The Particle Universe(continued)

The Particle Universe(continued)

Joakim Edsjö

Stockholm University

edsjo@physto.se

Joakim Edsjö

Stockholm University

edsjo@physto.se

OutlineOutline

• Cosmic rays from our own galaxy

Ways to search for dark matter

• High-energy cosmic rays

• Cosmic rays from our own galaxy

Ways to search for dark matter

• High-energy cosmic rays

CandidatesCandidates

The main dark matter candidates are:

– Baryonic dark matter

can only be a small part

– Axions

could be part of the DM

– Neutrinos

probably only part of the DM

– Weakly Interacting Massive Particles, WIMPs

could be a major part of the DM

Will focus on these!

WIMP Dark MatterWIMP Dark Matter

• Produced thermally in the early Universe

• A particle with a weak interaction cross section has ~ 1.

• In supersymmetric extensions of the standard model, such particles arise naturally.

€

h2 ≈3×10−27cm3s−1

σ annv

MSSM – Mass spectrumMSSM – Mass spectrum

Normal particles / fields Supersymmetric particles / fieldsInteraction eigenstates Mass eigenstates

Symbol Name Symbol Name Symbol Nameq = d , c , b , u , s , t quark ˜ q

L

, ˜ qR

squark ˜ q1

, ˜ q2

squarkl = e , μ , τ lepton ˜

lL

,˜ l

R

slepton ˜ l

1

,˜ l

2

sleptonν = ν

e

, νμ

, ντ

neutrino ˜ ν sneutrino ˜ ν sneutrinog gluon ˜ g gluino ˜ g gluinoW

±

H

m

W-bosonHiggs boson

˜ W

±

˜ H

1 / 2

m

winoHiggsino

˜ χ 1 , 2

±

chargino

B

W

3

H1

0

H2

0

H31

0

B-fieldW3-fieldHiggs bosonHiggs bosonHiggs boson

˜ B

˜ W

3

˜ H

1

0

˜ H

2

0

binowino

HiggsinoHiggsino

⎫

⎬

⎪

⎭

⎪

˜ χ 1 , 2 , 3 , 4

0

neutralino

R=+1 R=–1

The MSSM – parametersThe MSSM – parameters

μ - Higgsino mass parameter

M2 - Gaugino mass parameter

mA - mass of CP-odd Higgs bosontan - ratio of Higgs vacuum expectation values

m0 - scalar mass parameter

Ab - trilinear coupling, bottom sector

At - trilinear coupling, top sectorParameter

Unitμ

GeVM2GeV

ta n 1

mA

GeVm0

GeVAb/m01

At/m01

Min -50000 -50000 1 0 100 -3 -3Max +50000 +50000 60 10000 30000 3 3

The MSSM – generalThe MSSM – general

The Lightest Supersymmetric Particle (LSP)

Usually the neutralino. IfR-parity is conserved, it is stable.

The Neutralino –

Gaugino fraction

1. Select MSSM parameters

2. Calculate masses, etc

3. Check accelerator constraints

4. Calculate relic density

5. 0.025 < h2 < 0.5 ?

6. Calculate fluxes, rates,...

Calculation done with

˜ χ 10 =N11

˜ B +N12˜ W 3 +N13

˜ H 10 +N14

˜ H 20

Zg = N11

2+ N12

2

http://www.physto.se/~edsjo/darksusy/

Relic density – simple approachRelic density – simple approach

Decoupling occurs when

< H

We have

Γ = σ annv nχ

nχeq =gχ

mχT

2π

⎛ ⎝ ⎜ ⎞

⎠

3/2

e−mχ /T

H(T) =1.66g*1/2 T2

mPlanck

Γ ≈H ⇒ Tf ≈mχ

20

⇒ Ωχh2 ≈

3×10−27cm3s−1

σ annv

σ annv ≈ σ annv WIMP ⇒ Ω ≈1

Figure from Jungman, Kamionkowski and Griest, Phys. Rep. 267 (1996) 195.

Relic density – accurate approachRelic density – accurate approach

Solve the Boltzmann equation

– properly taking the thermal average <·>– including the full annihilation cross section (all

annihilation channels, thresholds, resonances).– including so called coannihilations between other

SUSY particles present at freeze-out.

dndt

=−3Hn− σ annv n2 −neq2

( )

Relic density vs mass and compositionRelic density vs mass and composition

The neutralino is cosmologically interesting for a wide range of masses and compositions!

The neutralino is cosmologically interesting for a wide range of masses and compositions!

LEP

h

2 < 0

.025

h 2 > 1

Low sampling

The m-Zg parameter spaceThe m-Zg parameter space

Higgsinos

Mixed

Gauginos

WIMP search strategiesWIMP search strategies

• Direct detection• Indirect detection:

– neutrinos from the Earth/Sun– antiprotons from the galactic halo– positrons from the galactic halo– gamma rays from the galactic halo– gamma rays from external galaxies/halos– synchrotron radiation from the galactic center /

galaxy clusters

• Direct detection• Indirect detection:

– neutrinos from the Earth/Sun– antiprotons from the galactic halo– positrons from the galactic halo– gamma rays from the galactic halo– gamma rays from external galaxies/halos– synchrotron radiation from the galactic center /

galaxy clusters

Direct detection - general principlesDirect detection - general principles

• WIMP + nucleus WIMP + nucleus

• Measure the nuclear recoil energy

• Suppress backgrounds enough to be sensitive to a signal, or...

• Search for an annual modulation due to the Earth’s motion around the Sun

Direct detection – scattering diagramsDirect detection – scattering diagrams

Spin-independent scattering

Spin-dependent scattering

+ diagrams with gluons

Diagrams from Jungman, Kamionkowski and Griest,Phys. Rep. 267 (1996) 195.

Direct detection – example spectraDirect detection – example spectra

Differential rate Gamma background in Ge-detector

Figures from Jungman, Kamionkowski and Griest,Phys. Rep. 267 (1996) 195.

Direct detection – current limitsDirect detection – current limits

Spin-independent scattering Spin-dependent scattering

Direct detection experiments have started exploring the MSSM parameter space!

Direct detection - DAMA claimDirect detection - DAMA claim

• Annual modulation seen – interpreted as WIMPs• However, not seen by other experiments...

Neutralino capture and annihilationNeutralino capture and annihilation

Sun

qq

χχ → ll → L → νμ

W±,Z,H

Earth

μDetector

velocitydistribution

scatt

capture

annihilation

ν interactions

interactions hadronization

→ cc ,bb ,tt ,τ+τ−,W±,Z0,H±H0

ν int.μ int.

νμ

Neutrino telescopes – how do they work?Neutrino telescopes – how do they work?

• The neutrino interacts with a nucleus in the ice and creates a muon.

• The muon emits Cherenkov radiation.

• The radiation is recorded by photomultipliers and the muon track can be reconstructed.

• The neutrino interacts with a nucleus in the ice and creates a muon.

• The muon emits Cherenkov radiation.

• The radiation is recorded by photomultipliers and the muon track can be reconstructed.

Neutrinos and muons from the Earth’s atmosphereNeutrinos and muons from the Earth’s atmosphere

Use the Earth as a filter by looking for upgoing muons.

Only atmospheric neutrinos remain as a background.

Use the Earth as a filter by looking for upgoing muons.

Only atmospheric neutrinos remain as a background.

Cosmic rays + atmosphere → π,K,K

π± → μ± +νμ(ν μ)

↓

e± +νe(ν e)+ν μ(νμ )

Limits: μ flux from the Earth/SunLimits: μ flux from the Earth/Sun

Earth Sun

Annihilation in the haloAnnihilation in the halo

Neutralinos can annihilate in the halo producing• antiprotons• positrons• gamma rays• synchrotron radiation (from e+/e– in magn. fields)

• neutrinos from the – Earth– Sun

Neutralinos can annihilate in the halo producing• antiprotons• positrons• gamma rays• synchrotron radiation (from e+/e– in magn. fields)

• neutrinos from the – Earth– Sun

Bergström and Snellman, ’84

Gondolo & Silk, ’00

Silk & Srednicki, ’84; Stecker, Rudaz & Walsh, ’85

Silk & Srednicki, ’84

Freese, ’86; Krauss, Srednicki & Wilczek, ’86Gaisser, Steigman & Tilav, ’86

Silk, Olive and Srednicki, ’85Gaisser, Steigman & Tilav, ’86

Gamma raysGamma rays

Monochromatic

At one-loop, neutralinos can annihilate to

i.e. monochromatic gamma rays.

Continuous

Neutralinos can also produce a continuum of gamma rays,

γγ ⇒ Eγ =mχ

Zγ ⇒ Eγ =mχ −mZ

2

4mχ

χχ → L → π0 → γγ

Features• directionality – no

propagation uncertainties• low fluxes, but clear

signature• strong halo profile

dependence

Features (compared to gamma lines)• much lower energy• many more gammas per annihilation• rather high fluxes, even away from the galactic center• not a very clear signature

Gamma lines – rates in GLASTGamma lines – rates in GLAST

Bergström, Ullio & Buckley, ’97NFW halo profile, ∆Ω ≈ 1 sr

Gamma lines – rates in ACTsGamma lines – rates in ACTs

Z

Bergström, Ullio & Buckley, ’97NFW halo profile, ∆Ω ≈ 10-5 sr

Gamma fluxes from simulated haloGamma fluxes from simulated halo

Continuous gammas Gamma lines

N-body simulations from Calcáneo-Roldan and Moore, Phys. Rev. D62 (2000) 23005.

Diffusion model of the Milky WayDiffusion model of the Milky Way

hg ≈ 0.1 kpchh ≈ 3–20 kpcr0 ≈ 8.5 kpcRh ≈ 20 kpc

Dl ≈ Dl0(1+R/R0)0.6

D0 ≈ 61027 cm2 s-1

R ≈ p/|Z|R0 ≈ 3 GV

Galaxy modelGalaxy model

Halo profile

Energy losses

Propagation model

The diffusion model with free escape at the boundaries

Modified isothermal sphere, Navarro, Frenk and White, Moore et al., etc.

Inelastic scattering gives rise to energy losses (included as a ‘tertiary’ source function for antiprotons).

The diffusion equationThe diffusion equation

∂Ndt

=∇ ⋅ D(R,r x )∇N(E,

r x )( ) −∇ ⋅

r u (

r x )N(E,

r x )( )−

∂∂E

b(E,r x )N(E,

r x )[ ]+Q(E,

r x )

Diffusion Galactic wind Energy loss Source

R =pZ

=Rigidity

N(E,r x ) = particle density

∂N∂t

=0 for stationary solutions

The diffusion, galaxy and energy loss parameters are derived from cosmic ray studies.

Cosmic ray compositionCosmic ray composition

• Li, Be and B are overabundant.

• Sc-Mn are overabundant

• This overabundance is believed to be due to spallation of C and Fe respectively by interactions with the interstellar medium.

• Observed abundances Diffusion equation Diffusion and galaxy parameters

• Observations of radioactive isotopes further constraints on diffusion and galaxy parameters.

Antiproton backgroundAntiproton background

Naively, the background below 1 GeV would be very small, but...

• energy losses

• p-He interactions

• reacceleration

are all important.

Background antiprotons are produced when cosmic rays hit the interstellar medium:

€

p + p → p + p + p + p

E th ≈ 7mp

Antiproton signalAntiproton signal

Easy to get high fluxes, but...

Antiprotons – fits to Bess dataAntiprotons – fits to Bess data

Background only Background + signal

No need for, but room for a signal.

Positron fluxes from neutralinosPositron fluxes from neutralinos

Compared to antiprotons,• energy losses are much more important• essentially only local halo properties are important• higher energies due to more prompt annihilation

channels (ZZ, W+W-, etc)• propagation uncertainties are higher• solar modulation uncertainties are higher

Positrons – signal fluxesPositrons – signal fluxes

Compared to antiprotons, the fluxes are typically lower (except at high masses), but...

Positrons – example spectraPositrons – example spectra

...the positron spectra can have features that could be detected!

The signal strength needs to be boosted, e.g. by clumps, though...

...and the fit is not perfect

WIMP conclusionsWIMP conclusions

• There is mounting evidence for dark matter in the Universe.

• There are many different dark matter candidates.• One of the favourite candidates are WIMPs, of which

supersymmetric neutralinos have the desired dark matter properties

• The WIMP rates (direct and indirect) in many different experiments can be high and sometimes have a nice feature to be distinguished from the background.

• There is mounting evidence for dark matter in the Universe.

• There are many different dark matter candidates.• One of the favourite candidates are WIMPs, of which

supersymmetric neutralinos have the desired dark matter properties

• The WIMP rates (direct and indirect) in many different experiments can be high and sometimes have a nice feature to be distinguished from the background.

About 100 muons/m2sec

proton

muons

mesons

Cosmic RaysCosmic Rays

High-energy cosmic raysHigh-energy cosmic rays

• Spectrum measured up to~ (a few)·1020 eV.

• Balloon and satellite experiments:below ~1016 eV

• Air shower arrays:up to ~1021 eV

• 1020 eV is about the same energy as a tennis ball from Boris Becker!

~E-2.7

~E-3.0

DetectorsDetectors

High Resolution Fly’s Eye(HiRes), under constructionAuger, under construction

Fly’s EyeAgasa

+ more detectors in tha past (Haverah Park, Yakutsk,...) and on the drawing board (OWL,...)

Orbiting Wide-angle Light-collectors OWL

Orbiting Wide-angle Light-collectors OWL

• Monitor 3 000 000 km2 of atmosphere with 10% efficiency.

• Record about 3 000 events/year above 1020 eV

Extensive Air Showers - DevelopmentExtensive Air Showers - Development

Number of particles in shower:

Multiplication process stops when the energy is c. Maximum number:

Shower maximum at:

€

N(x) = 2x

λ

€

Nmax =E

εc

€

xmax =λ

ln2ln

E

εc

Extensive Air ShowersExtensive Air Showers

Highest energy AGASA event observed: 2·1020 eV.

Extensive Air Showers - DirectionExtensive Air Showers - Direction

From timing information at the surface, the direction can be obtained.

Do they keep their direction?Do they keep their direction?

• The gyroradius for a charged particle (charge Ze) in a magnetic field is given by

• For small deflection angles,

• For high energies, E~p,

€

r =p

ZeB

€

θ ≈L

r=

LZeB

p

€

θ ≈3oZL

1 kpc

⎛

⎝ ⎜

⎞

⎠ ⎟

B

1 μG

⎛

⎝ ⎜

⎞

⎠ ⎟1019 eV

E

⎛

⎝ ⎜

⎞

⎠ ⎟

Greisen Zatsepin Kuzmin (GZK) cut-offGreisen Zatsepin Kuzmin (GZK) cut-off

Consider a cosmic ray proton. At high energy, it can interact with a CMB photon:

CM energy is enough to produce final state when

Mean free path for 1020 eV proton:

€

p + γCMB → Δ+ →p + π 0

n + π +

⎧ ⎨ ⎩

€

E p ≥1020 eV

€

λp ≈ 8 MPc

Energy spectrum at the ankleEnergy spectrum at the ankle

• AGASA events above 1020 eV

• Where do they come from?

Source location and GZK cut-offSource location and GZK cut-off

Either,

• the sources are nearby,

• the production energies are extremeley high,

• the estimated energies are wrong, or

• the highest-energies cosmic rays are not protons.

Cosmic Ray accelerationCosmic Ray acceleration

Scientific American, Credit: George Kelvin

• Cosmic rays are believed to be accelerated in shocks, e.g. around a supernova, black hole etc.

• Supernova remnants can accelerate up to ~1016 eV.

Possible sourcesPossible sources

• Highest energy cosmic rays can only be produced outside of our own galaxy