On the direct detection of supersymmetric Dark Matter

1
On the direct detection of supersymmetric Dark
Matter-

• Exploiting the signatures of the neutralino
  interaction
• J.D. Vergados
• University of Ioannina, Greece

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EVIDENCE FOR THE EXISTENCE OF DARK MATTER

• Gravitational effects around galaxies
• Cosmological Observations

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I. The Rotational Velocities (?2 does not fall as
1/r outside the galaxies)
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II Cosmological Evidence
for dark matter

• The 3 main reasons for the Big Bang Scenario
• The receding of Galaxies (red shift) (Hubble
  1929)
• The Microwave Background Radiation (CMBR Penzias
  and Wilson 1964)
• The Big Bang Nucleosynthesis (BBN, 1946)
• All bear a signature of dark matter
• (BBN also gave the first argument for CMBR, but
  nobody paid any attention)

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IIaBig Bang Nucleosynthesis (BBN) (Gamow 1946
Bethe (1948)

• Hydrogen is dominant in the Universe
• A fraction of only 25 is He and much less in the
  form of heavier elements (sensitive to n/p ratio)
• Via nuclear fusion the primordial hydrogen is
  transformed into heavier elements
• light (26.731MeV)
• The stars, however, are too young to have formed
  so much He.
• This much He must have been produced
  primordially, i.e. when the Universe was quite
  young (3 min old) and its temperature as high as
  that in the star interiors.

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IIa. Relative abundance

• Relative
• (with respect
• hydrogen)
• abundance
• of some
• elements
• vs the baryon
• density
• The critical
• density is
• 20 times larger
• From BBN
• D/H(2-5)x10-5
• From WMAP
• D/H2.5x10-5
• (see next slide)

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Relative abundance of elements in BBN

• The relative
• (With respect
• To hydrogen)
• abundance
• of elements
• BBN (left)
• D/H(2-5)x10-5
• WMAP (right)
• D/H2.5x10-5
• Notice the
• Ratio with
• Respect
• To the
• Critical
• Density

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IIb Cosmic Microwave Background Radiation (CMBR)
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Anisotropy in CMBR (continued) COBE 1982 (top)
and WMAP 2003 (bottom) with different resolution
Explanation of colors
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Anisotropy in the CMBR (cont.)
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IIc Light curves dL vs red shift z
(Generalization of Hubbles Law to Large
Distances)

• Upper continuous
• Middle continuous
• Lower continuous
• Dashed-
• Non accelerating
• universe

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Slicing the Pie of the Cosmos
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What is the nature of dark matter?

• It is not known. However
• It possesses gravitational interactions (from
  the rotation curves)
• No other long range interaction is allowed.
  Otherwise it would have formed atoms and ,
  hence, stars etc. So
• It is electrically neutral
• It does not interact strongly (if it did, it
  should have already been detected)
• It may (hopefully) posses some very weak
  interaction
• This will depend on the assumed theory
• Such an interaction may be exploited for its
  direct detection
• The smallness of the strength of such an
  interaction makes its direct detection extremely
  difficult.

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DARK MATTER CANDIDATES

• The axion 10-6 eVltma lt10-3 eV
• The neutrino It is rejected. It is not cold, not
  CDM.
• Supersymmetric particles.
• Three possibilities
• i) s-?et???? Excluded on the basis of results
  of underground experiments and accelerator
  experiments (LEP)
• ii) Gravitino Not directly detectable
• iii) ?xino Not directly detectable
• iv) A Majorana fermion, the neutralino or LSP
  
• (The lightest supersymmetric particle) A
  linear
• combination of the 2 neutral gauginos and
  the 2
• neutral Higgsinos. OUR CANDIDATE!

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The kinematics of the LSP-nucleus collision
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Conversion of the energy of the recoiling nucleus
into light, heat, ionization etc.

• The neutralino (LSP) is non relativistic.
• With few exceptions, it cannot excite the
  nucleus. It only scatters off elastically
• Measuring the energy of the recoiling nucleus is
  extremely hard
• -Low event rate (much less than 30 per Kg of
  target per year are expected).
• -Bothersome backgrounds (the signal is not
  very characteristic).
• -Threshold effects.

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Novel approaches Exploitation of other
signatures of the reaction

• The modulation effect The seasonal dependence
  of the rate due to the motion of the Earth.
• The excitation of the nucleus (in some rare cases
  that this is realistic) and detection of the
  subsequently emitted de-excitation ? rays.
• Asymmetry measurements in directional
  experiments (the direction of the recoiling
  nucleus must also be measured).
• Detection of other particles (electrons,
  X-rays), produced during the LSP-nucleus collision

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Some experimental considerations
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The SUSY INPUT

• Allowed parameter space Univerality at GUT
  scale - One mass m0
  for the scalars
  -One mass
  m1/2 for the fermions
  -Tanß, the ratio of vacuum
  expectation values of the
• Higss Hu ,Hd , i.e. ltvugt/ ltvdgt
  
  -The cubic coupling A0 (or mt)
  -The sign of µ, in µHu Hd
• Constrain These parameters are constrained via
  the renormalization group equation from the
  observable low energy quantities (all related to
  the above five parameters).
• (see, e.g., Ellis, Arnowitt, Nath, Bottino,
  Lazarides and collaborators)

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From the quark level to the nucleon level
(coherent)
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Spin Contribution ? Axial Current

• Going from quark to the nucleon level for the
  isovector component is standard (as in weak
  interactions)
  f1A (q) ? f1A gA f1A (q) , gA 1.24
• For the isoscalar this is not trivial. The naïve
  quark model fails badly (the proton spin crisis)
  f0A (q)
  ? f0A g0A f0A (q) , g0A 0.1

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The Differential cross section at the nuclear
level.

• ? is the neutralino velocity and u stands
  essentially for the energy transfer Q
• uQ/Q0 , Q040A-4/3 MeV
• F(u) The nuclear form factor
• F11 (u) The isovector spin response function

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Expressions for the nuclear cross section
(continued)

• With
• SSsps(µr/mp)2A2 (scalar
  interaction)
• sps is the scalar proton-LSP cross section
• µr is the LSP-nucleus reduced mass
• A is the nuclear mass
• SSpin is the expression for the spin induced
• cross section (to be discussed later).

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LSP Velocity Distributions

• Conventional
• Maxwell-Boltzmann (symmetric or axially
  symmetric) with characteristic velocity equal to
  the suns velocity around the galaxy, v0 220
  km/s, and escape velocity
• vesc 2.84v0 put in by hand.
• Other isothermal models employing Eddingtons
  theory
• ?(r)?F(r) ? f(r,v) (JDV-Owen)
• Non-thermal models
• Caustic rings (Sikivie , JDV), wimps in bound
  orbits etc
• Sgr Dwarf galaxy, anisotropic flux, (Green
  Spooner)

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The event rate for the coherent mode

• Can be cast in the form
• Where
• ?(0) the local neutralino density0.3
  GeV/cm3.
• sSp,? the neutralino-nucleon cross section.
  It can be extracted from
• the data once fcoh (A,m?) , which will be
  plotted below, is known.

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The factor fcoh(A,m?) for A127 (I) vs the LSP
mass (The dashed for threshold 10keV)
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The factor fcoh(A,m?) for A19 (F)(The Dashed
for threshold 10keV)
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Current Limits on coherent proton cross section
(astro-ph/0509259)
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A typical Scatter Plot (Universal set of
parameters) (Ceredeno, Gabrielli, Gomez and Munoz)
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A Scatter Plot (Non Universal) (Ceredeno,
Gabrielli, Gomez and Munoz)
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The event rate due to the spin

• Where f0A apan (isoscalar) and f1A ap-an
  (isovector) couplings at the nucleon level and
  O0(0), O1(0) the corresponding static spin matrix
  elements
• The event rate is cast in the form

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The factor fspin(A,m?) for A127 (I)(The Dashed
for threshold 10keV)
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The factor fspin(A,m?) for A19 (F)(The Dashed
for threshold 10keV)
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The constrained amplitude plane (ap,?,an,?) for
the ?127 system (arbitrary units), when they are
relatively real.
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The constrained (ap,?,an,?) plane relative phase
of the amplitudes dp/6 (-), dp/3 (-)and dp/2
(-)
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The constrained (sp,?,sn,?) plane for the ?127
system (arbitrary units). Under the curve on the
left, if the amplitudes have the same sign and
between the curves on the right for opposite sign.
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The constrained (sp,?,sn,?) plane relative phase
of amplitudes dp/6 (-), dp/3 (-)and dp/2 (-)
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THE MODULATION EFFECT vJune23515250km/s
vDec235-15220km/s
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THE MODULATION EFFECT(continued)

• aphase of the Earth
• (a0 around June 3nd)
• ?p/3 is the angle between the axis of gala?y
  and the axis of the ecliptic.
• hmodulation amplitude.
• R0 average rate.

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The Modulation Amplitude h for I On the left
zero energy cut off. On the right a cut off of
10keV
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The directional event rate

• The event rate in directional experiments is
• Rdir(?/2p)R01cos(a-amp)
• R0 is the average usual (non-dir) rate
• a the phase of the Earth (as usual)
• a m is the shift in the phase of the Earth (it
  depends on µr and the direction of observation)
• ?/2p is the reduction factor (it depends on µr
  and the direction of observation)
• ? and am depend only slightly on SUSY

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The event rate vs the polar angle(A19, left)
, (A127, right) for m?100 GeV and M-B
distribution
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The parameter ? vs the LSP massperpendicular to
the suns velocity (left) and opposite to it
(right)
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The modulation vs the LSP mass perpendicular to
the suns velocity (left) and opposite to it
(right)
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BR for transitions to the first excited state at
50 keV for I vs LSP mass (Ejiri Quentin,
Strottman and JDV) Note quenching of recoil
ignored
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The relative differential Rate, (dRe/dTe
)/Rrecoil, vs the electron energy T for electron
production in LSP-nucleus (Moustakides, Ejiri,
JDV).
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The Relative (with respect to recoil) rate of
ionization per electron vs a) Ethreshold for m?
100Gev (left) and b) m? for Ethreshold 0.2 keV
(right)
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But, there are Z electrons in an atom!
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Detection of hard X-rays

• After the ionization there is a probability for a
  K or L hole
• This hole de-excites via emitting X-rays or Auger
  electrons.
• Indicating with bnl the fluorecence ratio
  (determined experimentally)
• the fraction of X-rays per recoil is
• sX(nl) /sr bnl(snl/sr) with snl/sr the
  relative
• ionization rate discussed above

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Relative rate for inner electron hole production
in the case of 132Xe.

• nl enl(keV) (snl/sr)L (snl/sr)M (snl/sr)H
• is 34.56 0.034 0.221
  0.255
• 2s 5.45 1.211 1.461 1.463
  
• 2p 4.89 3.796 4.506 4.513
• WIMP masses indicated by subscript
• L?30GeV, M?100GeV, H?300GeV

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Detection of hard X-rays (events relative to
recoil) (continued)

• The interesting quantity is
• (sK (Kij)/sr)(s1s/sr) b1s B(Kij)
• Where
• bnlFluorecence ratio, Kij K-ij branch

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The K Xray rates in WIMP interactions in 132 Xe
for masses L?30GeV, M?100GeV, H?300GeV
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Conclusions Experimental ambitions
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Projected exclusion curve for scalar detectors
2003 Edelweiss and CDMS projections
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Projected exclusion curve for 3He detector
Background 0.01 day-1 Energy threshold 1
keV
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CONCLUSIONS-Standard Rates (theory)

• Most of the uncertainties come the fact that the
  allowed SUSY parameter space has not been
  sufficiently sharpened.
• The other uncertainties (nuclear form factor,
  structure of the nucleon, quenching factor,
  energy threshold) could affect the results by an
  order of magnitude.
• Most of the parameter space yields undetectable
  rates.
• The coherent contribution due to the scalar
  interaction is the most dominant.

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CONCLUSIONS-Modulation (theory)

• The modulation amplitude h is small less than 2
  and depends on the LSP mass. Its sign is also
  uncertain for intermediate and heavy nuclei.
• It may increase as the energy cut off remains big
  (as in the DAMA experiment), but at the expense
  of the number of counts. The DAMA experiment
  maybe consistent with the other experiments, if
  the spin interaction dominates.

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CONCLUSIONS-Directional Rates

• Good signatures, but the experiments are hard
  (the DRIFT experiment cannot tell the sense of
  direction of recoil)
• Large asymmetries are predicted
• The rates are suppressed by a factor ?/2p, ?lt0.6
• For a given LSP velocity distribution, ? depends
  on the direction of observation
• In the most favored direction ? is approximately
  0.6
• In the plane perpendicular to the suns velocity
  ? is approximately equal to 0.2

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CONCLUSIONS- Modulation in Directional Experiments

• The Directional rates also exhibit modulation
• In the most favored direction of observation,
  opposite to the suns motion, the modulation is
  now twice as large. (Maximum in June, Minimum in
  December)
• In the plane perpendicular to the suns motion
  the modulation is much larger. The difference
  between the maximum and the minimum can be as
  high as 50. It also shows a direction
  characteristic pattern (for observation
  directions on the galactic plane the maximum may
  occur in September or March, while normal
  behavior for directions perpendicular to the
  galaxy)

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CONCLUSIONS-Transitions to excited states

• Transitions to excited states are possible in few
  odd A nuclei.
• When allowed, are kinematically suppressed
• The branching ratio depends on the structure of
  the nucleus and the LSP mass
• In the case of Iodine, a popular target for
  recoils, it can be as high as 7 for LSP mass
  higher than 200 GeV

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CONCLUSIONS Electron production during
LSP-nucleus collisions

• During the neutralino-nucleus collisions,
  electrons may be kicked off the atom
• Electrons can be identified easier than nuclear
  recoils (Low threshold 0.25keV TPC detectors)
• The branching ratio for this process depends on
  the threshold energies and the LSP mass.
• For a threshold energy of 0.25 keV the ionization
  event rate in the case of a heavy target can
  exceed the rate for recoils by an order of 10.
• Detection of hard X-rays also seams feasible

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• THE END

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The Expanding Universe (Big Bang)

• IMPORTANT STEPS
• General Theory of Relativity (Einstein 1917)
• The Universe is finite
  with a finite past
• The Receding galaxies (Hubble 1929, 1932)
• The Big-bang theory (Gamow 1945)
• The discovery of Cosmic Microwave Background
  Radiation, CMBR, (Penzias and Wilson, 1964)
• The inflationary scenario (Guth 1990)
• The Cosmic Candle (supernova Ia)
• The discovery of anisotropies in CMBR (COBE 1992,
  WMAP 2003)

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Hubbles Law ?Ha

• Classically or Isotropic and Homogeneous
  Universe
• ?Ha (?velocity, adistance)
• ? is measured from red shift
• (it appears in special as well as general
  theory of relativity)
• 1z(?obs /?)
• The largest z measured is Z5.6 (HDF-5730)
• ?1216 (ultraviolet) becomes ? 8025
  (infrared)
• The distance a is measured with candles

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Prototype Cosmic Candles

• L Absolute Luminosity (emitted power)
• ? Relative Luminosity
• (Power per unit area of detector)
• That is Knowledge of L and Measurement of ?
• Determine the optical
  depth" D
• L depends on the physics governing the emitting
  source.

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Supernovae Ia

• A Double Star, one of which is a white Dwarf
• The white Dwarf is eating up the mass of the
  companion star
• When its mass is reaching the Shandrasheckar
  limit
• an explosion takes place
• One knows that it is a supernova Ia from the
  light curve and the color type

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The cycle of a large mass star SourceImagine the
Universe, NASA
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A white Dwarf is eating up the mass of a red giant
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The deepest picture of the sky (12 billion years
ago! Almost protogalaxies)
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Experimental verification of ?Ha Hubbles Law
(H0) -1 1010h -1 yrH0100h (km/s/Mpc),
0.6lthlt0.8
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The Quenching Factor
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Empirical Quenching Factor
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3He-? cross-section
For AX nucleus

• SI cross-section ?SI(AX) ? ?SI(p)A4
• SD cross-section ?SD(AX) ? ?SD(p)A2
• For 3He ?SD ? ?SI ? only ?SD considered

• ?(3He) ? mr2 (J1)/J (apltSpgtanltSngt)2
• with 3He spin content ltSpgt-0.05
• ltSngt0.49
• ? scattering on the unpaired neutron