter nuclei• Production of dark matter particles at colliders• Indirect detection of dark matter in cosmic ray signatures

[Max-Planck-Institut für Kernphysik]

]2WIMP Mass [GeV/c6 7 8 910 20 30 40 50 100 200 300 400 1000

]2W

IMP-

Nuc

leon

Cro

ss S

ectio

n [c

m

-4510

-4410

-4310

-4210

-4110

-4010

-3910

]2WIMP Mass [GeV/c6 7 8 910 20 30 40 50 100 200 300 400 1000

]2W

IMP-

Nuc

leon

Cro

ss S

ectio

n [c

m

-4510

-4410

-4310

-4210

-4110

-4010

-3910

DAMA/I

DAMA/Na

CoGeNT

CDMS

EDELWEISS

XENON100 (2010)

XENON100 (2011) Buchmueller et al.

[CERN] [Aprile et al. (2011)] [AMS collaboration]

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



Why Are We Interested in Unstable Gravitino Dark Matter?

I Smallness of observed neutrino masses motivates seesaw mechanism

I Can explain baryon asymmetry via thermal leptogenesis [Fukugita, Yanagida (1986)]• Requires high reheating temperature after inflation: TR & 109 GeV [Davidson, Ibarra (2002)]

I Supergravity predicts the gravitino as the spin-3/2 superpartner of the graviton

I Gravitinos are abundantly produced in thermal scatterings:

Ω3/2h2 ' 0.27

(TR

1010 GeV

)(100 GeV

m3/2

)(mg̃

1 TeV

)2[Bolz et al. (2001)]

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• Late decays with τ & O(1–1000 s) in conflict with BBN ⇒ Cosmological gravitino problem

Possible solution: Gravitino is the LSP and thus stable!



Why Are We Interested in Unstable Gravitino Dark Matter?

I Gravitino relic density:

Ω3/2h2 ' 0.27

(TR

1010 GeV

)(100 GeV

m3/2

)(mg̃

1 TeV

)2I Correct relic density possible for m3/2 > O(10) GeV ⇒ Gravitino dark matterI Still problematic:• NLSP can only decay to gravitino LSP:

τNLSP '48πM2Plm

23/2

m5NLSP≈ 9 days

( m3/210 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 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 parametrized by non-vanishing sneutrino VEV: ξ =〈ν̃〉v

I Cosmological bounds on R-violating couplings• Lower bound: The NLSP must decay fast enough to evade BBN constraints: ξ & O(10−11)• Upper bound: No washout of the lepton/baryon asymmetry: ξ . O(10−7)

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

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

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

M2Pl[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!



Phenomenology of Unstable Gravitino Dark Matter

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)]

• Gravitino decays lead to possibly observable signals at indirect detection experiments[Takayama, Yamaguchi (2000), Buchmüller et al. (2007), Bertone et al. (2007), Ibarra, Tran (2008), Ishiwata et al. (2008) etc.]

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



Bilinear R-Parity Violation: Neutralino–Neutrino Mixing

I Bilinear R-parity violation extends neutralino mass matrix to include neutrinos

I 7× 7 matrix with basis ψ0i = (−i γ̃, −i Z̃ , H̃0u , H̃0d , νi )T

M7N =

M1c2W + M2 s

2W (M2 −M1) sW cW 0 0 0

(M2 −M1) sW cW M1s2W + M2 c2W mZ sβ −mZ cβ −mZ ξj0 mZ sβ 0 −µ 00 −mZ cβ −µ 0 00 −mZ ξi 0 0 0

I Diagonalized by unitary matrix N7

I Mixing to neutrinos via neutrino–zino coupling: N7νi X ' −ξi UXZ̃I Analytical approximation shows dependence on SUSY parameters

• Uγ̃Z̃ ' mZ sin θW cos θWM2−M1M1 M2

• UZ̃ Z̃ ' −mZ(

sin2 θWM1

+cos2 θW

M2

)



Bilinear R-Parity Violation: Chargino–Charged Lepton Mixing

I Bilinear R-parity violation extends chargino mass matrix to include charged leptons

I 5× 5 matrix with basis vectors ψ− = (−iW̃−, H̃−d , `−i )

T andψ+ = (−iW̃ +, H̃+u , ec +i )

T

M5C =

M2√

2 mW sβ 0√2 mW cβ µ −mìj ξi cβ√2 mW ξi 0 mìj

I Diagonalized by unitary matrices U5 and V 5

I Mixing to left-handed leptons via lepton–wino coupling: U5ì X ' −√

2 ξi UXW̃I Mixing to right-handed leptons suppressed and negligibleI Analytical approximation shows dependence on SUSY parameters• UW̃W̃ '

mWM2

I Bilinear R-parity also induces mass mixing in the scalar sector• Mixing between SM-like Higgs and sneutrino proportional to sneutrino VEV



Gravitino Decay Channels: 2-body Decays

I 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{U2

Z̃ Z̃f(

m2Zm23/2

)+ ...

}• ΓW +`−i

'ξ2i m

33/2

32πM2Pl

(1− m

2W

m23/2

)2{U2

W̃W̃f(

m2Wm23/2

)+ ...

}• Γhνi '

ξ2i m33/2

196πM2Pl

(1− m

2h

m23/2

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



Gravitino Decay Channels: 3-body Decays

I For m3/2 < mW also three-body decays can play an important role [Choi et al. (2010)]

+ ...

•dΓZ∗νi

ds ∝ξ2i m

33/2

M2Pl((s−m2Z )

2+m2Z Γ2Z )

(1− s

m23/2

)2{s U2

Z̃ Z̃f(

sm23/2

)+ ...

}•

dΓW +∗`−i

ds ∝ξ2i m

33/2

M2Pl((s−m2W )

2+m2W Γ2W )

(1− s

m23/2

)2{s U2

W̃W̃f(

sm23/2

)+ ...

}•

dΓh∗νids ∝

ξ2i m33/2 m

2f s

M2Pl v2((s−m2h)

2+m2hΓ2h)

(1− s

m23/2

)4I I will concentrate on 2-body dacays in this talk



Gravitino Branching Ratios and Final State Particle Spectra

I Branching ratios are independent of strength of R-parity violation

I Ratio between γ νi and other channels is model-dependent

ΓΝi

Γ*Z*Νi

W{i

W*{i

ZΝi

hΝi

10 100 1000 10 000

10-5

10-4

10-3

0.01

0.1

1

Gravitino Mass HGeVL

Bra

nchi

ngR

atio

ΝΤ

ΝΜ

Νe

dH´ 103L

p

e

Γ

Ν

e

Νi

Ψ32 ® Z Νi , m32 = 100 GeV

0.01 0.1 1 10 100

0.001

0.01

0.1

1

10

100

Kinetic Energy HGeVL

Spec

trum

dNdHl

og10

TL

I Gravitino decays produce spectra of stable cosmic rays: γ, e, p, νe/µ/τ , d• Two-body decay spectra generated with PYTHIA• Deuteron coalescence treated on event-by-event basis in PYTHIA [Kadastik et al. (2009)]

Basis for phenomenology of indirect gravitino dark matter searches!


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 gamma rays, charged cosmic rays and neutrinos

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



What Is the Difference of Dark Matter Annihilations and Decays?

I Different angular distribution of the gamma-ray/neutrino flux from the galactic halo:

Dark Matter Annihilation

dJhalodE

=〈σv〉DM8πm2DM

dNdE

∫l.o.s.

ρ2halo(~l) d~l

particle physics astrophysics

Dark Matter Decay

dJhalodE

=1

4π τDM mDMdNdE

∫l.o.s.

ρhalo(~l) d~l

particle physics astrophysics

value at galactic anticenter

annihilation

decay

Einasto

NFW

Isothermal

-180 ° -90 ° 0 ° 90 ° 180 °

1

10

100

Galactic Longitude

Lin

e-of

-Si

ghtI

nteg

ralN

orm

aliz

edto

Ant

icen

ter

Annihilation (e.g. WIMP dark matter)• Annihilation cross section related to relic density• Strong signal from peaked structures• Uncertainties from choice of halo profile

Decay (e.g. unstable gravitino dark matter)• Lifetime unrelated to production in the early

universe

• Less anisotropic signal• Less sensitive to the halo model

Directional detection can distinguish unstable gravitino from standard WIMPs!



Gravitino Decay Signals in Cosmic-Ray Spectra

antiproton flux isotropic diffuse gamma-ray flux

ª

ª

ª

ó

ó

ó

¨

¨§

§

§

§

òò

ò

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ææ

ææ

ææææææ

ææææ æ æ

æ æ æ

background

Τ32 = 1027 s

m32 = 100 GeV 1 TeV 10 TeV

1 10 100 1000 10 000

10-3

0.01

0.1

1

10

100

Kinetic Energy HGeVL

T3´

Ant

ipro

ton

FluxHG

eV2

m-

2s-

1sr-

1L

ó IMAXìAMS-01æ PAMELA

ª MASS-91¨ CAPRICE94§ CAPRICE98

ò BESS 95+97ø BESS 98ô BESS 99÷ BESS 00à BESS-Polará BESS-Polar II

ì

ì

ìì ì

ìì

ì ì ì

ìì

ìà

àààà

àà

à

à

àà

æ

æ

æ

æ

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Τ32 = 1027 s

m32 = 100 GeV 1 TeV 10 TeV

0.1 1 10 100 1000 10 000

0.0001

0.0003

0.001

0.003

0.01

0.03

Energy HGeVL

E2´

Gam

ma-

Ray

FluxHG

eVm-

2s-

1sr-

1L

ì EGRET HSreekumar et al.L

à EGRET HStrong et al.L

æ Fermi LAT

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

I Isotropic diffuse gamma-ray spectrum exhibits power-law behaviour• Source not completely understood, but no sign of spectral features of a particle decay

I Even without astrophysical backgrounds lifetimes below O(1026–1027) s excluded• Gravitino decay cannot be the origin of the PAMELA and Fermi LAT cosmic-ray anomalies

Astrophysical sources like pulsars required to explain cosmic-ray excesses!



Antideuteron Signals from Gravitino Decays

I In particular sensitive at low energies due to small astrophysical background

I AMS-02 and GAPS will be able to put strong constraints on light gravitinos

BESS 97-00

GA

PSHL

DBL

GA

PSHU

LD

BL

AM

S-02

AM

S-02

background

Τ32 = 1027 s

m32 = 100 GeV 1 TeV 10 TeV

ΦF = 500 MV

0.1 1 10 100 1000

10-10

10-9

10-8

10-7

10-6

10-5

10-4

Kinetic Energy per Nucleon HGeVnL

HTnL´

Ant

ideu

tero

nFl

uxHm-

2s-

1sr-

1 L

Antideuterons are a valuable channel for light gravitino searches!



Neutrino Signals from Gravitino Decays

I Neutrinos provide directional information like gamma rays

I Gravitino signal features neutrino line at the end of the spectrumI Atmospheric neutrinos are the dominant background for the gravitino signal• Discrimination of neutrino flavours would allow to reduce the background• Signal-to-background ratio best at the end of the spectrum and for large gravitino masses

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ô

ô ô

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ì

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ì

æ

æ

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æ

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æ

æ

æ

æ

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ΝΤΝe

ΝΜ

Τ32 = 1026 s

m32 = 100 GeV 1 TeV 10 TeV

1 10 100 1000 10 000 100 000

10-4

10-3

0.01

0.1

1

10

100

103

EnergyHGeVL

E2´

Neu

trin

oF

luxH

GeV

m-

2s-

1sr-

1L

ô FréjusΝeò FréjusΝΜ

Super-KamiokandeΝΜAMANDA -II ForwardΝΜ

ì AMANDA -II Unfolding ΝΜIceCube-40ΝΜ

æ IceCube-40 UnfoldingΝΜ

Neutrinos are a valuable channel for heavy gravitino searches!



Neutrino Detection with Upward Through-Going Muons

I Muon tracks from charged current DIS of muon neutrinos off nuclei outside the detector

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

atmospheric background

Τ32 = 1026 s

m32 = 100 GeV 1 TeV 10 TeV

1 10 100 1000 10000 100000

0.1

1

10

100

103

104

105

Energy HGeVL

MuonFluxHkm-2yr-

1L

Upward Through-Going Muons

Τ32 = 1026s

m32 = 100 GeV 1 TeV 10 TeV

1 10 100 1000 10000 100000

0.01

0.1

1

10

Energy HGeVLStatisticalSignificance



Neutrino Detection – Improvements Using Showers

I Hadronic and electromagnetic showers from charged current DIS of electron and tau neutrinosand neutral current interactions of all neutrino flavours inside the detector

Disadvantages• TeV-scale showers 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

atmospheric background

Τ32 = 1026 s

m32 = 100 GeV 1 TeV 10 TeV

1 10 100 1000 10 000 100 000

1

10

100

103

104

105

106

Energy HGeVL

Show

erR

ateHk

m-

3yr-

1 L

Shower Events

Τ32 = 1026 s

m32 = 100 GeV 1 TeV 10 TeV

1 10 100 1000 10 000 100 000

0.01

0.1

1

10

100

Energy HGeVLSt

atis

tical

Sign

ific

ance

Showers are potentially the best channel for dark matter searches in neutrinos!



Limits on the Gravitino Lifetime

excluded by diffuse flux

excluded by line searches

1 10 100 1000 10 000

1024

1025

1026

1027

1028

1029


Gra

vitin

oL

ifet

imeHsL

Fermi LAT diffuse fluxVertongen et al. photon lineFermi LAT photon line

excluded by

antiproton flux

excluded by electron + positron flux

excluded

by

positron

fraction

antideuteron sensitivity

100 1000 10 000

1024

1025

1026

1027

1028


Gra

vitin

oL

ifet

imeHsL

PAMELA e+He+ + e-L

PAMELA p

Fermi LAT H.E.S.S. e+ + e-

I Cosmic-ray data give bounds on gravitino lifetime• Photon line bounds very strong for low gravitino masses• Uncertainties from charged cosmic-ray propagation• Background subtraction will improve bounds• Antideuterons can be complementary to photon line

searches for low gravitino masses

• Neutrino bounds are competitive for heavy gravitinos

Wide range of bounds from multi-messenger approach!

exclusion from

through-going muons

after 1 year at IceCube + DeepCore

100 1000 10 000

1024

1025

1026

1027


Gra

vitin

oL

ifet

imeHsL


Implications for the LHC




Implications for the LHC: Stau NLSP

I NLSP decays before BBN but may be metastable on collider scales

I Stau decay channels: τ̃R → τ νµ, µ ντ and τ̃L → t̄R bLI Characteristic signatures:• Slow particle with long ionising charged track• Displaced vertex with missing energy and muon track or jet

I Minimal decay length from washout limit: 4 mm

101 102 103

m3/2 [GeV]

102

103

m˜� 1

[G

eV

]

100

1000

10000

Stau NLSP: Minimal allowed decay length c��̃1

[m]

Min O.P.

O.P. in

scena

rio (B)

m3/2>m�̃1

EWPT

[Huang et al. (2011)]

I Gamma-ray limits from galaxy clusters constrain decay length [Huang et al. (2011)]

I Minimal decay lengths from current limits: O(100) m – O(10) kmMichael Grefe (IFT UAM/CSIC) Gravitino Dark Matter with Broken R-Parity IFIC València – 21 June 2012 26 / 32


Implications for the LHC: Neutralino NLSP

I Neutralino decay channels: χ̃01 → Z νi ,W +`−i , h νiI Bino decay length is directly related to gravitino decay widthI Characteristic signatures:• Displaced vertices far from the interaction point• For too small R-parity violation indistinguishable from stable neutralino

decay chain with secondary vertices

101 102 103

m3/2 [GeV]

102

103

m˜�

0 1 [

GeV

]

1

10

100 1

000

1000

0

Neutralino NLSP: Minimal allowed decay length χ��̃01 [m]

Min O.P.

O.P. in

scena

rio (A)

m3/2>m� 01

EWPT

[Bobrovskyi et al. (2011)] [Huang et al. (2011)]

I Gamma-ray limits from galaxy clusters constrain decay length [Huang et al. (2011)]

I Minimal decay lengths from current limits: O(100) m – O(10) km


Limits on the Amount of R-Parity Violation





I Limits on gravitino lifetime constrain the strength of R-parity violation: τ3/2 ∝M2Pl

ξ2 m33/2• Limits from photon line searches dominate for small gravitino masses• For heavier gravitino bounds from all cosmic-ray channels are comparable

cosmic-ray limits LHC sensitivity for bino-like NLSP decaysΞ = 10-7

Ξ = 10-11

1 10 100 1000 10 000

10-12

10-11

10-10

10-9

10-8

10-7


R-

Pari

tyV

iola

ting

Para

met

erΞ

IceCube ΝΜ prospects

Super-Kamiokande ΝΜ

GAPSAMS-02 d prospects

PAMELA p

Fermi LAT diffuse Γ

Fermi LAT Γ line

[Bobrovskyi et al. (2011)]I The LHC has the potential to detect NLSP decays beyond cosmic-ray constraints• Good sensitivity with clean decay chain: χ̃01 → Z νi and Z → µ

+µ−

• Taking all channels can improve sensitivity another order of magnitude [Bobrovskyi et al. (2011)]

Indirect and collider searches probe interesting range of R-parity violation!


Conclusions and Outlook




Conclusions

• Gravitino dark matter with broken R-parity is well motivated from cosmology

• Consistent with thermal leptogenesis and big bang nucleosynthesis

• The Gravitino lifetime is naturally in the range of indirect detection experiments

• Cannot explain the PAMELA and Fermi LAT excesses due to constraints fromgamma rays and antiprotons

• Multi-messenger approach constrains gravitino lifetime and strength of R-parityviolation



Outlook

• Forthcoming experiments like AMS-02 will greatly improve cosmic-ray data

• Antideuteron searches will probe light gravitino dark matter

• Neutrino experiments like IceCube will probe heavy gravitino dark matter

• LHC may discover decays of metastable NLSPs beyond cosmic-ray constraints onR-parity violation

• We are living in interesting times for dark matter searches!

Thanks for your attention!



Outlook

• Forthcoming experiments like AMS-02 will greatly improve cosmic-ray data

• Antideuteron searches will probe light gravitino dark matter

• Neutrino experiments like IceCube will probe heavy gravitino dark matter

• LHC may discover decays of metastable NLSPs beyond cosmic-ray constraints onR-parity violation

• We are living in interesting times for dark matter searches!

Thanks for your attention!


Motivation for Unstable Gravitino Dark MatterGravitino Dark Matter with Broken R-ParityIndirect Detection of Gravitino Dark MatterImplications for the LHCLimits on the Amount of R-Parity ViolationConclusions and Outlook

Documents

Gravitino Dark Matter with Broken R-Paritymgrefe/files/Grefe_IFIC2012.pdfMichael Grefe (IFT UAM/CSIC) Gravitino Dark Matter with Broken R-Parity IFIC Valencia – 21 June 2012 10