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On the direct detection of supersymmetric Dark Matter-: 

On the direct detection of supersymmetric Dark Matter- Exploiting the signatures of the neutralino interaction J.D. Vergados University of Ioannina, Greece

EVIDENCE FOR THE EXISTENCE OF DARK MATTER: 

EVIDENCE FOR THE EXISTENCE OF DARK MATTER Gravitational effects around galaxies Cosmological Observations

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

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

II: Cosmological Evidence for dark matter: 

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)

IIa:Big Bang Nucleosynthesis (BBN) (Gamow 1946 & Bethe (1948): 

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.

IIa. Relative abundance : 

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/H=2.5x10-5 (see next slide)

Relative abundance of elements in BBN: 

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/H=2.5x10-5 Notice the Ratio with Respect To the Critical Density

IIb: Cosmic Microwave Background Radiation (CMBR): 

IIb: Cosmic Microwave Background Radiation (CMBR)

Anisotropy in CMBR (continued):  COBE 1982 (top) and WMAP 2003 (bottom) with different resolution: 

Anisotropy in CMBR (continued): COBE 1982 (top) and WMAP 2003 (bottom) with different resolution Explanation of colors

Anisotropy in the CMBR (cont.): 

Anisotropy in the CMBR (cont.)

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

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

Slicing the Pie of the Cosmos: 

Slicing the Pie of the Cosmos

What is the nature of dark matter? : 

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.

DARK MATTER CANDIDATES: 

DARK MATTER CANDIDATES The axion: 10-6 eV<ma <10-3 eV The neutrino: It is rejected. 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) 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!

The kinematics of the LSP-nucleus collision: 

The kinematics of the LSP-nucleus collision

Conversion of the energy of the recoiling nucleus into light, heat, ionization etc.: 

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. -Quenching factors.

Novel approaches: Exploitation of other signatures of the reaction: 

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 γ 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

Some experimental considerations: 

Some experimental considerations

The SUSY INPUT : 

The SUSY INPUT Allowed parameter space: Univerality at GUT scale: - One mass m0 for 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 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)

From the quark level to the nucleon level (coherent): 

From the quark level to the nucleon level (coherent)

Spin Contribution  Axial Current: 

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

The Differential cross section at the nuclear level.: 

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-4/3 MeV F(u): The nuclear form factor F11 (u): The isovector spin response function

Expressions for the nuclear cross section (continued): 

Expressions for the nuclear cross section (continued) With ΣS=σps(μr/mp)2A2 (scalar interaction) σps is the scalar proton-LSP cross section μr is the LSP-nucleus reduced mass A is the nuclear mass ΣSpin is the expression for the spin induced cross section (to be discussed later).

LSP Velocity Distributions: 

LSP Velocity Distributions Conventional: 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. Other isothermal models employing Eddington’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)

The event rate for the coherent mode: 

The event rate for 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.

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

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

The factor fcoh(A,mχ) for A=19 (F)(The Dashed for threshold 10keV): 

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

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

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

A typical Scatter Plot (Universal set of parameters) (Ceredeno, Gabrielli, Gomez and Munoz): 

A typical Scatter Plot (Universal set of parameters) (Ceredeno, Gabrielli, Gomez and Munoz)

A Scatter Plot (Non Universal) (Ceredeno, Gabrielli, Gomez and Munoz): 

A Scatter Plot (Non Universal) (Ceredeno, Gabrielli, Gomez and Munoz)

The event rate due to the spin: 

The event rate due to the spin Where f0A= 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:

The factor fspin(A,mχ) for A=127 (I)(The Dashed for threshold 10keV): 

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

The factor fspin(A,mχ) for A=19 (F)(The Dashed for threshold 10keV): 

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

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

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

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

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

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.: 

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.

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

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

THE MODULATION EFFECT vJune=235+15=250km/s vDec=235-15=220km/s: 

THE MODULATION EFFECT vJune=235+15=250km/s vDec=235-15=220km/s

THE MODULATION EFFECT(continued): 

THE MODULATION 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.

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

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

The directional event rate: 

The directional event rate The event rate in directional experiments is: Rdir=(κ/2π)R0[1+cos(α-αmπ)] R0 is 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 μr and the direction of observation) κ/2π is the reduction factor (it depends on μr and the direction of observation) κ and αm depend only slightly on SUSY

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

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

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

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

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

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

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: 

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

The relative differential Rate, (dRe/dTe )/Rrecoil, vs the electron energy T for electron production in LSP-nucleus (Moustakides, Ejiri, JDV).: 

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

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): 

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)

But, there are Z electrons in an atom!: 

But, there are Z electrons in an atom!

Detection of hard X-rays: 

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: σX(nℓ) /σr = bnl(σnℓ/σr) with σnℓ/σr the relative ionization rate discussed above

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

Relative rate for inner electron hole production in the case of 132Xe. nℓ εnℓ(keV) (σnℓ/σr)L (σnℓ/σr)M (σnℓ/σr)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

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

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

The K Xray rates in WIMP interactions in 132 Xe for masses: L30GeV, M100GeV, H300GeV: 

The K Xray rates in WIMP interactions in 132 Xe for masses: L30GeV, M100GeV, H300GeV

Conclusions: Experimental ambitions: 

Conclusions: Experimental ambitions

Slide56: 

Projected exclusion curve for scalar detectors 2003 Edelweiss and CDMS projections

Slide57: 

Projected exclusion curve for 3He detector Background = 0.01 day-1 Energy threshold = 1 keV

CONCLUSIONS-Standard Rates (theory): 

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.

CONCLUSIONS-Modulation (theory): 

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.

CONCLUSIONS-Directional Rates: 

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

CONCLUSIONS- Modulation in Directional Experiments: 

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)

CONCLUSIONS-Transitions to excited states: 

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

CONCLUSIONS: Electron production during LSP-nucleus collisions: 

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

Slide64: 

THE END

The Expanding Universe (Big Bang): 

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)

Hubble’s Law: υ=Ha: 

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”

Prototype Cosmic Candles: 

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

Supernovae Ia: 

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

The cycle of a large mass star Source:Imagine the Universe, NASA: 

The cycle of a large mass star Source:Imagine the Universe, NASA

A white Dwarf is eating up the mass of a red giant: 

A white Dwarf is eating up the mass of a red giant

The deepest picture of the sky (12 billion years ago! Almost protogalaxies): 

The deepest picture of the sky (12 billion years ago! Almost protogalaxies)

Experimental verification of υ=Ha Hubble’s Law: (H0) -1= 1010h -1 yr;H0=100h (km/s/Mpc), 0.6<h<0.8: 

Experimental verification of υ=Ha Hubble’s Law: (H0) -1= 1010h -1 yr; H0=100h (km/s/Mpc), 0.6<h<0.8

The Quenching Factor: 

The Quenching Factor

Empirical Quenching Factor: 

Empirical Quenching Factor

Slide75: 

3He- cross-section SI cross-section : SI(AX)  SI(p)×A4 SD cross-section : SD(AX)  SD(p)×A2 For 3He : SD  SI  only SD considered For AX nucleus: (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