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### On the direct Searching for Cold Dark Matter-

Exploiting the signatures of the WIMP interaction

J.D. Vergados

University of Ioannina, Greece

HEP2006 Ioannina 13/04/2006

EVIDENCE FOR THE EXISTENCE OF DARK MATTER

- Gravitational effects around galaxies
- Cosmological Observations

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I. The Rotational Velocities (υ2 does not fall as 1/r outside the galaxies)

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Cosmological Constraints in the (Ω,Λ) Plane

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Slicing the Pie of the CosmosWMAP3:ΩCDM =0.24±0.02,ΩΛ=0.72±0.04, Ωb =0.042±0.003WMAP1: As follows:

HEP2006 Ioannina 13/04/2006

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 iselectrically 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.

HEP2006 Ioannina 13/04/2006

DARK MATTER CANDIDATES

- The axion:10-6 eV<ma <10-3 eV
- The neutrino: It is not dominant. It is not cold, not CDM.
- Supersymmetric particles.

Three possibilities:

i) s-νετρίνο: Excluded on the basis of results of underground experiments and accelerator experiments(LEP)

ii) Gravitino: Not directly detectable

iii) Αxino: Not directly detectable

iv)AMajorana fermion, the neutralino orLSP

(The lightest supersymmetric particle): A linear

combination of the2 neutral gauginos and the 2

neutral Higgsinos. MOST FAVORITE CANDIDATE!

- Particles from theories in extra dimensions (Kaluza-Klein WIMPS)

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A. SUSY MODELS WITH R-PARITY: The neutralino χ

- Standard model particles have R-parity=1
- All SUSY particles have R-parity -1
- Lightest SUSY particle absolutely stable
- A linear combination of the 4 neutral fermions (two gauginos and two Higgsinos) i.e.

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A1. SUSY MODELS: The neutralino(Z-exchange Axial current)

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A2. SUSY MODELS: The neutralino(squark-exchange Axial +scalar)

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A3. SUSY MODELS: The neutralino(Higgs-exchangeScalar coherent cross section)

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B. Universal Extra Dimension Theories

- Kaluza-Klein Theories: A tower of new particles
- Postulate a discreet symmetry: K-K parity
- The even modes (ordinaryparticles) have K-K parity +1
- The odd modes (exotic) have K-K parity -1
- The lightest odd mode is absolutely stable
- The interactions of the new particles are the same with those of SM
- Only the particle’s mass is unknown parameter

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B1 Kaluza-Klein theoriesThe lightest particle is the brother of the B boson, the B(1).K-K quark exchange.

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B1 K-K theories WIMP: B(1). K-K q(1) exchange. (with Moustakides and Oikonomou)

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B1. Kaluza-Klein theories (cont.)The lightest particle is the B(1).Higgs-Exchange.

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B1. Kaluza-Klein theories (cont.)WIMP is the B(1).Higgs-Exchange.

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B1. Kaluza-Klein theories (cont.)WIMP is the B(1). Δ=0.05. mh invisibleσp on the left, σn on the right.

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B1. Kaluza-Klein theories (cont.)WIMP is the B(1). Δ=0.8mh 100-200 GeVσp on the left, σn on the right.

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B2. Kaluza-Klein theories The lightest particle is the brother of neutrino, the ν(1).Ζ-Exchange & Higgs Exchange.

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B2 WIMP is the ν(1).Ζ-Exchange Dominates.

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B2. Kaluza-Klein theories WIMP is the ν(1).Ζ(1) -Exchange

- ν(1)->νconversion!

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B2.ν(1)->νconversionExotic! Energy transfer: About half the mass of the WIMP!Could observations have missed it?

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Nuclear Recoil after the LSP-nucleus collision ( Elastic for SUSY WIMPS)

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Conversion of the energy of the recoiling nucleus into detectable form (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.

-Quenching factors.

HEP2006 Ioannina 13/04/2006

Novel approaches: Exploitation ofother signatures of the reaction

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

HEP2006 Ioannina 13/04/2006

The SUSY INPUT

- Allowed parameter space: Universality at GUT scale: - One mass m0for the scalars-One mass m1/2 for the fermions -Tanβ, the ratio of vacuum expectation values of the

Higss Hu ,Hd ,i.e. <vu>/ <vd> -The cubic coupling A0 (or mt) -The sign of μ, in μHu Hd

- These parameters are constrained via the renormalization group equations 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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The Differential cross section at the nuclear level.

- υ is the neutralino velocity and u stands essentially for the energy transfer Q:
- u=Q/Q0 , Q0=40A-4/3MeV
- 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

- ΣS=σps(μr/mp)2A2 (scalar interaction)
- σps is the scalar proton-LSP cross section
- μr isthe LSP-nucleus reduced mass
- A is the nuclear mass
- ΣSpin is the expression for the spin induced

cross section (to be discussed later).

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LSP Velocity Distributions

- Conventional: Isothermal models
- (1) Maxwell-Boltzmann (symmetric or axially symmetric) with characteristic velocity equal to the sun’s velocity around the galaxy, v0 =220 km/s, and escape velocity

vesc =2.84v0 put in by hand.

- (2)Modification of M-B characteristic velocity: nv0 , n>>1

(Tetradis and JDV )

- Adiabatic models employingEddington’s theory:

ρ(r)Φ(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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Theevent ratefor the coherent mode

- Can be cast in the form:
- Where:

ρ(0):the local neutralino density≈0.3 GeV/cm3.

σSp,χ: the neutralino-nucleon cross section. It can be extracted from

the data once fcoh (A,mχ), which will be plotted below, is known.

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The factorfcoh(A,mχ) for A=127 (I) vs the LSP mass(The dashed for threshold 10keV)

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The factorfcoh(A,mχ) for A=19 (F)(The Dashed for threshold 10keV)

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Current Limits on coherent proton cross section (astro-ph/0509259)

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THE MODULATION EFFECTvJune=235+15=250km/svDec=235-15=220km/s

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THEMODULATION EFFECT*(continued)

- α=phase of the Earth

(α=0 around June 3nd)

- γ=π/3 is the angle between the axis of galaχy and the axis of the ecliptic.
- h=modulation amplitude.
- R0 =average rate.
- * with N. Tetradis (calculations with non standard M-B)

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TheModulation Amplitudeh for 127IQth=0, Isothermal model (M-B),On theleft n=1, on the right n=3

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TheModulation Amplitudeh for 127IQth=10keV, Isothermal model (M-B),On theleft n=1, on the right n=3

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TheModulation Amplitudeh for 127IQth=0thick, Qth=5keVfine Qth=10dash; Eddington Theory

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BR for transitions to thefirst excited stateat 50 keV for Ivs LSP mass (Ejiri; Quentin, Strottman and JDV) Note: quenching of recoil ignored

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The Relative (with respect to recoil) rate of ionization per electron vs: a) Ethreshold for mχ =100Gev (left)and b) mχ for Ethreshold = 0.2 keV (right)

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But, there are Z electrons in an atom!

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Detection ofhard 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 bnℓthe fluorecence ratio (determined experimentally)
- the fraction of X-rays per recoil is:

σX(nℓ) /σr = bnl(σnℓ/σr) with σnℓ/σr the relative

ionization rate to be discussed next

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Relative rate forinner electron hole productionin the case of 132Xe.

- nℓεnℓ(keV) (σnℓ/σr)L (σnℓ/σr)M (σnℓ/σr)H
- is34.560.0340.2210.255
- 2s 5.45 1.2111.4611.463
- 2p 4.89 3.796 4.506 4.513
- WIMP masses indicated by subscript:

L30GeV, M100GeV, H300GeV

HEP2006 Ioannina 13/04/2006

The K Xray rates in WIMP interactions in 132 Xe for masses: L30GeV, M100GeV, H300GeV

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Conclusions: Experimental ambitions for Recoils

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CONCLUSIONS A: K-K WIMPS

- Theoretical advantages: Only the masses are unknown parameters
- Experimental advantages: The WIMP energy is an order of magnitude bigger

The energy transfer to the nucleus is in the MeV region. WIMPS need not be detected via the hard recoil measurements. One can excite the nucleus

- Limits K-K Nucleon cross sectionscan be extracted fromcurrent limits via:
- σ(K-K)(coh) ≈10(-6)pb[m(K-K)/200GeV](1/2)
- σ(K-K)(spin) ≈10(-2)pb[m(K-K)/200GeV](1/2)

HEP2006 Ioannina 13/04/2006

CONCLUSIONS- SUSY WIMPS 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.

HEP2006 Ioannina 13/04/2006

CONCLUSIONS-Modulation (theory)

- The modulation amplitude h is small less than 2% and depends on the LSP mass.
- It crucially depends on the velocity distribution
- 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.

HEP2006 Ioannina 13/04/2006

CONCLUSIONS-Transitions to excited states

- For neutralino 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
- * For K-K WIMPS it is quite easy

HEP2006 Ioannina 13/04/2006

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

HEP2006 Ioannina 13/04/2006

THE END

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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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Anisotropy in the CMBR (cont.)

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IIc: Light curves : dL vs red shift z (Generalization of Hubble’s Law to Large Distances)

- Upper continuous
- Middle continuous
- Lower continuous
- Dashed-

Non accelerating

universe

HEP2006 Ioannina 13/04/2006

B1 Kaluza-Klein theories WIMP:B(1)K-K q(1)exchange-The axial current.

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B2 WIMP isthe ν(1).(continued)Ζ-Exchange Dominates.

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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 =gAf1A (q) , gA =1.24
- For the isoscalar this is not trivial. The naïve quark model fails badly (the proton spin crisis) f0A (q) f0A =g0Af0A (q) , g0A=0.1

HEP2006 Ioannina 13/04/2006

The relative differential Rate, (dRe/dTe )/Rrecoil, vs the electron energyT for electron production in LSP-nucleus (Moustakidis, Ejiri, JDV).

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

- The interesting quantity is:
- (σK (Kij)/σr)=(σ1s/σr)b1s B(Kij)
- Where:
- bnℓ=Fluorecence ratio, Kij =K-ij branch

HEP2006 Ioannina 13/04/2006

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 κ/2π, κ<0.6
- For a given LSP velocity distribution, κ depends on the direction of observation
- In the most favored direction κ is approximately 0.6
- In the plane perpendicular to the sun’s velocity κ is approximately equal to 0.2

HEP2006 Ioannina 13/04/2006

CONCLUSIONS- Modulation in Directional Experiments

- The Directional rates also exhibit modulation
- In the most favored direction of observation, opposite to the sun’s motion, the modulation is now twice as large. (Maximum in June, Minimum in December)
- In the plane perpendicular to the sun’s 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)

HEP2006 Ioannina 13/04/2006

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

- Wheref0A=ap+an(isoscalar) and f1A=ap-an(isovector) couplings at the nucleon level and Ω0(0), Ω1(0)the corresponding static spin matrix elements
- The event rate is cast in the form:

HEP2006 Ioannina 13/04/2006

The factorfspin(A,mχ) for A=127 (I)(The Dashed for threshold 10keV)

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The factorfspin(A,mχ) for A=19 (F)(The Dashed for threshold 10keV)

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The constrained amplitude plane(ap,χ,an,χ) for theΑ=127 system(arbitrary units), when they are relatively real.

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The constrained (ap,χ,an,χ) plane: relative phase of the amplitudes δ=π/6 (-), δ=π/3 (-)and δ=π/2 (-)

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The constrained(σp,χ,σn,χ) plane for the Α=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.

HEP2006 Ioannina 13/04/2006

The constrained (σp,χ,σn,χ)plane: relative phase of amplitudes δ=π/6 (-), δ=π/3 (-)and δ=π/2 (-)

HEP2006 Ioannina 13/04/2006

The directional event rate

- The event rate in directional experiments is:

Rdir=(κ/2π)R0[1+cos(α-αmπ)]

- R0is the average usual (non-dir) rate
- α the phase of the Earth (as usual)
- α m is the shift in the phase of the Earth (it depends on μrand the direction of observation)
- κ/2π is the reduction factor (it depends on μrand the direction of observation)
- κ and αm depend only slightly on SUSY

HEP2006 Ioannina 13/04/2006

The event rate vs the polar angle(A=19, left) , (A=127, right) for mχ=100 GeV and M-B distribution

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The parameter κ vs the LSP mass:perpendicular to the sun’s velocity (left) and opposite to it (right)

HEP2006 Ioannina 13/04/2006

The modulation vs the LSP mass:perpendicular to the sun’s velocity (left) and opposite to it (right)

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IIa:Big 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.

HEP2006 Ioannina 13/04/2006

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)

HEP2006 Ioannina 13/04/2006

Hubble’s Law: υ=Ha

- Classically or Isotropic and Homogeneous Universe:

υ=Ha (υ=velocity, a=distance)

- υ is measured from red shift

(it appears in special as well as general theory of relativity)

- 1+z=(λobs/λ)

The largest z measured is: Z=5.6 (HDF-5730)

λ=1216 (ultraviolet) becomes λ= 8025 (infrared)

- The distance a is measured with “candles”

HEP2006 Ioannina 13/04/2006

Prototype Cosmic Candles

L= Absolute Luminosity (emitted power)

Ι=Relative Luminosity

(Power per unit area of detector)

That is Knowledge ofLandMeasurement of Ι

Determine the “optical depth" D

Ldepends on the physics governing the emitting source.

HEP2006 Ioannina 13/04/2006

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

HEP2006 Ioannina 13/04/2006

The cycle of a large mass star Source:Imagine 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 υ=HaHubble’s Law: (H0) -1= 1010h-1 yr;H0=100h (km/s/Mpc), 0.6<h<0.8

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IIb: Cosmic Microwave Background Radiation (CMBR)

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The Quenching Factor

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Some experimental considerations

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Empirical Quenching Factor

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The Modulation Amplitudeh for I On the left zero energy cut off. On the right a cut off of 10keV

HEP2006 Ioannina 13/04/2006

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 (J+1)/J (ap<Sp>+an<Sn>)2

with 3He spin content: <Sp>=-0.05

<Sn>=0.49

scattering on the unpaired neutron

HEP2006 Ioannina 13/04/2006

for scalar detectors

2003 Edelweiss and

CDMS projections

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ELEGANT V NaI

UKDMC NaI

NAIAD projection

Projected exclusion curve for 3He detector

Background

= 0.01 day-1

Energy

threshold

= 1 keV

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Three years later!SDSS DR4:Sloan Digital Sky Survey Data Rlease 4

HEP2006 Ioannina 13/04/2006

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