1 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
2 EVIDENCE FOR THE EXISTENCE OF DARK MATTERGravitational effects around galaxies Cosmological Observations HEP2006 Ioannina 13/04/2006
3 I. The Rotational Velocities (υ2 does not fall as 1/r outside the galaxies)HEP2006 Ioannina 13/04/2006
4 Cosmological Constraints in the (Ω,Λ) PlaneHEP2006 Ioannina 13/04/2006
5 Slicing the Pie of the Cosmos WMAP3: ΩCDM =0. 24±0. 02, ΩΛ =0. 72±0Slicing the Pie of the Cosmos WMAP3: ΩCDM =0.24±0.02, ΩΛ =0.72±0.04 , Ωb =0.042±0.003 WMAP1: As follows: HEP2006 Ioannina 13/04/2006
6 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. HEP2006 Ioannina 13/04/2006
7 DARK MATTER CANDIDATESThe axion: eV
8 A. SUSY MODELS WITH R-PARITY: The neutralino χStandard 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. HEP2006 Ioannina 13/04/2006
9 A1. SUSY MODELS: The neutralino (Z-exchange Axial current)HEP2006 Ioannina 13/04/2006
10 A2. SUSY MODELS: The neutralino (squark-exchange Axial +scalar)HEP2006 Ioannina 13/04/2006
11 A3. SUSY MODELS: The neutralino (Higgs-exchangeScalar coherent cross section)HEP2006 Ioannina 13/04/2006
12 B. Universal Extra Dimension TheoriesKaluza-Klein Theories: A tower of new particles Postulate a discreet symmetry: K-K parity The even modes (ordinary particles) 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 HEP2006 Ioannina 13/04/2006
13 B1 Kaluza-Klein theories The lightest particle is the brother of the B boson, the B(1). K-K quark exchange. HEP2006 Ioannina 13/04/2006
14 B1 K-K theories WIMP: B(1). K-K q(1) exchangeB1 K-K theories WIMP: B(1). K-K q(1) exchange. (with Moustakides and Oikonomou) HEP2006 Ioannina 13/04/2006
15 B1. Kaluza-Klein theories (cont. ) The lightest particle is the B(1)B1. Kaluza-Klein theories (cont.) The lightest particle is the B(1). Higgs-Exchange. HEP2006 Ioannina 13/04/2006
16 B1. Kaluza-Klein theories (cont.) WIMP is the B(1). Higgs-Exchange.HEP2006 Ioannina 13/04/2006
17 B1. Kaluza-Klein theories (cont. ) WIMP is the B(1). Δ=0. 05B1. Kaluza-Klein theories (cont.) WIMP is the B(1). Δ=0.05. mh invisible σp on the left, σn on the right. HEP2006 Ioannina 13/04/2006
18 B1. Kaluza-Klein theories (cont. ) WIMP is the B(1). Δ=0B1. Kaluza-Klein theories (cont.) WIMP is the B(1). Δ=0.8 mh GeV σp on the left, σn on the right. HEP2006 Ioannina 13/04/2006
19 B2. Kaluza-Klein theories The lightest particle is the brother of neutrino, the ν(1). Ζ-Exchange & Higgs Exchange. HEP2006 Ioannina 13/04/2006
20 B2 WIMP is the ν(1). Ζ-Exchange Dominates.HEP2006 Ioannina 13/04/2006
21 B2. Kaluza-Klein theories WIMP is the ν(1). Ζ(1) -Exchangeν(1)->ν conversion! HEP2006 Ioannina 13/04/2006
22 B2. ν(1)->ν conversion ExoticB2. ν(1)->ν conversion Exotic! Energy transfer: About half the mass of the WIMP! Could observations have missed it? HEP2006 Ioannina 13/04/2006
23 Nuclear Recoil after the LSP-nucleus collision ( Elastic for SUSY WIMPS)HEP2006 Ioannina 13/04/2006
24 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
25 Novel approaches: Exploitation of other signatures of the reactionThe 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 HEP2006 Ioannina 13/04/2006
26 The SUSY INPUT Allowed parameter space: Universality 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.
27 From the quark level to the nucleon level (coherent)HEP2006 Ioannina 13/04/2006
28 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 HEP2006 Ioannina 13/04/2006
29 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). HEP2006 Ioannina 13/04/2006
30 LSP Velocity DistributionsConventional: 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 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) HEP2006 Ioannina 13/04/2006
31 The event rate for the coherent modeCan 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. HEP2006 Ioannina 13/04/2006
32 The factor fcoh(A,mχ) for A=127 (I) vs the LSP mass (The dashed for threshold 10keV)HEP2006 Ioannina 13/04/2006
33 The factor fcoh(A,mχ) for A=19 (F) (The Dashed for threshold 10keV)HEP2006 Ioannina 13/04/2006
34 Current Limits on coherent proton cross section (astro-ph/0509259)HEP2006 Ioannina 13/04/2006
35 THE MODULATION EFFECT vJune=235+15=250km/s vDec=235-15=220km/sHEP2006 Ioannina 13/04/2006
36 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. * with N. Tetradis (calculations with non standard M-B) HEP2006 Ioannina 13/04/2006
37 The Modulation Amplitude h for 127I Qth=0, Isothermal model (M-B), On the left n=1, on the right n=3HEP2006 Ioannina 13/04/2006
38 The Modulation Amplitude h for 127I Qth=10keV, Isothermal model (M-B), On the left n=1, on the right n=3 HEP2006 Ioannina 13/04/2006
39 The Modulation Amplitude h for 127I Qth=0thick, Qth=5keVfine Qth=10dash; Eddington TheoryHEP2006 Ioannina 13/04/2006
40 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 HEP2006 Ioannina 13/04/2006
41 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) HEP2006 Ioannina 13/04/2006
42 But, there are Z electrons in an atom!HEP2006 Ioannina 13/04/2006
43 Detection of hard X-raysAfter 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 to be discussed next HEP2006 Ioannina 13/04/2006
44 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 2s 2p WIMP masses indicated by subscript: L30GeV, M100GeV, H300GeV HEP2006 Ioannina 13/04/2006
45 The K Xray rates in WIMP interactions in 132 Xe for masses: L30GeV, M100GeV, H300GeVHEP2006 Ioannina 13/04/2006
46 Conclusions: Experimental ambitions for RecoilsHEP2006 Ioannina 13/04/2006
47 CONCLUSIONS A: K-K WIMPSTheoretical 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 sections can be extracted from current 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
48 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
49 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
50 CONCLUSIONS-Transitions to excited statesFor 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
51 CONCLUSIONS: Electron production during LSP-nucleus collisionsDuring 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
52 THE END HEP2006 Ioannina 13/04/2006
53 II: Cosmological Evidence for dark matterThe 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) HEP2006 Ioannina 13/04/2006
54 Anisotropy in the CMBR (cont.)HEP2006 Ioannina 13/04/2006
55 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
56 B1 Kaluza-Klein theories WIMP:B(1) K-K q(1)exchange-The axial current.HEP2006 Ioannina 13/04/2006
57 B2 WIMP is the ν(1). (continued) Ζ-Exchange Dominates.HEP2006 Ioannina 13/04/2006
58 Spin Contribution Axial CurrentGoing 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 HEP2006 Ioannina 13/04/2006
59 The relative differential Rate, (dRe/dTe )/Rrecoil, vs the electron energy T for electron production in LSP-nucleus (Moustakidis, Ejiri, JDV). HEP2006 Ioannina 13/04/2006
60 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
61 CONCLUSIONS-Directional RatesGood 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
62 CONCLUSIONS- Modulation in Directional ExperimentsThe 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
63 A typical Scatter Plot (Universal set of parameters) (Ceredeno, Gabrielli, Gomez and Munoz)HEP2006 Ioannina 13/04/2006
64 A Scatter Plot (Non Universal) (Ceredeno, Gabrielli, Gomez and Munoz)HEP2006 Ioannina 13/04/2006
65 The event rate due to the spinWhere 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: HEP2006 Ioannina 13/04/2006
66 The factor fspin(A,mχ) for A=127 (I) (The Dashed for threshold 10keV)HEP2006 Ioannina 13/04/2006
67 The factor fspin(A,mχ) for A=19 (F) (The Dashed for threshold 10keV)HEP2006 Ioannina 13/04/2006
68 The constrained amplitude plane (ap,χ,an,χ) for the Α=127 system (arbitrary units), when they are relatively real. HEP2006 Ioannina 13/04/2006
69 The constrained (ap,χ,an,χ) plane: relative phase of the amplitudes δ=π/6 (-), δ=π/3 (-)and δ=π/2 (-) HEP2006 Ioannina 13/04/2006
70 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
71 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
72 The directional event rateThe 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 HEP2006 Ioannina 13/04/2006
73 The event rate vs the polar angle (A=19, left) , (A=127, right) for mχ=100 GeV and M-B distributionHEP2006 Ioannina 13/04/2006
74 The parameter κ vs the LSP mass: perpendicular to the sun’s velocity (left) and opposite to it (right) HEP2006 Ioannina 13/04/2006
75 The modulation vs the LSP mass: perpendicular to the sun’s velocity (left) and opposite to it (right) HEP2006 Ioannina 13/04/2006
76 HEP2006 Ioannina 13/04/2006
77 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
78 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
79 Hubble’s Law: υ=Ha υ=Ha (υ=velocity, a=distance)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
80 Prototype Cosmic CandlesL= 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. HEP2006 Ioannina 13/04/2006
81 Supernovae Ia A Double Star, one of which is a white DwarfThe 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
82 The cycle of a large mass star Source:Imagine the Universe, NASAHEP2006 Ioannina 13/04/2006
83 A white Dwarf is eating up the mass of a red giantHEP2006 Ioannina 13/04/2006
84 The deepest picture of the sky (12 billion years agoThe deepest picture of the sky (12 billion years ago! Almost protogalaxies) HEP2006 Ioannina 13/04/2006
85 Experimental verification of υ=Ha Hubble’s Law: (H0) -1= 1010h -1 yr; H0=100h (km/s/Mpc), 0.6
86 IIb: Cosmic Microwave Background Radiation (CMBR)HEP2006 Ioannina 13/04/2006
87 HEP2006 Ioannina 13/04/2006
88 The Quenching Factor HEP2006 Ioannina 13/04/2006
89 Some experimental considerationsHEP2006 Ioannina 13/04/2006
90 Empirical Quenching FactorHEP2006 Ioannina 13/04/2006
91 The Modulation Amplitude h for I On the left zero energy cut offThe Modulation Amplitude h for I On the left zero energy cut off. On the right a cut off of 10keV HEP2006 Ioannina 13/04/2006
92 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 (J+1)/J (ap
93 Projected exclusion curvefor scalar detectors 2003 Edelweiss and CDMS projections HEP2006 Ioannina 13/04/2006
94 Projected exclusion curve for 3He detectorBackground = 0.01 day-1 Energy threshold = 1 keV CRESST Saphire ELEGANT V NaI UKDMC NaI NAIAD projection HEP2006 Ioannina 13/04/2006
95 Three years later! SDSS DR4:Sloan Digital Sky Survey Data Rlease 4HEP2006 Ioannina 13/04/2006