Dark Matter and Dark Energy components chapter 7cdeclerc/astroparticles/... · The early universe...

Dark Matter and Dark Energy components

chapter 7

Lecture 3

See also Dark Matter awareness week December 2010

http://www.sissa.it/ap/dmg/index.html

The early universechapters 5 to 8chapters 5 to 8

Particle Astrophysics , D. Perkins, 2nd edition, Oxford

5. The expanding universe6 Nucleosynthesis and baryogenesis6. Nucleosynthesis and baryogenesis7. Dark matter and dark energy components8. Development of structure in early universe

excercises

Slides + book http://w3 iihe ac be/~cdeclerc/astroparticlesSlides + book http://w3.iihe.ac.be/ cdeclerc/astroparticles

OverviewOb ti f d k tt it ti l ff t• Observation of dark matter as gravitational effects– Rotation curves galaxies, mass/light ratios in galaxies

V l iti f l i i l t– Velocities of galaxies in clusters– Gavitational lenses

Primordial nucleosynthesis– Primordial nucleosynthesis– Anisotropies in CMB radiation

• Nature of dark matter particles:• Nature of dark matter particles:– Baryons and MACHO’s– NeutrinosNeutrinos– Axions

• Weakly Interacting Massive Particles (WIMPs)Weakly Interacting Massive Particles (WIMPs) Experimental WIMP searches

• Dark energy• Dark energy

2011-12 Dark Matter-Dark Energy 3

Previously• Universe is flat k=0

• Dynamics given by Friedman equationDynamics given by Friedman equation

( ) ( )( ) ( )

22 8

3NR t G

R ttπ⎛ ⎞

=⎜ ⎟⎜ ⎟⎝ ⎠

H t totρ≡

• Cosmological redshift

( ) 3R t⎜ ⎟⎝ ⎠

( )( ) ( )0

01 0R t

z z t+ = =

• Closure parameter

( ) ( )0R t

( ) ( )tρΩClosure parameter

• Ener densit e ol es ith time

( ) ( )( )c

tt

ρρ

Ω =

Ω =0• Energy density evolves with time

( ) ( )( ) ( )( ) ( ) ( )2 3 4 220 01 1 1r kH t H z t z z⎡ ⎤= + +Ω + + +Ω +⎣ ⎦00m ΛΩ t Ω t

Ωk=0


( ) ( )( ) ( )( ) ( ) ( )0 0 k⎣ ⎦00 Λ

Dark matter : Why and how much?luminous

1%

dark baryonic

4%

NeutrinoHDM<1%

• Several gravitationalobservations show that more

i i h U i h cold dark matter

18%

matter is in the Universe than wecan ‘see’

• These particles interact only

dark

• These particles interact onlythrough weak interactions and gravity dark

energy76%

gravity

• The energy density of DarkMatter today is obtained fromyfitting the ΛCDM model to CMB and other observations

( )( )

50 10

0 24rad t

t

−Ω ≈

Ω ≈( )0 0.24matter tΩ ≈

( ) ( )( ) ( )( ) ( )2 3 420 0 0 01 1m rH t H t z t z tΛ⎡ ⎤= Ω + +Ω + +Ω⎣ ⎦


( ) ( )( ) ( )( ) ( )0 0 0 01 1m rH t H t z t z tΛΩ + +Ω + +Ω⎣ ⎦

Dark matter nature• The nature of most of the dark matter is still unknown

Is it a particle? Candidates from several models of physicsbeyond the standard model of particle physicsbeyond the standard model of particle physics

Is it something else? Modified newtonian dynamics?

• the answer will come from experiment


Velocities of galaxies in clusters and M/L ratio

G l t tiGalaxy rotation curves

Gravitational lensing

Bullet Cluster

PART 1GRAVITATIONAL EFFECTS OF DARK MATTER

Bullet Cluster

GRAVITATIONAL EFFECTS OF DARK MATTER


Evidence for dark matter - 1 b d ff l h• Observations at different scales : more matter in the

universe than what is measured as electromagneticd ( bl l h d )radiation (visible light, radio, IR, X-rays, g-rays)

• Visible matter = stars, interstellar gas, dust : light & atomicspectra (mainly H)

• Velocities of galaxies in clusters Æ high mass/light ratiosg g / g

1 10 500MW clusterM M M= ≈ ≈1 10 500MW clusterL L L

= ≈ ≈

• Rotation curves of stars in galaxies Æ large missing mass up to large distance from centre


Dark matter in galaxy clusters 1k ( ) d /l h l• Zwicky (1937): measured mass/light ratio in COMA cluster

is much larger than expected– Velocity from Doppler shifts (blue & red) of spectra of galaxies

– Light output from luminosities of galaxies

vCOMA cluster

1000 galaxies

v 1000 galaxies

20Mpc diameter100 Mpc(330 Mly) from Earth

Optical (Sloan Digital Sky Survey)

100 Mpc(330 Mly) from Earth


Optical (Sloan Digital Sky Survey)+ IR(Spitzer Space Telescope

NASA

Dark matter in galaxy clustersf l f l d f f• Mass from velocity of galaxies around centre of mass of

cluster using virial theorem

( ) ( )10

12

KE GPE=

⎫

Mv10

7

( ) 10500

10 cluster sun

M velocities M M ML LL L

⎫> ⎪ ⎛ ⎞ ⎛ ⎞⇒ ≈ ×⎬ ⎜ ⎟ ⎜ ⎟≈ ⎝ ⎠ ⎝ ⎠⎪⎭

M ML L

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

⎭

Missing mass

P d l ti i i ‘d k’ i i ibl

COMA SUNL L⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠Missing mass

• Proposed explanation: missing ‘dark’ = invisible mass

• Missing mass has no interaction with electromagneticradiation


Galaxy rotation curves• Stars orbiting in spiral galaxies

• gravitational force = centrifugal forcegravitational force centrifugal force

( )2 Mmmv r G<( )2

Mmmvr r

r G<=

• Star inside hub v r∼Star inside hub

• Star far away from hub

1vr

∼


r

NGC 1560 galaxy

Optical blue filterOptical blue filter

HI 21cm line from gas


Universal features• Large number of rotation curves of spiral galaxies measured

by Vera Rubin – up to 110kpc from centre

• Show a universal behaviour


Milky Way rotation curve

Solar system


Dark matter halo G l i b dd d i d k h l• Galaxies are embedded in dark matter halo

• Halo extends to far outside visible regionHalo of dark matter

HALO

DISK


Dark matter halo models• Density of dark matter is larger

near centre due to gravitationalMilky Way halo models

attraction near black hole

• Halo extends to far outside visible

Vcm

-3)

region

•• darkdark mattermatter profile profile inside MilkyW i d ll d f ty

(GeV

Way is modelled frommeasurements of rotation curvesof many galaxies

Solar system

M D

ensi

t

of many galaxies

DM

Dark Matter-Dark Energy

Distance from centre (kpc)

162011-12

Evidence for dark matter -2• Gavitational lensing by galaxy clusters Æ effect larger than

expected from visible matter only


Gravitational lensing principle• Photons emitted by source S (e.g. quasar) are deflected by

massive object L (e.g. galaxy cluster) = ‘lens’

• Observer O sees multiple images


Lens geometries and images


Observation of gravitational lenses• First observation in 1979: effect on twin quasars Q0957+561

• Mass of ‘lens’ can be deduced from distortion of image

• only possible for massive lenses : galaxy clusters

Distorted behind

Gala ies in Abell cl sterGalaxies in Abell cluster


Different lensing effects• Strong lensing:

– clearly distorted images, e.g. Abell 2218 clustery g g

– Sets tight constraints on the total mass

• Weak lensing:Weak lensing: – only detectable with large sample of sources

– Allows to reconstruct the mass distribution over whole– Allows to reconstruct the mass distribution over wholeobserved field

• Microlensing:Microlensing: – no distorted images, but intensity of source changes with time

when lens passes in front of sourcewhen lens passes in front of source

– Used to detect Machos


Collision of 2 clusters : Bullet cluster• Optical images of galaxies at different redshift: Hubble

Space Telescope and Magellan observatory

• Mass map contours show 2 distinct mass concentrations– weak lensing of many background galaxiesweak lensing of many background galaxies

– Lens = bullet cluster

0.72 Mpc0.72 Mpc

Cluster 1E0657-56


Bullet cluster in X-raysX f h d d Ch d b• X rays from hot gas and dust - Chandra observatory

• mass map contours from weak lensing of many galaxies


Bullet cluster = proof of dark matter• Blue = dark matter mapped from gravitational lensing

• Is faster than gas and dust : no electromagnetic interactions

• Red = gas and dust = baryonic matter – slowed down because of electromagnetic interactions

d f d l h• Modified Newtonian Dynamics cannot explain this


Alternative theories• Newtonian dynamics is different over (inter)-galactic

distances

• Far away from centre of cluster or galaxy the accelerationof an object becomes smallof an object becomes small

• Explains rotation curves

D t l i B ll t Cl t• Does not explain Bullet Cluster


Baryons

MACHOs = Massive Compact Halo Objectsp jNeutrinosAxions

WIMPs = Weakly Interacting Massive Particles →Part 3

PART 2THE NATURE OF DARK MATTER


What are we looking for?• Particles with mass – interact gravitationally

• Particles which are not observed in radio, IR, visible, X-rays, g-rays : neutral and weakly interacting

• Candidates:

• Dark baryonic matter: baryons, MACHOs

• light particles : primordial neutrinos, axions

• Heavy particles : need new type of particles like neutralinos, … = WIMPs

• To explain formation of structures majority of dark matter particleshad to be non-relativistic at time of freeze-out

fi Cold Dark Matter


Total baryon contenty

Visible baryons

Neutral and ionised hydrogen – dark baryonsy g y

Mini black holes

MACHOs

BARYONIC MATTER


Baryon content of universe ΩB=.044

• measurement of light elementabundances He mass fraction

• and of He mass fraction Y

• And of CMB anisotropies

• Interpreted in Big Bang Nucleosynthesis model D/H abundance

N ( ) 106.1 0.6 10BNNγ

η −= = ± ×


0.044 0.005B⇒ Ω = ±

Baryon budget of universe• From BB nucleosynthesis and CMB fluctuations:

• Related to history of universe at

0.05baryonsΩ ≈

z=109 and z=1000

• Most of baryonic matter is in stars, gas, dust 0 01Ω ≈• Small contribution of luminous matter

• fi 80% of baryonic mass is dark

0.01lumΩ ≈

• Ionised hydrogen H+, MACHOs, mini black holes

• Inter Gallactic Matter = gas of hydrogen in clusters of galaxies

• Absorption of Lya emission from distant quasars yields neutralp y q yhydrogen fraction in inter gallactic regions

• Most hydrogen is ionised and invisible in absorption spectra fi formdark baryonic matter


Mini black holes• Negligible contribution from mini black holes

• BHs must have MBH < 105 M

710BH−Ω <

BHs must have MBH 10 M

• Heavier BH would yield lensing effects which are not observedobserved


Massive Astrophysical Compact Halo Objectsp y p j

Dark stars in the halo of the Milky Way

Observed through microlensing of large number of stars

MACHOSg g g


MicrolensingLi h f i lifi d b i i l l• Light of source is amplified by gravitational lens

• When lens is small (star, planet) multiple images of source cannot be distinguished : addition of images = amplification

• But : amplification effect varies with time as lens passes in p f ff pfront of source - period T

• Efficient for observation of e.g. faint starsEfficient for observation of e.g. faint stars


Period T

Microlensing - MACHOs• Amplification of signal by addition of multiple images of source

• Amplification varies with time of passage of lens in front of p f p gsource 2 2

1 / 12 4x xx x

T

⎡ ⎤⎛ ⎞= + +⎢ ⎥⎜ ⎟

⎢ ⎥⎝ ⎠ ⎣ ⎦∼A t

• Typical time T : days to months – depends on distance & velocity

2 4 T⎢ ⎥⎝ ⎠ ⎣ ⎦

• Typical time T : days to months – depends on distance & velocity

• MACHO = dark astronomical object seen in microlensing• M 0 001 0 1M• M ª 0.001-0.1M

• Account for very small fraction of dark baryonic matter

• MACHO project launched in 1991: monitoring during 8 years of microlensing in direction of Large Magellanic Cloud


Optical depth – experimental challenge l d h b b l h d• Optical depth t = probability that source undergoes

gravitational lensing

• For r = NLM = Mass density of lenses along line of sight

• Optical depth depends on 2⎛ ⎞ ρDp p p

– distance of source DS

– number of lenses

23

Gc

τ π ⎛ ⎞= ⎜ ⎟⎝ ⎠

ρSD

number of lenses

• Near periphery of bulge of Milky Way

fi Need to record microlensing for millions of stars

( ) 7per source 10τ −≈

fi Need to record microlensing for millions of stars

• Experiments: MACHO, EROS, superMACHO, EROS-2

• EROS-2: 33x106 stars monitored, one candidate MACHO found fi less than 8% of halo mass are MACHOs


Example of microlensing• source = star in Large

Magellanic Cloud (LMC, di 50k )

Blue filter

distance = 50kpc)

• Dark matter lens in form of MACHO between LMC starMACHO between LMC star and Earth

• Could it be a variable star?• Could it be a variable star?

• No: because same observation of luminosity in red and blue

red filter

of luminosity in red and bluelight : expect that gravitationaldeflection is independent of wavelength


To do• Meebrengen naar examen


STANDARD NEUTRINOS AS DARKMATTER


Standard neutrinos• Standard Model of Particle Physics – measured at LEP

2.984 0.009fermion familiesN = ±

→ 3 types of light left-handed neutrinos

ith M <45G V/ 2

fermion families

with Mν<45GeV/c2

• Fit of observed light element

abundances to BBN model (lecture 2)

3.5t i iN <

• Neutrinos have only weak and

3.5neutrino speciesN <

eut os a e o y ea a dgravitational interactions


Relic neutrinos• Non-baryonic dark matter = particles

– created during hot phase of early universeg p y

– Stable and surviving till today

• Neutrino from Standard Model = weakly interacting, smallNeutrino from Standard Model weakly interacting, smallmass, stable → dark matter candidate

• Neutrino production and annihilation in early universe• Neutrino production and annihilation in early universe

sweak interaction , ,i ie e i eγ ν ν μ τ+ −↔ + ←⎯⎯⎯⎯⎯⎯→ + =

• Neutrinos freeze-out during radiation dominated era

, ,i iγ μ

g

• When interaction rate W << H expansion rate

• at kT ~ 3MeV and t > 1s• at kT 3MeV and t > 1s


Cosmic Neutrino Background• Relic neutrino density and temperature today

• for given species (ne, nm, nt ) (lecture 2)for given species (ne, nm, nt ) (lecture 2)

-33 11311

N N cmNν γν⎛ ⎞= =⎜ ⎟⎝ ⎠

+

( ) ( )1340 0⎛ ⎞

11ν γν ⎜ ⎟⎝ ⎠

( ) ( )40 011

T Tν γ⎛ ⎞= =⎜ ⎟⎝ ⎠

1.95K

• Total density for all flavours

• Hi h densit of order of CMB b t diffi lt to dete t!

3340N cmν−≈

• High density, of order of CMB – but difficult to detect!


Neutrino mass • If all critical density today is built up of neutrinos

ρ 2

, ,47

e

m c eVνμ τ

= ⇒∑ νm <16eV c1c

νν

ρρ

= Ω = Ω =

• Measure end of electron energy spectrum in tritium beta decay

3 31 2 eH He e ν−→ + +

2m eV c<


m eV cν <

Neutrino mass

3 31 2 eH He e ν−→ + +

t rat

e

0.0m eVν =

Coun

t

1.0m eVν =2m eV cν <

2011-12 Dark Matter-Dark Energy 43Electron energy (keV)

Neutrinos as hot dark matter• Relic neutrinos are numerous

• have very small mass < eVhave very small mass < eV

• can only be Hot Dark Matter – HDM

W l ti i ti h d li f th tt• Were relativistic when decoupling from other matterkTª3MeV

• Relativistic particles prevent formation of large-scalestructures – through free streaming they ‘iron away’ the structures

• From simulations of structures: maximum 30% of DM is hot


simulationsHot dark matter warm dark matter cold dark matterHot dark matter warm dark matter


Observations2dF galaxy survey

Postulated to solve ‘strong CP’ problem

Could be cold dark matter particle

AXIONS p


Strong CP probleml f• QCD lagrangian for strong interactions

( )QCD quark gauge standard θ= + +L L L L 2a aS Fg T F F μν=L θ

• Term Lθ is generally neglected

• violates P and T symmetry → violates CP symmetry

216F Fμνθ π

=L θ

violates P and T symmetry → violates CP symmetry

• Violation of T symmetry would yield a non-zero neutron electric dipole moment ( )15 1610predictedd θ −−electric dipole moment ( )15 16. . . 10 .predictede d m e cmθ≈ ×

• Experimental upper limitsexperiment 2510e d m e cm−< 1010θ −≤


p. . . 10 .e d m e cm< 1010θ ≤

Strong CP probleml b d h h l b l ( )• Solution by Peccei-Quinn : introduce higher global U(1)

symmetry, which is broken at an energy scale fa

• This extra term cancels the Lθ term2

a aS FA g T FF μνϕ⎛ ⎞⎜ ⎟L θ

• With broken symmetry comes a boson field φ = axion with

216a aS FA

A

g Ff

F μνμνπ

ϕ⎜ ⎟⎝

=⎠

L θ −

• With broken symmetry comes a boson field φa = axion withmass 1010~ 0.6A

GeVm meVf

• Axion is light and weakly interacting

AAf

• Is a pseudo-scalar with spin 0- ; Behaves like π0

• Decay rate to photons2 3A AG mγγDecay rate to photons

2011-12 Dark Matter-Dark Energy 4864A A

Aγγ

γγ πΓ =

Axion as cold dark matter• formed boson condensate in very early universe

• Therefore candidate as cold dark matter

• if mass ª eV its lifetime is larger than the lifetime of universe

Æ stable

• Production in plasma in Sun or SuperNovae

• Searches via decay to 2 photons in magnetic fieldproduction decayAγ γ γ γ+ ⎯⎯⎯⎯→ ⎯⎯⎯→ +

2 3

64A A

AG mγγ

γγ πΓ =

• CAST experiment @ CERN: axions from Sun

• If axion density = critical density today then

64π

y y y

6 3 210 10Am eV c− −≈ −1 aν

ρ= Ω = Ω =


cν ρ

Axions were not yet observed

GeV

-1)

plin

g(G

Axion model di i

n-γ

coup predictions

Some are excluded by CAST limits

Axi

on

Axion mass (eV)Combination of mass and coupling below CAST l ll ll d b


limit are still allowed by experimentCAST has best sensitivity

Weakly Interacting Massive Particles

PART 3y g

WIMPS AS DARK MATTER


summary up to now

luminous1%

dark baryonic

4%

Neutrino HDM<1%

• Standard neutrinos can be Hot DM

<1%

cold dark matter

18%

• Most of baryonic matter is dark

18%• cold dark matter (CDM) is still

of unknow type

dark energy

76%• Need to search for candidates

f b i ld d k 76%for non-baryonic cold darkmatter in particle physicsbeyond the SMbeyond the SM

0.05 0.01 00.18 .24CDMmatter Baryons HDMν ΩΩ = Ω +Ω + ≈ + + =


Non-baryonic CDM candidates• Axions

– To reach density of order ρc their mass must be very small

– No experimental evidence yet

2 6 310 10Am c eV− −≈ −p y

• Most popular candidate for CDM : WIMPsost popu a ca d date o C s

• Weakly Interacting Massive ParticlesWeakly Interacting Massive Particles• present in early hot universe – stable – relics of early universe• Cold : Non-relativistic at time of freeze-outCold : Non relativistic at time of freeze out• Weakly interacting : conventional weak couplings to standard

model particles - no electromagnetic or strong interactions


p g g• Massive: gravitational interactions (gravitational lensing …)

WIMP candidates• Massive neutrinos:

– standard neutrinos have low masses – contribute to HDM

– Massive standard neutrinos up to MZ/2 = 45GeV/c2 are excluded by LEP

– Non-standard neutrinos in models beyond standard model

• Neutralino χ = Lightest SuperSymmetric Particle (LSP) in R-parity( ) hconserving SuperSymmetry (SUSY) theory

– Lower limit from accelerators ª 50 GeV/c2

– Stable particle – survived from primordial era of universe

• Other SUSY candidates: sneutrinos, gravitinos, axinos

• Kaluza-Klein states from models with universal extra dimensions

•


…….

Expected mass range • Assume WIMP interacts weakly and is non-relativistic at freeze-

out

Whi h ll d?• Which mass ranges are allowed?

• Cross section for WIMP annihilation vs mass leads to abundancevs massvs mass

2 21) 4 ~ ~M s Mσ= →2s2

2

1) 41 12) 4 ~ ~

M s M

M s M

χ χ

χχ

σ

σ

→

= →2Ws > M

s < M

χ

( ) 1~tΩ ( )0 vtχΩ

σ


Expected mass range: GeV-TeV• Assume WIMP interacts

weakly and is non-relativisticat freeze out

HDM neutrinos

CDM WIMPsat freeze-out

• Which mass ranges are allowed?

neutrinos

allowed?

• Cross section for WIMP annihilation vs mass leads to

Wannihilation vs mass leads to abundance vs mass

2 21) 4M s Mσ→2s2

2

1) 4 ~ ~1 12) 4 ~ ~

M s M

M s M

χ χ

χ

σ

σ

= →

= →2W

W

s > M

s < M

MWIMP (eV)

s M χ

( )01~v

tχΩσ


vσ

Cross sections and densities -1• WIMP with mass M must be non-relativistic at freeze-out • gas in thermal equilibrium Could be neutralino or

h kl2

2

Boltzman gaskT Mc⎛ ⎞

→other weakly interacting

massive particle

( )3

22

number density2

MckTMT eT

π

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

−⎛ ⎞= ⎜ ⎟⎝ ⎠

N, ...f fχ χ+ ↔ +

• Freeze-out when annihilation rate < expansion rate H

2π⎝ ⎠

( )freeze oAnnihilation utW H tσ −= ≤χvN

, , ,...f f W W e eχ χ + − + −→ ++ + +


• Cross section s depends on model parameters

Cross sections and densities -2

• assume that couplings are of order of weak interactions2v G M∼σ GF = Fermi

R it i t

Fv G M∼σ

( )1* 221 66 g T

GF Fermi constant

• Rewrite expansion rate ( ) ( )1.66

PL

g TH T

M=

• Freeze-out condition

( ) 223

2 2

2

F

MTc

ke G TMT M f

⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

−⎡ ⎤⎢ ⎥ ⎡ ⎤ ≈⎣ ⎦⎢ ⎥( )W N H Tσ

f t t 100

( ) FPL

e GM

MT M f⎡ ⎤⎣ ⎦⎢ ⎥⎢ ⎥⎣ ⎦

( )FOW N v H Tσ= ≈

• f = constants ≈ 100

• Solve for P = Mcc2/kT at freeze-out ( )2

25c

P FOkM

Tχ= ≈


FOkT

Cross sections and densities - 3

• At freeze-out annihilation rate ≈ expansion rate( ) ( )FOv H Tσ ≈FON T

• WIMP number density today for T0 = 2.73K

( ) ( )FOv H TσFON T

( ) ( ) ( )( )

( ) ( )3 230

3FO FOFO PLT T TR T

R TM×

≈=0N t FON T

• Energy density today

( ) ( ) ( )30R T vσ0 FO

Energy density today

( )0

3 3110 6 10TM GeV s

vt

vNχ χρ

σ σ

−−×= ∼ ∼P

M

2

25FO

ckM

Tχ= ≈P

v vσ σPLM

( )2

3 1510 mt c sχρ −

−=Ω

1910FOk

GeV

T

≈PLM


( )0c

mv

t c sχ ρ=Ω ∼

σ

Dependspon model

y Increasing <σAv>

dens

ity

today

Num

ber

P~25

N

P=M/T (time ->)

( )25

3 110~t cm s−

−Ω


( )0 ~t cm svχΩ

σ

Cross sections and densities - 4• Relic abundance of WIMPs today

2510−

( ) 3 10 ~ 10t cm s

vχ−Ω

σ

• For ( ) ( )35 210X cm O pbσ χ χ −+ → ≈ ≈1χΩ =

• O(weak interactions) fi weakly interacting particles canmake up cold dark matter with correct abundancemake up cold dark matter with correct abundance

• Velocity of relic WIMPs at freeze-out from kinetic energy

0.3v cχ ≈2 312 2

FOkTM vχ = ( )123~ 0.3v

c≈P


2 2 c

Neutralino is good candidate for cold dark matter

SUSY = extension of standard model at high energy

SUPERSYMMETRYg gy


What are we looking for?• Particle with charge = 0

• With mass in [GeV-TeV] domainWith mass in [GeV TeV] domain

• Only interacting through gravitational and weakinteractionsinteractions

• Stable

• Decoupled from radiation before BBN era

• Has not yet been observed in laboratory = accelerators


Why SuperSymmetry• Gives a unified picture of matter (quarks and leptons) and

interactions (gauge bosons and Higgs bosons)• Introduces symmetry between fermions and bosons

Q fermion boson Q boson fermion= =

• Fills the gap between electroweak and Grand Unified Theoryl

Q f Q f

scale2

1710 10WM GeV −≈ =19 1010PLM GeV

≈ =

• Solves problems of Standard Model, like the hierarchy problem: = divergence of radiative corrections to Higgs massP id d k tt did t


• Provides a dark matter canndidate

SuperSymmetric particles• Need to introduce new particles: supersymmetric particles

• Associate to all SM particles a superpartner with spin ±1/2Associate to all SM particles a superpartner with spin ±1/2 (fermion ↔ boson) fi sparticles

• minimal SUSY: minimal supersymmetric extension of the• minimal SUSY: minimal supersymmetric extension of the SM – reasonable assumptions to reduce nb of parameters

P t li t b d t i d f• Parameters = masses, couplings - must be determined fromexperiment

• Searches at colliders: so particles seen yet

M accessible range> d i sensitivityσ <M accessible range> production sensitivityσ <


The new particle table

Particle table (arXiv:hep-ph/0404175v2)


( p p / )

Neutralinos as dark matter• Supersymmetric partners of gauge bosons mix to

neutralino mass eigenstates

• Lightest neutralino

• R-parity quantum number

1 0 00 11 12 3 13 1 14 2N B N W N H N Hχ χ= = + + +

R parity quantum number

• baryon number B, lepton number L, spin s

SM ti l R 1 d ti l R 1

( )3 21 B L sR + +≡ −

• SM particles: R = 1 and sparticles: R = -1p p q g X+ → + +

• In R-parity conserving models Lightest Supersymmetric

0 01 1q q g qqχ χ→ + → +

In R parity conserving models Lightest SupersymmetricParticle (LSP) is stable

• LSP = lightest neutralino fi dark matter candidate


• LSP = lightest neutralino fi dark matter candidate

Expected abundance vs mass

Wch

2• variation of neutralinodensity as function of

2hχΩ

Wmass

• Allowed by collider and direct search upper limitsdirect search upper limitson cross sections

W=[.05-0.5]

Ω [ ]

Predictions of Constrained Minimal

Supersymmetric extension of the Ω= [0.04 – 1.0]Supersymmetric extension of the Standard Model with 7 free

parameters

N li (G V)

• Expected mass range 50GeV – few TeV


Neutralino mass (GeV)50GeV few TeV ( )M GeVχ

The difficult path to discovery

WIMP DETECTIONp y


three complementary strategies


Production at accelerators• Controlled production in laboratory: particle accelerators

• LHC @ CERNLHC @ CERN


Example from LHC

Probed masses up to ~ TeVProbed masses up to TeVSo signal was observed

H. Bachacou EPS2011

0 0j t 0 01 1p p q g jets χ χ+ → + → + +


N Nχ χ ′+ → +


( ) 44 2 810 10p cm pbσ χ − −< =experiment

WIMPs in the Milky Way halo• Assume galaxy with dark halo• Energy density in galactic halo gy y g

from rotation curves and simulationssimulations

3~ 0.3GeV cmχρ

• WIMP velocity in halo

χρ

O(galactic objects)

1~ 270v km sχ−


Direct detection challenges

pRM

N χχ

ρσ∝ pM χ

χ

• low rate Ælarge detectorg

• very small signal Æ low thresholdÆ low threshold

• large background : protect againstprotect againstcosmic rays, radioactivityradioactivity, …


Annual and diurnal modulation• Annual modulations due to movement of solar system in

galactic WIMP halo – 30% effect

• Diurnal modulations due to Earth rotation – 2% effect

• Observed by DAMA – not confirmed by other experimentsObserved by DAMA not confirmed by other experiments


DAMA/LIBRA experiment• In Gran Sasso underground laboratory

• Measure scintillation light from nuclear recoil in NaI crystalsMeasure scintillation light from nuclear recoil in NaI crystals

• Observe modulation of 1 year (full curve) with phase of 152 5 days152.5 days

• If interpreted as SUSY dark matter: M ~ 10-50 GeV/c2


Combining different experiments


d l ( l ) l

Noble liquids: XENON100• 1400m under mountain in Gran Sasso tunnel (Italy) : lower

rate of cosmic background

• Sensitive core = 100kg liquid Xenon at -106°C• Pure materials – low radioactivityy

• Recoil nucleus ionises liquid Xenon

• Measure signal from ionisation and scintillation light• Measure signal from ionisation and scintillation light produced during recoil of nucleon

D bl i l h l i f k• Double signal helps against fake events

• Started data taking in 2009



XENON100


Combining different experiments


Indirect detection of WIMPsS h f i l f ihil i f WIMP i h Milk W h l• Search for signals of annihilation of WIMPs in the Milky Way halo

• Detect the produced antiparticles, gamma rays, neutrinos

• accumulation near galactic centre or in heavy objects like the Sun due to gravitational attraction


Neutrino signals• Expect WIMPs to accumulate in heavy objects like Sun

χχ Earthρχ velocity

distribution

Sun

νμσcΝ ν int.

Detectorμμ

Gcapture

qq Detector

Gannihilation

qqll μχχ ν→ → →


annihilation

, ,W Z Hμ

±

Neutrino detection

South Pole station Cherenkov light pattern emitted by the muon isemitted by the muon isregistered by an array of photomultiplier tubes (PMT)

ayer Photomultiplier tubes

photomultiplier tubes (PMT)

m ic

e la

p

3km

νµ*

85

νμ2011-12 Dark Matter-Dark Energy

Signal and background

A few 10’000 atmosphericneutrinos per year fromBG neutrinos per year fromnorthern hemisphere

BG

Max. a few neutrinos per year from WIMPs

signalper year from WIMPs

~1010 atmospheric~10 atmosphericmuons per year fromsouthern hemisphere

BG

86

p

2011-12 Dark Matter-Dark Energy

IceCube search resultsNeutralino 250 GeV to WWDataBackgroundBackground

s

• Search for neutrinos fromf eve

nts

• Search for neutrinos fromWIMP annihilation in the Sun

• No significant signal foundmbe

rof

No significant signal found

• Rate is compatible withatmospheric background

Num

atmospheric background

• Set upper limit on possible flux

ψ(deg)

nal?


Sign

Combining the experimental searches( ) 2

SD p cmσ χ ⎡ ⎤⎣ ⎦

Direct detectionIceCube

SUSY modelsallowed by


experiments IceCube allowed by accelerator results

SummaryOb ti f d k tt it ti l ff t• Observation of dark matter as gravitational effects– Rotation curves galaxies, mass/light ratios in galaxies– Velocities of galaxies in clusters– Gavitational lenses– Primordial nucleosynthesis– Anisotropies in CMB radiation

• Nature of dark matter particles:– Baryons and MACHO’s– Neutrinos– Neutrinos– Axions

• Weakly Interacting Massive Particles (WIMPs) • Experimental WIMP searches

– Accelerators– Direct detection experimentsDirect detection experiments– Indirect detection

• Dark energy2011-12 Dark Matter-Dark Energy 89

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