Dark Matter Searches

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Dark Matter Searches

• Laura Baudis
• University of Florida
• Heidelberg, October 11 - 14, 2004

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The Cosmological Inventory
Science (20 June 2003)
we now have extraordinary evidence for dark
matter and dark energy and have to take them
seriously no matter how disturbing they seem.
Max Tegmark
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Dark matter candidates

• ?B ?visible
• Baryonic dark matter (difficult to hide large
  amounts of baryons in the halo!)
• ?M ?B
• Non-baryonic dark matter (neutrinos, new
  particles,)

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Baryonic dark matter

• Hydrogen (frozen, cold or hot gas)
• one can show that snowballs would sublime and the
  gas would have T 1.3 x 106 K
• (hot gas! Not observed - would emit x-rays)
• Mass disadvantaged stars, jupiters
• red dwarfs (M 0.08 - 0.5 Mo) shine due to H
  burning in their cores
• brown dwarfs (M H-burning, brightest when born, continue to cool
  and dim
• Remnants of massive stars
• white dwarfs 0.5 Mo, remnants of stars with 1-8
  Mo
• neutron stars
• black holes
• Candidates testable by gravitational
  micro-lensing of stars in the LMC or SMC
• By observing millions of stars and examining
  their intensity as a function of time.

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Red and brown dwarfs

• Extremely abundant in the disk, buldge and
  spheroid but - the dark matter in the halo of
  the Milky Way is not due to red or brown dwarfs
• Red dwarfs are ruled our because they are not
  seen in sufficient abundance in long exposure of
  the high latitude wide-field camera of HST
  fields
• less than 1 of the halo is in red dwarfs
• Brown dwarfs are ruled out because the timescale
  of the micro-lensing events are too long
• White dwarfs seem about 100 times rarer than red
  or brown dwarfs main problem is that the
  progenitors would disgorge too many metals into
  the ISM

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Remnants of massive stars

• Can halo be made of dead stellar remnants of
  stars whose initial masses were M 1Mo?
• Problem a large population of these objects
  would contaminate the disk with heavy elements
  and would prevent the existence of extremely low
  metallicity objects which have been observed
  (since 40 of the stars initial mass is ejected,
  and most of this mass is in the form of heavy
  elements)
• Thus either dust (from ejecta) or dead remnant
  would be expected to produce too large a
  metallicity
• Star formation is a very inefficient mechanism
  for producing dark matter!
• Many generations of stars would be required to
  cycle through their lifetimes to continually trap
  more matter in remnants

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Black holes

• Primordial black holes - they would have probably
  formed before nucleosynthesis and thus would not
  count as baryonic dark matter
• Black holes which were formed as the final stage
  of stars history, and its formation was preceded
  by mass loss or supernovae - see previous
  discussion
• Black holes which were formed directly from very
  massive stars (m 100 Mo) through gravitational
  instability with no mass loss (limits from
  overheating the disk and stellar systems) - there
  could exist a large populations of these black
  holes as baryonic dark matter

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Searching for MACHOS (1)
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Searching for MACHOS (2)

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Searching for MACHOS (3)

• The targets are
• the Galactic Centre
• (study of bulge structure, exotic lenses)
• the Galactic Disk
• (study of disk structure)
• the Magellanic Clouds
• LMC SMC
• (compact halo objects, baryonic dark matter)

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The EROS experiment
EROS1 (1990-1995) photographic plates (25
deg2) a 0.4 deg2 CCD camera on a 40 cm
telescope EROS2 (1996-2002) dedicated 1
meter telescope at La Silla obs. (Chile)
simultaneous imaging in 2 passbands ( V and
I) 2 x 1 deg2 CCD cameras (4 x 8 M pixels)
100 images/night
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Searching for MACHOS with EROS

• 25.5 million stars monitored
• (39 deg2 scattered over 64 deg2).
• 5 years (1996-2001) of data available .
• Time sampling 1 measurement/4-7 days.
• Selection efficiency 16 _at_ 50 days
• 4 micro-lensing candidates found
• 1 more candidate from EROS1
• (1990-1995)

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LMC 3 year analysis mlensing candidates
EROS2 5
EROS2 3
te24 1 days
te44 3 days
EROS2 7
te33 2 days
te36 2 days
EROS2 6
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LMC 1996-1999 analysis
prediction (standard halo)

• 21 mlensings
• expected for
• 3 years of data
• halo of 0.5 Mo Machos
• fMACHO 100
• 4 candidates observed
• (mass 0.2 Mo)

observed events
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Combined EROS1EROS2 LMC 1996-1999
SMC 1996-1998 limit
fMACHO Standard Halo with fMACHO 100 ruled out
(MMACHO in 10-2 - 0.08 Mo) EROS central value f
MACHO 10 BUT no signal claimed
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SMC 1996-2001 analysis

• 5.2 million stars monitored over
• 8.6 square degrees.
• Time sampling
• 1 measurement /2.5 days.
• 5 years (1996-2001) of data available
• Total photometric sampling efficiency
• 15 _at_ 50 days.
• 4 mlensing candidates found
• (5 yr analysis, preliminary)

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EROS2 SMC 5 year analysismlensing candidates
tE101 days
tE612 days
tE390 days
tE243 days
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Comparison of LMC and SMC candidates
Halo lenses Same tE distributions for LMC/SMC
lenses.  Self-lensing  LMC expect tE
40 days SMC expect tE 100 days
SMC candidates not compatible with 0.5 Mo
Machos. Optical depth towards SMC too large for
self-lensing ? some SMC candidates likely
variable stars
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EROS 95 CL exclusion limits
The Galactic dark matter is made of MACHOs with mass in 10-6-10-2 Mo dwarfs excluded by EROS (95 CL)
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Particle physics candidates

• Neutrinos
• Axions
• Supersymmetric dark matter
• WIMPzillas, SIMPzillas

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Neutrinos (1)

• In the standard big bang model, copious numbers
  of neutrinos were produced in the early universe.
  
• The universe today is thought to be filled with
  1.7 K thermal neutrino radiation, the neutrino
• complement to the thermal radiation background
  (neutrinos decouple 2 MeV)
• The number density of light neutrinos can be
  expressed as
• rn mn Yn ng
• where Yn nn/ng is the density of ns relative
  to photons, which today is 411 photons/cm3.
• One can show that in an adiabatically expanding
  Universe Yn 3/11 (e e- annihilate when the T
• drops below 2 MeV, dumping their energy into
  photons).
• If these neutrinos are massive, then they can
  make a significant contribution to the total
  energy
• density of the universe
• 
  ?nh2 (?mn/94eV)
• From ?Mh2 0.3 upper bound on neutrino mass
  mtot ?mn 28 eV

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Neutrinos (2)

• Neutrinos are massive (neutrino oscillation
  experiments)
• Upper limits from direct mass determinations
• Upper limits/detection from neutrinoless double
  beta decay
• Upper limits from cosmology

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Neutrino oscillations (1)

• If neutrinos have mass, then there is a spectrum
  of 3 neutrino mass eigenstates that
• are the analogues of the charge-lepton mass
  eigenstates e, m, t.
• A neutrino state is a superposition of mass
  eigenstates (U is the unitary lepton mixing
  matrix)
• na ? Uai ni
• To see how neutrinos change flavors, or
  oscillate in vacuum, one has to apply
  Schrödingers equation
• to the ni component of na in the rest frame of
  this component
• ni(ti) e-imiti ni(0), where mi is the mass
  and ti the time in the ni frame.
• The phase factor can be written exp -imiti
  exp -i(Ei-pi)L exp-i(mi2/2p)L
• It follows that after a neutrino born as na has
  propagated a distance L, its state vector has
  become
• na(L) ?Uai exp-i(mi2/2p)L ni
• The probability that after traveling a distance L
  it has flavor nb, is P 2

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Neutrino oscillations (2)

• Examplefor 2 flavors, the unitarity mixing
  matrix takes the form
• U cos q sin q na
• -sin q cos q nb
• n1 n2
• Where q is the mixing angle
• The probability that a neutrino changes flavor
  is
• P( na - nb) sin2 2q sin2 1.27 Dm2 (L/E)
• Evidence for neutrino oscillations
• Solar neutrino experiments ne - nm
• Atmospheric neutrino experiments nm - nt
• Reactor neutrino experiment ne - nm
• Accelerator neutrino experiments ne - nm

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Neutrino Oscillations (3)

• Neutrino 2004
• Great improvement on Dm212

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Neutrino Oscillations (4)
Neutrino 2004 Atmospheric neutrinos
Accelerator neutrinos
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Neutrino oscillations (5)
Mass of the heaviest can not be less than
sqrt(Dmatm) 0.03 eV But what are the masses
of the eigenstates?
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Neutrino Direct Mass Measurements
Oscillations gives only Dm2 mmax
Dm2 Neutrinos can be degenerate In any case,
density of cosmological neutrinos at minimum
?10-3density of stars

• Direct measurement
• Extremely important to fix mass hierarchy and
  amount in universe
• Electron neutrino
• Tritium beta decay mve
• Future Katrin sub eV
• Other neutrinos
• mvµ mn decay, improve to 10
  keV)
• mvt npn decay, improve to 5
  MeV)

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Neutrinoless Double Beta Decay
Contrains the sum of the neutrinos Majorana
masses weighted by their couplings to
electrons e 0.35 eV
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Neutrinoless Double Beta

• Important to check!
• Running experiments
• CUORICINO (130Te)
• - CUORE
• NEMO 3 - Super NEMO
• XMASS (Xe)
• In project
• 76Ge
• Heidelberg-MoscowIGEX material
• in naked Genius like detector
• Majorana (US)
• 136Xe
• EXO (USA)
• enriched Ba detection with single laser
  spectroscopy
• 100 Mo
• MOON (Japan)

Low Temperature Detector
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Neutrino Mass Limit from Cosmology
Neutrinos erase structure at
small scale

• Light neutrinos produce structure
• on large scales, including
• filaments and voids.
• For mn 100 eV they are
• relativistic at the time of their
• decoupling, and due to free
• streaming erase perturbations
• out to very large masses given
• by the Jeans mass
• MJ 3 x 1018 M0/mn2 (eV)
• Typical galactic mass scales are
• 1012 M0
• Large structures form first and
• galaxies are expected to
• fragment out later
• Problem galaxies form

Smaller scales
Larger scales
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The power spectrum

• density fluctuations are described in terms of
  the power spectrum
• P(k) square of the Fourier transform of the
  density field P(k) dk2,
• where k is related to the l of the fluctuation,
  k 2p/l (galaxies are formed from perturbations
  of l 1 Mpc)
• The power spectrum is described by a power law
  P(k) kn, where n 1 corresponds to
  fluctuations in the gravitational potential that
  are the same on all scales
• Galaxy clustering described by the 2-point
  correlation function measures the excess
  probability of finding 2 galaxies separated by a
  given distance. It is found to follow a power
  law
• z (r/6h-1 Mpc)-1.8
• The Fourier transform of z is the power spectrum
  of the distribution of galaxies

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Power Spectrum of Structure

• Consider the Fourier Transform of 2-point
  correlation of matter distribution
• Measured by a variety of
• techniques that overlap in
• distance scale
• Show good agreement
• How do we explain overall
• shape?

LARGER SCALES
SMALLER SCALES
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What Determines Structure Power Spectrum?

• Suggest that primordial matter distribution
  fluctuations are scale invariant i.e. fractal,
  no length scale preferred
• P(k) kn, with n1 , space-time has same
  wrinkliness on each resolution scale
• Growth of fluctuations calculated by solving
  equations of fluid in an expanding Universe,
  taking into account
• Gravity
• Pressure, arising from EM interactions of
  relativistic component
• At early times, high z
• Perturbations are small, so possible to linearize
• In absence of fluid pressure and expansion
• Over densities would grow exponentially
• In an expanding Universe exp() become power laws
• Pressure term
• Provides a restoring force against collapse
• However, max size at which this can operate is
  set by speed of oscillations cs in medium

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What Determines Structure Power Spectrum(2)?

• The primordial power spectrum is not what we
  observe today, as density fluctuations can be
  affected by causal microphysical processes once
  the scale of these fluctuations is inside the
  horizon scale (the distance over which light can
  travel from
• t 0 to the time in question).
• In an expanding Universe gravity is ineffective
  at causing the growth of density fluctuations as
  long as the dominant form of energy resides in
  radiation - such primordial fluctuations in
  baryons will be damped out due to their coupling
  to the radiation gas
• Once the Universe becomes matter dominated,
  primordial fluctuations on scales smaller than
  the horizon size can begin to grow
• This suggests that an initial power law spectrum
  of fluctuations will turn over for large
  wavenumbers which entered inside the causal
  horizon during the early period of radiation
  domination

primordial
processed
Causal processes inside horizon
k
k
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What Determines Structure Power Spectrum? (3)

• Two epochs in early universe
• Radiation dominated
• Pressure is important
• Matter dominated
• Pressure no longer important
• Transition radiation to matter dominated occurs
  at zeq 104
• Reason for transition is that Ws are diluted by
• expansion scale expansion a(t) (1z)-1
• Radiation Wrada(t)4 (think of it as wavelength
• being stretch as well as volume term)
• Matter Wma(t)3 (volume dilution)

dk
Matter dominated
kh the horizon scalegrows with time
k
kkh
Radiation dominated
Start with P(k)k
k
Large Scale
Small Scale
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Measuring the power spectrum

• Galaxy Redshift Surveys
• Measure angular position
• and distance using redshift
• CfA (1980s) 30,000 galaxies,
• out to z0.05 (v15,000 km/s)
• See Voids, bubble, sheets filaments
• Las Campanas (1990s) additional
• 26,000 galaxies,
• out to v60,000 km/s
• 2dFGRS (2000s)
• 250,000 galaxies,
• 5 of sky (shown)
• SDSS, Sloan Digital Sky Survey
• (on going)
• 1 Mgalaxies, 25 of sky

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Limits on Neutrino Mass
Add CMBR Measure ?m! SmvSmaller scales
Larger scales
Applies to sterile neutrino if mixes enough with
other neutrinos
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Neutrino mass from Cosmology

All upper limits 95 CL, but different assumed
priors !
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Neutrino masses (Altarelli Neutrino 2004)
Most natural Supersymmetry
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Axions (1)

• Pseudo-goldstone bosons that get a very small
  mass due to QCD effects in a way
• Associated with the solution of the strong CP
  problem.
• Axion fields can be represented as an angular
  field.
• Small mass (10-5 eV) if they are thermally
  produced in the early Universe they would
• provide a negligibly small contribution to ?!
• But non-thermal production!

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Axions (2)
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Axions (3)

• At early times their potential (a function of an
• angular variable going from -p to p) changes.
• No energy is stored in the axion field
• Once the axion gets a mass, energy is stored
• in the axion field, which dynamically rolls
• to the bottom of its potential
• The time it takes to begin rolling is inversely
• proportional to the curvature of its potential,
• and thus inversely proportional to the axion
• mass.
• The smaller the mass, the longer the energy
• Gets stored before it begins to redshift
• And the greater the remnant axion density
• For m 10-5 eV ? 1

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Axions (4)

• Generated by the Peccei-Quinn mechanism to
  conserve
• CP-symmetry in the Strong Interaction
• Like an ultra-light, ultra-weakly interacting
  p0
• All couplings proportional to its mass gaii
  ma
• Abundance roughly inverse to mass Wa
  ma7/6
• Current mass limits 106 eV
• (overclosure)
  (SN1987a)

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Axion-photon coupling gagg
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Detecting axions (Sikivie, 1983)
Ultra-low noise microwave receiver
Superconducting magnet
High-Q microwave cavity
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The signal is the total energy of the axion
The axion mass range is scanned by tuning the
cavity Resonance condition hn mac21
O(b210-6)
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The parameter space
250 MHz
250 GHz
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Axion experiment (UFLivermore)
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Superheavy dark matter

• SIMPzillas, WIMPzillas (Kolb 98),
• M 1013 GeV,
• strongly or weakly
• interacting (or in between)
• SIMPzillas ruled out
• by direct detection experiments
• WIMPzillas extremely hard
• to detect - due to high mass,
• rates suppressed by many orders
• of magnitude

EDELWEISS
IceCube
CDMS
CDMS Soudan
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More particle physics candidates

• Popular extensions of the Standard Model of
  particle physics
• Supersymmetry complete symmetry between fermions
  - bosons
• provides excellent
  dark matter candidate neutralino
• Extra dimensions particles and fields of the SM
  can propagate in extra spatial
• dimensions
• the lightest
  Kaluza-Klein particle (first excitation of the
  particles
• of the SM) is viable
  dark matter candidate

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Supersymmetry (1)

• When promoted from a global to a local symmetry
  (SUGRA) it leads to a theory with general
  coordinate invariance - promise of unifying
  gravity with the other forces
• Stabilizes the hierarchy problem weak scale (300
  GeV) . GUT scale (1014GeV). Planck scale (1019
  GeV) radiative corrections to the masses of
  scalar particles are quadratically divergent, but
  in SUSY the corrections due to fermions and
  bosons cancel, thereby stabilizing existing mass
  hierarchies
• promises unification of gauge couplings at GUT
  scale
• Super-partners arent know - SUSY must be
  spontaneously broken and spartners 100 GeV
• MSSM 6 spin-0 squarks, 6 spin-0 sleptons, 12
  spin-1/2 gauginos, 4 spin-1/2 higgsinos, 1
  spin-3/2 gravitino (masses weak scale)
• Because of the global symmetry (R parity) the LSP
  (neutralino) must be stable
• To stabilize the weak scale SUSY must be unbroken
  down to an energy scale weak scale, thus
  sparticle masses are expected to be comparable to
  the weak scale

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Supersymmetry (2)
Indirect empirical evidence for SUSY the
strengths of the different gauge interactions
measured at LEP at low energies are consistent
with unification at high energies if there are
low-mass supersymmetric particles
Unification of gauge coupling at a GUT scale
MGUT 1016 GeV a second hint LEP
low-energy data are fitted well by the Standard
Model if there is a light Higgs boson with mass 200 GeV, consistent with the range mh 130 GeV
predicted by supersymmetry
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Supersymmetry (3)
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Supersymmetry (4)
SUSY
Standard Model
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Supersymmetry (5)

• To prevent rapid proton decay, conservation of
  R-parity
• R (-1) 3BL2S
• R 1 for SM particles
• R - 1 for SUSY particles
• Sparticles can only decay into an odd number of
  sparticles (SM particles).
• The lightest sparticle (LSP) is stable and is an
  excellent dark matter candidate!
• LSP sneutrino, gravitino, axino, neutralino

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The lightest SUSY particle

• Sneutrinos cosmological interesting if mass
  region 550 GeV - 2300 GeV
• But scattering cross section is much larger than
  the limits found by direct detection
• experiments!
• Gravitinos superpartner of the graviton only
  gravitational interactions, very difficult to
• observe. Also, can pose problems for cosmology
  (overproduction in the early Universe
• destroy abundance of primordial light elements in
  some scenarios)
• Axinos superpartner of the axion,
  phenomenological similar to gravitino
• Neutralinos by far the best studied DM
  candidate we will discuss in detail

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The lightest neutralino (1)

• The superpartners of the B, W3 gauge bosons (or
  the photon and the Z boson) and
• the neutral Higgs bosons H10 and H20, are called
  binos (B), winos (W3) and
• Higgsinos (H10 and H20). These mix into 4
  Majorana fermionic eigenstatesneutralinos.
• The neutralino mass matrix
• tanb ratio of vev of higgs bosons, qw
  weinberg angle, M1, M2 bino and wino mass
• parameters
• lightest neutralinos linear combination

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The lightest neutralino (2)

• The neutralino interactions most relevant for
  dark matter searches are
• self annihilation
• elastic scattering of nucleons
• Neutralinos are expected to be extremely NR in
  the present epoch, so one can keep only the a
  term in the expansion in the annihilation cross
  section
• sv a bv2 O(v4)
• At low velocities, the leading channels for
  neutralino annihilations to
• fermion-antifermion pairs
• gauge boson pairs
• final states containing the Higgs boson

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SUSY models (1)

• MSSM although relatively simple, more than 100
  free parameters!
• For practical studies, number of free parameters
  is reduced by (theoretically well
• motivated) assumptions.
• In general, 2 philosophies
• set boundary conditions at GUT scale, run the RGE
  down to the weak scale
• phenomenological MSSM fix the parameters at
  the weak scale, no strong theoretical
  justifications for the constraints

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SUSY models (2)

• mSUGRA phenomenological model based on series of
  theoretical assumptions, namely MSSM parameters
  obey a set of boundary conditions at the GUT
  scale
• Gauge coupling unification
• a1(MU) a2(MU) a3(MU) aU
• Unification of the gaugino masses
• M1(U) M2(U) M3(U) m1/2
• Universal scalar masses
• sfermion and higgs boson masses m0
• Universal trilinear coupling
• Au(U) Ad(U) Al(U) A0
• 5 free parameters tanb, , m1/2, m0, A0 and
  sign(m) (m higgsino mass parameter)

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SUSY models (3)

• mSUGRA phenomenological model based on series of
  theoretical assumptions,
• namely MSSM parameters obey a set of boundary
  conditions at the GUT scale

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SUSY models (4)

• Universal scalar mass versus universal gaugino
  mass
• Light blue allowed region for 0.1 ?ch2 0.3
• Dark blue allowed region for 0.094 ?ch2
  0.123

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Constraints on SUSY parameter space (1)
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Constraints on SUSY parameter space (2)

• COLLIDERS
• Searches for charged particles at LEP2 upper
  limits on chargino and slepton masses
• mcharginos 103 GeV
• msleptons 87 - 99 GeV
• (if chargino mass unification assumed mc 50
  GeV
• Searches for colored particles squarks and
  gluinos typical limit from Tevatron 200 GeV
• (leads to exclusion contours in the squark and
  gluino mass plane)
• Higgs searches current bound from LEP2 mh GeV, SUSY predicts mh
• b - sg decay (contribution from SUSY to SM can
  be substantial), CLEO, BELLE compatible with SM
• Bs - mm- (BR small in SM, SUSY tan6b),
  Tevatron run I consistent with SM
• gm-2 measurement E821 at BNL reports a
  measurement of the muon anomalous magnetic moment
• which is 3s away from the SM prediction
  (contribution could be due to SUSY!)
• COSMOLOGY (WMAP)

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Constraints on SUSY parameter space (3)
mSUGRA model Brown region LSP is a
selectron, thus not a viable DM candidate Green
region excluded by b - sg constraint Long
blue region provides a relic density of 0.1
?h2 0.3 Pink region 2s range for gm-2 (dashed
curves 1s bound)
Limit on Higgs mass from LEP2
Limit on chargino mass from LEP2
99 GeV selectron mass contour from LEP2