Dark Matter - IIHE

Dark Matter

Lecture 3

See also Dark Matter awareness week December 2010

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

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 1 0 1 0 1r kH t H z z z⎡ ⎤= + +Ω + + +Ω +⎣ ⎦ΛmΩ 0 Ω 0

Ωk=0

2010‐11 Dark Matter 2

( ) ( )( ) ( )( ) ( ) ( )( )0 k⎣ ⎦Λ

Dark matter : Why and how much?

luminous1%

dark baryonic

4%

Neutrino HDM<1%

• Several gravitationalobservations show that more

i i h U i h cold dark matter18%

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

5100.24

rad

matter

−Ω =

Ω =matter

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


⎣ ⎦

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

• There are candidates from several models of physicsThere are candidates from several models of physicsbeyond the standard model of particle physics

• the answer will come from experiment• the answer will come from experiment


Overview lecture 3 b f d k l ff• Observation of dark matter as gravitational effects

– Velocities of galaxies in clusters

– Rotation curves of stars and dust in galaxies

– Gavitational lenses

– Collisions of clusters : Bullet cluster

• Nature of dark matter particles– Baryons

– MACHOs = Massive Compact Halo Objectsp j– Neutrinos– Axionso s

– WIMPs = Weakly Interacting Massive Particles• Experimental WIMP searches: direct and indirect detectionExperimental WIMP searches: direct and indirect detection


Velocities of galaxies in clusters and M/L ratio

G l t tiGalaxy rotation curves

Gravitational lensing

Bullet Cluster

GRAVITATIONAL EFFECTS OF DARKBullet Cluster

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 10 500

MW clusterL L L= ≈ ≈

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


Dark matter in galaxy clustersk ( ) 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

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

• Proposed explanation: missing ‘dark’ = invisible mass

Mi i h i t ti ith l t ti

COMA SUNL L⎝ ⎠ ⎝ ⎠

• Missing mass has no interaction with electromagneticradiation


Galaxy rotation curves• Stars orbiting in spiral galaxies

• gravitational force = centrifugal forcegravitational force centrifugal force

( )2 mM r Gmv <( )2

mM r Gmvr r

<=

• Star inside hub v r∼Star inside hub

• Star far away from hub

1vr

∼


r

NGC 1560 galaxy


Universal features• Large number of rotation curves of spiral galaxies measuredby Vera Rubin – up to 110kpc from centre

• Show a universal behaviour


Milky Way rotation curve

Solar system


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

• Mass in galaxies grows with distance from centre

• Halo extends to far outside visible region

HALO

DISK


Dark matter halo model• Density of dark matter is larger

near centre due to gravitationalattraction near black hole

• Halo extends to far outside visible

m‐3)

region

• dark matter profile insideMilkyW i d ll d f Solar system(G

eVcm

Way is modelled frommeasurements of rotation curvesof many galaxies

Solar system

Den

sity

of many galaxies DDark MatterDistance from centre (kpc)

152010‐11

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


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 observedAllows to reconstruct the mass distribution over whole observedfield

• 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 mattermapped 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)‐galacticdistances

• 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

THE 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 in large quantities: primordial neutrinos, axions

• Heavy particles in small quantities: need new type of particles likeneutralinos, … =WIMPs

• To explain formation of structures majority of dark matter particleswere non relativistic at time of freeze‐out

• fi Cold Dark Matter


Total baryon content

Visible baryonsy

Neutral and ionised hydrogen – dark baryons

Micro black holes

MACHOs

Exotic baryonic matter

BARYONIC MATTERy


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 −= = ± ×

Ω 0 044 0 0052010‐11 Dark Matter 28

⇒ BΩ = 0.044 ± 0.005

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, exotic matter

• 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 spectrafi formdark baryonic matter


Lya forest and neutral hydrogen gasHydrogen atomsAbsorb UV light

Emission of UV light by quasarMeasurement of

b ig y ql= 1216 ǺLyman a

absorption spectrayields amount of neutral H transition in Hneutral H


Lya forest• Hydrogen spectrum from distant quasar – absorption atdifferent redshift values due to atomic hydrogen

1216 Å emission

Absorption at different z


Micro black holes• Negligible contribution from micro 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

• small contribution of MACHOS = dark stars – observed in Milky Way through gravitational microlensing


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 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

• A few have been observed in halo of Milky Way

• 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 foundfi 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


NEUTRINOS AS DARK MATTER


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,Neutrino from Standard Model weakly interacting, massive, 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⎛ ⎞ 1 95K V

11ν γν ⎜ ⎟⎝ ⎠

( ) ( )40 011

T Tν γ⎛ ⎞= =⎜ ⎟⎝ ⎠

1.95K ≈ meV

• 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 2

, ,

47 16e

m c eV m eV cν νμ τ

= ⇒ <∑1c

νν

ρρ

= Ω = Ω =

• Measure end of electron energy spectrum in tritium beta decay

3 31 2 eH He e ν−→ + +

2m eV cν <


Neutrino oscillations and mass• 3 neutrino flavours ne, nm, nt• If different, non‐zero masses , expect mixing

1 2 3 1e e ee U U UU U U

νν

νν

⎛ ⎞⎜ ⎟= ⎜ ⎟

⎛ ⎞⎜ ⎟⎜ ⎟

⎛ ⎞⎜ ⎟⎜ ⎟

Flavour mass 1 2 3

1 2 3

2

3

µ µ µU U UU U Uτ

μ

τ τ τ

ν

ν

νν

= ⎜ ⎟⎜

⎜ ⎟ ⎜ ⎟⎜ ⎟⎝⎟⎟ ⎝⎝ ⎠⎠ ⎠⎜

Flavoureigenstates eigenstates

• During propagation flavour eigenstates oscillate – in the simplifiedcase of 2 flavours l and l’

⎝ ⎠

( ) 2 2' 'sin 2 sin 1.27eff

l l llLPE

ν ν θ ⎛ ⎞→ ≈ ⎜ ⎟⎝ ⎠

2ll'Δm

• Observations of oscillations at muon‐neutrino beams lead to upperlimit for most massive neutrino


2 3 2 3 223 2.5 10 0.02 0 5.5 1m e mV e eV Vν

− −Δ <≈ × ⇒ × =

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 problemf ll d f• CPT = symmetry of all interactions – no evidence of

breaking from experiment

• QCD lagrangian for strong interactions

( )QCD quark gauge standard θ= + +L L L L2

a aS Fg T F F μν=L θ

• Term L is generally neglected ; non perturbative

( )QCD quark gauge θ216

F Fμνθ π=L θ

• Term Lθ is generally neglected ; non‐perturbative

• violates P and T symmetry→ violates CP symmetry

• Violation of T symmetry would yield a non‐zero neutron electric dipole moment ( )15 1610predictede d m e cmθ −−≈ ×

• Experimental upper limits. . . 10 .e d m e cmθ≈ ×

experiment 2510e d m e cm−< 1010θ −≤2010‐11 Dark Matter 46

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 term

2a 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 6106A

GeVm eV=

• Axion is light and weakly interacting

6AA

m eVf

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

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

2010‐11 Dark Matter 4764A A

Aγγ

γγ πΓ =

Axion as cold dark matter• Very small coupling ‐ 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 photon 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)

pling(G

Axion model di i

n‐γcoup predictions

Some are excluded by CAST limits

Axion

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

WIMPS ‐ INTRODUCTIONy g


summary up to now

luminous1%

dark baryonic

4%

Neutrino HDM<1%

• Neutrinos can be Hot DM

• Most of baryonic matter is dark <1%

cold dark matter18%

• cold dark matter (CDM) is still18%

of unknow type

dark energy76%

• Need to search for candidates for non‐baryonic cold dark

tt i ti l h i 76%matter in particle physicsbeyond the SM

( ) ( ) ( ) 5

00 0.76 0 0 0 1

180 0

0 05 0 01 0 24K r

−ΛΩ ≈ Ω ≈ Ω ≈ ≈

Ω Ω + + +ΩΩ +2010‐11 Dark Matter 51

0.180.05 0.01 0.24m B Ca DM Mr H DνΩ = Ω + ≈ + + =ΩΩ +

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: there are only 3 standard neutrino families

– Non‐standard neutrinos in models beyond standard model

( )• Neutralino χ = Lightest SuperSymmetric Particle (LSP) in R‐parityconserving SuperSymmetry (SUSY) theory

l f l / 2– Lower limit from accelerators ª 40 GeV/c2

– Stable particle – survived from primordial era of universe

• Other SUSY particles: sneutrinos, gravitinos, axinos

• Kaluza‐Klein states from models with universal extra dimensions


• …….

Cross sections and densities -1• If WIMPs are CDM they must be non‐relativistic at freeze‐out –

gas in thermal equilibrium Could be neutralino or h kl( )2

32

Boltzman gasM

Mc kT M T

TM

χ−⎛ ⎞

⎜ ⎟

→ →

⎛ ⎞

other weakly interactingmassive particle

( ) number density2

TTT M eπ

⎜ ⎟⎝ ⎠⎛ ⎞= ⎜ ⎟

⎝ ⎠N , ...f fχ χ+ ↔ +

• Freeze‐out when annihilation rate < expansion rate H

( )fA ihil ti tW H tσ= ≤χvN ( ), , ,...

freeze oAnnihilation utW H t

f f W W e e

σ

χ χ + − + −

−

→ ++

≤

+ +

χvN

• Cross section s depends on model parameters – still unknown


Cross sections and densities -2

• One generally assumes that couplings are of order of weakinteractions 2v G M∼σ GF = Fermi

• Rewrite expansion rate

Fv G M∼σ

( )1

* 221 66 g T

GF Fermi constant

• Rewrite expansion rate ( )1.66

PL

g TH

M=

• Freeze‐out condition

( )2

23 22MT Te fMGMT

⎛ ⎞⎜ ⎟−

⎝ ⎠⎡ ⎤

⎡ ⎤ ≤⎢ ⎥ ⎣ ⎦( )W N v H tσ= ≤

• f = cst ≈ 100

( )PL

Fe fMGMTM

⎡ ⎤ ≤⎢ ⎥ ⎣ ⎦⎢ ⎥⎣ ⎦

( )FOW N v H tσ= ≤

• f = cst ≈ 100

• Solve for P = Mcc2/kT at freeze‐out2

25FO

cP

kM

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

vσ×

≈=0N t FON T

• Energy density today

( )0R T vσ

Energy density today

( )0

3 3110 6 10TM GeV s

vt

vNχ χρ

σ σ

−−×

= ∼ ∼PM

2

25FO

ckM

Tχ= ≈P

v vσ σPLM

( )2

3 1510 mt c sχρ −

−=Ω

1910FOk

GeV

T

≈PLM


( )0c

mv

t c sχχ ρ

=Ω ∼σ

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

2510ρ −

( ) 3 10

10

c

mv

t c sχχ

ρρ

−=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

( )1

221 3 3 0.32 2

kT vMvc

= → →∼ ∼ v ≈ 0.3 cP


2 2 c

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→2s < M2

2

1) 41 12) 4

M s M

M s M

χ χ

χ

σ

σ

= →

= →

∼ ∼

∼ ∼W

W

2

s < M

s > M

MWIMP (eV)

s M χ

( )01v

tχΩ ∼σ


vσ

Neutralino is good candidate for cold dark matter

SUSY = extension of standard model at high energy

SUPERSYMMETRYg gy


SuperSymmetry -1• 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 the hierarchy problem: divergence of radiative corrections to Higgs massP id d k tt did t


• Provides a dark matter canndidate

SuperSymmetry -2• 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

• Masses of SUSY particles are above ~40 GeV/c2 from• Masses of SUSY particles are above ~40 GeV/c2 fromnegative searches at LEP, HERA and Tevatron

i i l SUSY i i l t i t i f th• minimal SUSY: minimal supersymmetric extension of the SM – reasonable assumptions to reduce nb of parameters

• Parameters ‐masses, couplings ‐must be determined fromexperiment

• Supersymmetry is broken at electroweak scale


The new particle table

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


( p p / )

neutralinos• Supersymmetric partners of gauge bosons mix to neutralino mass eigenstates

• Lightest neutralino = mixing of 4 fields1 0 0N B N W N H N H+ + +

I t d R it t b

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

( )3 21 B L sR + +≡ −• Introduce R‐parity quantum number

• f(baryon number B, lepton number L, spin s)

( )1R ≡

• SM particles: R = 1 and sparticles: R = ‐1

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

• LSP = lightest neutralinofi dark matter candidate


• LSP = lightest neutralinofi dark matter candidate

neutralino density vs mass

Wch

2• variation of neutralinodensity as function of

Wmass

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

• R‐parity conserving SUSYW=[.05‐0.5]

• R‐parity conserving SUSY

• Scan over 7‐dimensionalSUSY parameter space Ω [ ]SUSY parameter space

• Expected mass range 50GeV – few TeV

Ω= [0.04 – 1.0]

N li (G V)

50GeV – few TeV


Neutralino mass (GeV)

The difficult path to discovery

WIMP DETECTIONp y


three complementary strategies


Production at colliders• Controlled production at particle collisions

• Searches at LEP, HERA and Tevatron were negative butSearches at LEP, HERA and Tevatron were negative but allowed to exclude regions of SUSY parameter space


Direct detection principle• Detector on Earth traverses ‘wind’ of dark matter in galaxy halo• WIMPs interact in detector – weak interaction ! Very low rate

M il t (N’ X) i d t t• Measure recoil spectrum (N’ or X) in detector

elastic scatteringN Nχ χ ′+ → +

• Recoil energy < 50 keV

ginelastic scatteringN X

χ χχ χ+ → +Recoil energy < 50 keV

• Need to measure very small effects

• Challenges:• low rate Æ large detector• very small signal Æ low threshold• Low background :

protect against cosmic rays, radioactivity, …2010‐11 Dark Matter 68

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


Dark Matter - IIHE

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