1. Physics of Masssive Neutrinos Milos 20-24/05/08 Direct Dark Matter Searches- Can Solar neutrinos be a background? J.D. Vergados* J.D. Vergados* Cyprus Technical University (CUT), Cyprus Cyprus Technical University (CUT), Cyprus * In collaboration with H. Ejiri

2. Physics of Masssive Neutrinos Milos 20-24/05/08 Motivation for considering Solar Neutrino background The low counting rate expected for WIMP detection The low counting rate expected for WIMP detection The large number of neutrino events expected in Supernova Neutrino Detectors. The large number of neutrino events expected in Supernova Neutrino Detectors. We have found: For p=10 Atm, R=4m, D=10 kpc, U ν =0.5x10 53 ergs For p=10 Atm, R=4m, D=10 kpc, U ν =0.5x10 53 ergs # of events (no quenching, zero threshold) # of events (no quenching, zero threshold) He Ne Ar Kr Xe He Ne Ar Kr Xe 1.25 31.6 153 614 1880 1.25 31.6 153 614 1880

3. Physics of Masssive Neutrinos Milos 20-24/05/08 EVIDENCE FOR THE EXISTENCE OF DARK MATTER Gravitational effects around galaxies Gravitational effects around galaxies Extended X-ray sources. Extended X-ray sources. The recent observation of the collision of two galaxy clusters (to-day 3.5  10 9 ly away from us, 2  10 6 ly apart) The recent observation of the collision of two galaxy clusters (to-day 3.5  10 9 ly away from us, 2  10 6 ly apart) Cosmological Observations (confirmed by the recent WMAP3 &WMAP05) : Dark matter and dark energy dominance Cosmological Observations (confirmed by the recent WMAP3 &WMAP05) : Dark matter and dark energy dominance

4. Physics of Masssive Neutrinos Milos 20-24/05/08 Ia: Weighing a Galaxy! Scale10 kpc=10000pc=30000 ly Scale10 kpc=10000pc=30000 ly The rotational velocity does not fall outside the visible galaxy! The rotational velocity does not fall outside the visible galaxy!

5. Physics of Masssive Neutrinos Milos 20-24/05/08 If we could see Dark Matter

6. Physics of Masssive Neutrinos Milos 20-24/05/08 Ib: Collision of the Galaxy Clusters: 1E 0657-56; Optical (orange-white), Χ-rays (magenta, with the bullet on the right), & microlensing (blue  > Dark Matter)

7. Physics of Masssive Neutrinos Milos 20-24/05/08 II: Cosmological Evidence for dark matter The 3 main reasons for the Big Bang Scenario: The 3 main reasons for the Big Bang Scenario: The receding of Galaxies (red shift) (Hubble 1929) The receding of Galaxies (red shift) (Hubble 1929) The Microwave Background Radiation (CMBR – Penzias and Wilson 1964) The Microwave Background Radiation (CMBR – Penzias and Wilson 1964) The Big Bang Nucleosynthesis (BBN, 1946) The Big Bang Nucleosynthesis (BBN, 1946) All bear a signature of dark matter All bear a signature of dark matter

8. Physics of Masssive Neutrinos Milos 20-24/05/08 Slicing the Pie of the Cosmos WMAP3: Ω CDM =0.24±0.02, Ω Λ =0.72±0.04, Ω b =0.042±0.003

9. Physics of Masssive Neutrinos Milos 20-24/05/08 Cosmological Constraints in the (Ω Λ,Ω m ) Plane (From M. Kowalski et al, asrto-ph/08)

10. Physics of Masssive Neutrinos Milos 20-24/05/08 Dark Matter exists! What is the nature of dark matter? It is not known. However: It is not known. However: It possesses gravitational interactions (from the rotation curves) 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 No other long range interaction is allowed. Otherwise it would have formed “atoms” and, hence, stars etc. So It is electrically neutral It is electrically neutral It does not interact strongly (if it did, it should have already been detected) It does not interact strongly (if it did, it should have already been detected) It may (hopefully!) posses some very weak interaction It may (hopefully!) posses some very weak interaction This will depend on the assumed theory  This will depend on the assumed theory  WIMPs (Weakly Interacting Massive Particles) Such an interaction may be exploited for its direct detection Such an interaction may be exploited for its direct detection The smallness of the strength of such an interaction and its low energy makes its direct detection extremely difficult. The smallness of the strength of such an interaction and its low energy makes its direct detection extremely difficult.

11. Physics of Masssive Neutrinos Milos 20-24/05/08 DARK MATTER (WIMP) CANDIDATES The axion: 10 -6 eV<m a <10 -3 eV The axion: 10 -6 eV<m a <10 -3 eV The neutrino: It is not dominant. It is not cold, not CDM. The neutrino: It is not dominant. It is not cold, not CDM. Supersymmetric particles. Supersymmetric particles. Four possibilities: Four possibilities: i) s-νετρίνο: Excluded on the basis of results of underground experiments and accelerator experiments (LEP) i) s-νετρίνο: Excluded on the basis of results of underground experiments and accelerator experiments (LEP) ii) Gravitino: Not directly detectable ii) Gravitino: Not directly detectable iii) Αxino: Not directly detectable iii) Αxino: Not directly detectable iv) A Majorana fermion, the neutralino or LSP iv) A Majorana fermion, the neutralino or LSP (The lightest supersymmetric particle): A linear (The lightest supersymmetric particle): A linear combination of the 2 neutral gauginos and the 2 combination of the 2 neutral gauginos and the 2 neutral Higgsinos. MOST FAVORITE CANDIDATE! neutral Higgsinos. MOST FAVORITE CANDIDATE! Particles from Universal Extra Dimension Theories (e.g. Kaluza- Klein WIMPs) Particles from Universal Extra Dimension Theories (e.g. Kaluza- Klein WIMPs) The Lightest Technibaryon, LTB (Gudnason-Kouvaris-Sannino) The Lightest Technibaryon, LTB (Gudnason-Kouvaris-Sannino)

12. Physics of Masssive Neutrinos Milos 20-24/05/08 A: SUSY MODELS The most favorable candidate is the neutralino (a Majorana Fermion) The most favorable candidate is the neutralino (a Majorana Fermion) The rates predicted depend on the choice of the parameters in the SUSY allowed parameter space. The rates predicted depend on the choice of the parameters in the SUSY allowed parameter space. Detectable rates near the present experimental goals are predicted to be possible, but unlikely. Detectable rates near the present experimental goals are predicted to be possible, but unlikely. One may use the available limits to constrain the nucleon cross section. One may use the available limits to constrain the nucleon cross section.

13. Physics of Masssive Neutrinos Milos 20-24/05/08 A SUSY CADIDATE- the LSP (R-parity conservation) Allowed parameter space: Universality at GUT scale: - One mass m 0 for the scalars -One mass m 1/2 for the fermions -Tanβ, the ratio of vacuum expectation values of the Allowed parameter space: Universality at GUT scale: - One mass m 0 for the scalars -One mass m 1/2 for the fermions -Tanβ, the ratio of vacuum expectation values of the Higss H u,H d, i.e. / -The cubic coupling A 0 (or m t ) -The sign of μ, in μH u H d Higss H u,H d, i.e. / -The cubic coupling A 0 (or m t ) -The sign of μ, in μH u H d These parameters are constrained via the renormalization group equations from the observable low energy quantities (all are related to the above five parameters). (see, e.g.,: Ellis, Arnowitt, Nath, Bottino, Lazarides, Munoz, Gomez and their collaborators) These parameters are constrained via the renormalization group equations from the observable low energy quantities (all are related to the above five parameters). (see, e.g.,: Ellis, Arnowitt, Nath, Bottino, Lazarides, Munoz, Gomez and their collaborators)

14. Physics of Masssive Neutrinos Milos 20-24/05/08 B. Universal Extra Dimension Theories (e.g. Servant et al) Kaluza-Klein Theories: A tower of new particles Kaluza-Klein Theories: A tower of new particles Postulate a discreet symmetry: K-K parity Postulate a discreet symmetry: K-K parity The even modes (ordinary particles) have K-K parity +1 The even modes (ordinary particles) have K-K parity +1 The odd modes (exotic) have K-K parity -1 The odd modes (exotic) have K-K parity -1 The lightest odd mode is absolutely stable The lightest odd mode is absolutely stable The interactions of the new particles are the same with those of SM The interactions of the new particles are the same with those of SM Essentially only the particle’s mass is unknown parameter Essentially only the particle’s mass is unknown parameter

15. Physics of Masssive Neutrinos Milos 20-24/05/08 LSP Velocity Distributions Conventional: Isothermal models Conventional: Isothermal models (1) Maxwell-Boltzmann (symmetric or axially symmetric) (1) Maxwell-Boltzmann (symmetric or axially symmetric) with characteristic velocity equal to the sun’s velocity around the center of the galaxy, υ ΜΒ = υ 0 = 220 km/s, with characteristic velocity equal to the sun’s velocity around the center of the galaxy, υ ΜΒ = υ 0 = 220 km/s, and escape velocity υ esc =2.84υ 0 put in by hand. and escape velocity υ esc =2.84υ 0 put in by hand. (2) Modification of M-B characteristic velocity υ ΜΒ following the (2) Modification of M-B characteristic velocity υ ΜΒ following the interaction of dark matter with dark energy: interaction of dark matter with dark energy: υ ΜΒ = nυ 0, υ esc =n2.84 υ 0, n>1 υ ΜΒ = nυ 0, υ esc =n2.84 υ 0, n>1 (Tetradis, Feassler and JDV ) (Tetradis, Feassler and JDV ) Adiabatic models employing Eddington’s approach: Adiabatic models employing Eddington’s approach: ρ(r)  Φ(r)  f(r,v) (JDV-Owen) ρ(r)  Φ(r)  f(r,v) (JDV-Owen) Realistic axially symmetric velocity distributions obtained via simulations  Tsallis type functions (Host, Hansen and JDV) Realistic axially symmetric velocity distributions obtained via simulations  Tsallis type functions (Host, Hansen and JDV) Other non-thermal models: Other non-thermal models: Caustic rings (Sikivie, JDV), WIMP’s in bound orbits etc Caustic rings (Sikivie, JDV), WIMP’s in bound orbits etc Sgr Dwarf galaxy, anisotropic flux, (Green & Spooner) Sgr Dwarf galaxy, anisotropic flux, (Green & Spooner)

16. Physics of Masssive Neutrinos Milos 20-24/05/08 Principles of WIMP Detection (WIMP: Weakly Interacting massive particle)

17. Physics of Masssive Neutrinos Milos 20-24/05/08 A: Conversion of the energy of the recoiling nucleus into detectable form (light, heat, ionization etc.) The WIMP is non relativistic, β≤10 -3. The WIMP is non relativistic, β≤10 -3. With few exceptions, it cannot excite the nucleus. It only scatters off elastically: With few exceptions, it cannot excite the nucleus. It only scatters off elastically: Measuring the energy of the recoiling nucleus is extremely hard: Measuring the energy of the recoiling nucleus is extremely hard: -Low event rate (much less than 10 per Kg of target per year are expected). -Low event rate (much less than 10 per Kg of target per year are expected). -Bothersome backgrounds (the signal is not very characteristic). -Bothersome backgrounds (the signal is not very characteristic). -Threshold effects. -Threshold effects. -Quenching factors. -Quenching factors.

18. Physics of Masssive Neutrinos Milos 20-24/05/08 The event rate for the coherent mode The number of events during time t is given by: The number of events during time t is given by:Where: t depends on nuclear physics, the WIMP mass and the velocity distribution t depends on nuclear physics, the WIMP mass and the velocity distribution ρ(0): the local WIMP density≈0.3 GeV/cm 3. ρ(0): the local WIMP density≈0.3 GeV/cm 3. μ r is the WIMP-Nucleus reduced mass μ r is the WIMP-Nucleus reduced mass σ S p,χ : the WIMP-nucleon cross section. It is computed in a particle model. σ S p,χ : the WIMP-nucleon cross section. It is computed in a particle model. It can be extracted from the data once f coh (A,m χ ) is known It can be extracted from the data once f coh (A,m χ ) is known

19. Physics of Masssive Neutrinos Milos 20-24/05/08 The coherent differential rate kg-y/keV for m χ =100 GeV (intermediate target ( 131 Xe))

20. Physics of Masssive Neutrinos Milos 20-24/05/08 The coherent differential rate kg-y/keV for m χ =100 GeV (light target ( 32 S))

21. Physics of Masssive Neutrinos Milos 20-24/05/08 The coherent total rate kg-y as a function of the WIMP mass (intermediate target ( 131 Xe))

22. Physics of Masssive Neutrinos Milos 20-24/05/08 The coherent total rate kg-y for σ=10 -9 pb top intermediate target ( 131 Xe), Bottom: light target 32 S

23. Physics of Masssive Neutrinos Milos 20-24/05/08 Novel approaches: Exploitation of other signatures of the reaction The modulation effect: The seasonal, due to the motion of the Earth, dependence of the rate. The modulation effect: The seasonal, due to the motion of the Earth, dependence of the rate. The excitation of the nucleus (in some cases, heavy WIMP etc, that this is realistic) and detection of the subsequently emitted de- excitation γ rays. The excitation of the nucleus (in some cases, heavy WIMP etc, 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). 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 Detection of other particles (electrons, X-rays), produced during the LSP-nucleus collision

24. Physics of Masssive Neutrinos Milos 20-24/05/08 The bothersome backgrounds Anyway it will be necessary to detect nuclear recoils Anyway it will be necessary to detect nuclear recoils At this level, processes which are ordinarily harmless can become a serious background, since they have the same signature with the good events. At this level, processes which are ordinarily harmless can become a serious background, since they have the same signature with the good events. One must see some recoil events. The background is minimized but still there. One must see some recoil events. The background is minimized but still there. One such background may come from solar neutrinos. One such background may come from solar neutrinos.

25. Physics of Masssive Neutrinos Milos 20-24/05/08 The differential elastic neutrino- nucleus cross section M V and M A are the nuclear matrix elements associated with the vector and axial current and T A is the nuclear recoil energy. M V and M A are the nuclear matrix elements associated with the vector and axial current and T A is the nuclear recoil energy.

26. Physics of Masssive Neutrinos Milos 20-24/05/08 The coherent (due to neutrons) neutrino nucleus elastic scattering

27. Physics of Masssive Neutrinos Milos 20-24/05/08 Kinematical relations (for any target)

28. Physics of Masssive Neutrinos Milos 20-24/05/08 The maximum nuclear recoil energy as a function of E ν

29. Physics of Masssive Neutrinos Milos 20-24/05/08 The maximum nuclear recoil energy as a function of the WIMP velocity for the indicated values of (A, m χ )

30. Physics of Masssive Neutrinos Milos 20-24/05/08 The average nuclear recoil energy as a function of the WIMP mass for the indicated values of A

31. Physics of Masssive Neutrinos Milos 20-24/05/08 The Solar neutrino spectrum

32. Physics of Masssive Neutrinos Milos 20-24/05/08 The Boron solar neutrino spectrum (top) and flux (bottom, Log-log plot)

33. Physics of Masssive Neutrinos Milos 20-24/05/08 The elastic neutrino-nucleus cross section (cm 2 keV -1 ) for an intermediate target (top) and a light target (bottom)

34. Physics of Masssive Neutrinos Milos 20-24/05/08 Event rates for nuclear recoils: (a) for WIMP induced and (b) Boron solar neutrino induced

35. Physics of Masssive Neutrinos Milos 20-24/05/08 The Quenching factor: The quenching factor for a given detector is the ratio of the signal height of a nuclear recoil event divided by the corresponding one of an electron with the same energy. The quenching factor for a given detector is the ratio of the signal height of a nuclear recoil event divided by the corresponding one of an electron with the same energy. The quenching factor must be determined experimentally for a given detector. The quenching factor must be determined experimentally for a given detector. In our calculation it was adequate to multiply the energy by an energy dependent quenching factor given by a Lidhard type theory. In our calculation it was adequate to multiply the energy by an energy dependent quenching factor given by a Lidhard type theory.

36. Physics of Masssive Neutrinos Milos 20-24/05/08 The Quenching factor: A=131 (top) and A=32 (bottom)

37. Physics of Masssive Neutrinos Milos 20-24/05/08 Due to quenching the rate is not affected but the energy is shifted downwards (thick line). Target A=131

38. Physics of Masssive Neutrinos Milos 20-24/05/08 Due to quenching the rate is not affected but the energy is shifted downwards (thick line). Target A=32

39. Physics of Masssive Neutrinos Milos 20-24/05/08 The solar neutrino differential rate: A=32 target. For threshold energy 1 keV the detectable portion is above the thin line (no quenching) and the thick line (quenching)

40. Physics of Masssive Neutrinos Milos 20-24/05/08 The solar neutrino differential rate: A=131 target. For threshold energy 1 keV the detectable portion is above the thin line (no quenching) and the thick line (quenching)

41. Physics of Masssive Neutrinos Milos 20-24/05/08 The WIMP differential rate: WIMP mass 100 GeV & A=131 target. For threshold energy 2 keV the detectable portion is above the thin line (no quenching) and the thick line (quenching)

42. Physics of Masssive Neutrinos Milos 20-24/05/08 The ratio of the event rates R(Q th )/R(Q th =0) as a function of Q th ( in kev) for WIMP mass of 100 GeV and A=131. No quenching (thin line) Quenching (thick line)

43. Physics of Masssive Neutrinos Milos 20-24/05/08 The ratio of the event rates R(Q th )/R(Q th =0) as a function of Q th ( in kev) for WIMP mass of 100 GeV and A=32. No quenching (thin line) Quenching (thick line)

44. Physics of Masssive Neutrinos Milos 20-24/05/08 The ratio of the event rates R(Q th )/R(Q th =0) as a function of Q th ( in kev) for boron solar neutrinos and A=131. No quenching (thin line) Quenching (thick line)

45. Physics of Masssive Neutrinos Milos 20-24/05/08 The ratio of the event rates R(Q th )/R(Q th =0) as a function of Q th ( in kev) for boron solar neutrinos and A=32. No quenching (thin line) Quenching (thick line)

46. Physics of Masssive Neutrinos Milos 20-24/05/08 Conclusions: No experiment has directly seen any WIMP events. The expected event rate is very low. So.. The coherent WIMP event rate for a target of 1 Kg of mass in the case of a heavy WIMP increases with A. The coherent WIMP event rate for a target of 1 Kg of mass in the case of a heavy WIMP increases with A. The coherent neutrino event rate for a target of 1 Kg of mass varies as N 2 /A. The recoil energy decreases with A. The coherent neutrino event rate for a target of 1 Kg of mass varies as N 2 /A. The recoil energy decreases with A. Both rates decrease as the threshold energy increases, but the solar neutrino event rate does much more so. Both rates decrease as the threshold energy increases, but the solar neutrino event rate does much more so. Both are sensitive to quenching, but its effect on the solar neutrino event rate is much more dramatic. Both are sensitive to quenching, but its effect on the solar neutrino event rate is much more dramatic. The WIMP event rate is sensitive to the nuclear form factor, but the solar neutrino event rate is not. The WIMP event rate is sensitive to the nuclear form factor, but the solar neutrino event rate is not.

47. Physics of Masssive Neutrinos Milos 20-24/05/08 Conclusions The boron neutrinos are not a serious background to WIMP detection, unless the event rate turns out to be The boron neutrinos are not a serious background to WIMP detection, unless the event rate turns out to be less than 1 event per ton per year less than 1 event per ton per year Even below this level one can minimize the neutrino background by a judicious choice of the target and exploiting the energy cut off Even below this level one can minimize the neutrino background by a judicious choice of the target and exploiting the energy cut off

48. Physics of Masssive Neutrinos Milos 20-24/05/08 Conclusions: Directional experiments The neutrino background gives an entirely different signature compared to the WIMP signal in Directional Experiments*. In such experiments this background can be discarded at any level The neutrino background gives an entirely different signature compared to the WIMP signal in Directional Experiments*. In such experiments this background can be discarded at any level * Experiments in which the direction of the recoiling nucleus is also observed.

49. Physics of Masssive Neutrinos Milos 20-24/05/08 THE END THE END

50. Physics of Masssive Neutrinos Milos 20-24/05/08 Techniques for direct WIMP detection

51. Physics of Masssive Neutrinos Milos 20-24/05/08 Techniques for direct WIMP detection

52. Physics of Masssive Neutrinos Milos 20-24/05/08 World Status (BUS 2006)

53. Physics of Masssive Neutrinos Milos 20-24/05/08 THE MODULATION EFFECT v June =235+15=250km/s v Dec =235-15=220km/s

54. Physics of Masssive Neutrinos Milos 20-24/05/08 THE MODULATION EFFECT* (continued) R=R 0 (1+b sinγ cosα)=R 0 (1+h cosα) R=R 0 (1+b sinγ cosα)=R 0 (1+h cosα) (α=0 around June 3nd) (α=0 around June 3nd) γ= π/2-γ ’, γ ’ ≈ π/3 is the angle between the axis of galaχy and the axis of the ecliptic. γ= π/2-γ ’, γ ’ ≈ π/3 is the angle between the axis of galaχy and the axis of the ecliptic. h=modulation amplitude. h=modulation amplitude. R 0 =average rate. R 0 =average rate. *n=2 corresponds to calculations with non standard M-B (Tetradis, Faeesler and JDV) *n=2 corresponds to calculations with non standard M-B (Tetradis, Faeesler and JDV)

55. Physics of Masssive Neutrinos Milos 20-24/05/08 The Modulation Amplitude h for 127 I Q th =0, 10 keV, Isothermal model (M-B), On top n=1, at the bottom n=2

56. Physics of Masssive Neutrinos Milos 20-24/05/08 The Modulation Amplitude h (light target) Q th =0, Isothermal model (M-B), n=1 (Left), n=2 (right)

57. Physics of Masssive Neutrinos Milos 20-24/05/08 The Modulation Amplitude h (light target) Q th =10 keV, Isothermal model (M-B), n=1 (Left), n=2 (right)

58. Physics of Masssive Neutrinos Milos 20-24/05/08 The directional event rate* (The direction of recoil is observed) The event rate in directional experiments is: The event rate in directional experiments is: R dir =(κ/2π)R 0 [1+h m cos(α-α m π)] R dir =(κ/2π)R 0 [1+h m cos(α-α m π)] R 0 is the average usual (non-dir) rate R 0 is the average usual (non-dir) rate α the phase of the Earth (as usual) α the phase of the Earth (as usual) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ and α m depend only slightly on SUSY parameters κ and α m depend only slightly on SUSY parameters * Calculations by Faessler and JDV * Calculations by Faessler and JDV

59. Physics of Masssive Neutrinos Milos 20-24/05/08 The parameter κ vs the polar angle in the case of A=32; m χ =100 GeV definite sense (Left), Both senses (Right)

60. Physics of Masssive Neutrinos Milos 20-24/05/08 The parameter κ vs the polar angle in the case of A=127; m χ =100 GeV definite sense (Left), Both senses (Right)

61. Physics of Masssive Neutrinos Milos 20-24/05/08 The parameter h m vs the polar angle in the case of A=32; m χ =100 GeV One sense (Left), Both senses (Right)

62. Physics of Masssive Neutrinos Milos 20-24/05/08 The phase α m vs the polar angle in the case of A=32; m χ =100 GeV One sense (Left), Both senses (Right)

63. Physics of Masssive Neutrinos Milos 20-24/05/08 NON RECOIL MEASUREMENTS (a) Measurement of ionization electrons produced directly during the WIMP-nucleus collisions (Moustakidis, Ejiri and JDV) (a) Measurement of ionization electrons produced directly during the WIMP-nucleus collisions (Moustakidis, Ejiri and JDV) (b) Measurement of hard X-rays following the de-excitation of the atom in (a) (b) Measurement of hard X-rays following the de-excitation of the atom in (a) (Ejiri, Moustakidis and JDV) (Ejiri, Moustakidis and JDV) (c) Excitation of the Nucleus and observation of the de-excitation γ rays (c) Excitation of the Nucleus and observation of the de-excitation γ rays

64. Physics of Masssive Neutrinos Milos 20-24/05/08 Relative rate for electron ionization (there are Z electrons in an atom!)

65. Physics of Masssive Neutrinos Milos 20-24/05/08 Detection of hard X-rays (Ejiri, Moustakidis, and J.D.V) After the ionization there is a probability for a K or L hole After the ionization there is a probability for a K or L hole This hole de-excites via emitting X-rays or Auger electrons. This hole de-excites via emitting X-rays or Auger electrons. the fraction of X-rays per recoil is: the fraction of X-rays per recoil is: σ X(n ℓ ) /σ r = b nl (σ n ℓ /σ r ) with σ n ℓ /σ r the relative σ X(n ℓ ) /σ r = b nl (σ n ℓ /σ r ) with σ n ℓ /σ r the relative ionization rate per orbit and b n ℓ the fluorescence ratio (determined experimentally) ionization rate per orbit and b n ℓ the fluorescence ratio (determined experimentally)

66. Physics of Masssive Neutrinos Milos 20-24/05/08 K X-ray BR in WIMP interactions in 132 Xe vs masse: L 30GeV, M 100GeV, H 300GeV

67. Physics of Masssive Neutrinos Milos 20-24/05/08 Excitation of the nucleus: Appears possible in the exotic models ≈40 keV n 2 (m χ /100GeV) ≈40 keV n 2 (m χ /100GeV) T χ,max ≈ 215 keV n 2 (m χ /100GeV). Thus T χ,max ≈ 215 keV n 2 (m χ /100GeV). Thus m χ =500GeV, n=2  ≈0.8 MeV, T χ,max ≈ 4 MeV m χ =500GeV, n=2  ≈0.8 MeV, T χ,max ≈ 4 MeV

68. Physics of Masssive Neutrinos Milos 20-24/05/08 Unfortunately, Not all available energy is exploitable! For ground to ground transitions (q  momentum, Q  energy) For ground to ground transitions (q  momentum, Q  energy) For Transitions to excited states For Transitions to excited states Sharply peaked at ξ=1 Sharply peaked at ξ=1

69. Physics of Masssive Neutrinos Milos 20-24/05/08 The recoil energy in keV for A=127 and Δ=50 keV. M χ =30 GeV, M χ =100 GeV, M χ =200 GeV, M χ =200 GeV, M χ =400 GeV.

70. Physics of Masssive Neutrinos Milos 20-24/05/08 The average nuclear recoil energy: A=127; Δ=50 keV (left), Δ=30 keV (right)

71. Physics of Masssive Neutrinos Milos 20-24/05/08 BR for transitions to the first excited state at 50 keV of I vs LSP mass (Ejiri; Quentin, Strottman and JDV) Relative to nucleon recoil i) no quenching ii) Left  E th =0 keV, Right  E th =10 keV

72. Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS A: K-K WIMPS Theoretical advantages: Only the masses are unknown parameters. The couplings are S.M Theoretical advantages: Only the masses are unknown parameters. The couplings are S.M Experimental advantages: The WIMP energy is an order of magnitude bigger Experimental advantages: The WIMP energy is an order of magnitude bigger The energy transfer to the nucleus is a bit higher. One has a better chance to excite the nucleus The energy transfer to the nucleus is a bit higher. One has a better chance to excite the nucleus Limits K-K Nucleon cross sections can be extracted from current limits via: Limits K-K Nucleon cross sections can be extracted from current limits via: σ (K-K) (coh) ≈(A/Z) 2 10 (-6) pb [m (K-K) /200GeV] σ (K-K) (coh) ≈(A/Z) 2 10 (-6) pb [m (K-K) /200GeV] σ (K-K) (spin) ≈10 (-2) pb [m (K-K) /200GeV] σ (K-K) (spin) ≈10 (-2) pb [m (K-K) /200GeV]

73. Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS- SUSY WIMPS Standard Rates (theory) Most of the uncertainties come from the fact that the allowed SUSY parameter space has not been sufficiently sharpened. Most of the uncertainties come from 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 also affect the results by an order of magnitude. The other uncertainties (nuclear form factor, structure of the nucleon, quenching factor, energy threshold) could also affect the results by an order of magnitude. Most of the parameter space yields undetectable rates. Most of the parameter space yields undetectable rates. The coherent contribution due to the scalar interaction is the most dominant. The coherent contribution due to the scalar interaction is the most dominant.

74. Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS-Modulation (theory) The modulation amplitude h is small, less than 2% and depends on the LSP mass. The modulation amplitude h is small, less than 2% and depends on the LSP mass. It crucially depends on the velocity distribution It crucially depends on the velocity distribution Unfortunately even its sign is uncertain for intermediate and heavy nuclei. Unfortunately even its sign is 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. 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. The modulation is reduced further in the case of exotic WIMP velocity distributions The modulation is reduced further in the case of exotic WIMP velocity distributions

75. Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS -Directional Experiments The predicted rates are down by at least a factor of 4π compared to those of the standard experiments. However: The predicted rates are down by at least a factor of 4π compared to those of the standard experiments. However: Strong correlations of the event rates with the sun’s direction of motion are expected. Thus large asymmetries are expected. Strong correlations of the event rates with the sun’s direction of motion are expected. Thus large asymmetries are expected. The modulation now is much larger. The location of its maximum depends on the direction of observation. Thus it cannot be mimicked by seasonal variations of the background. The modulation now is much larger. The location of its maximum depends on the direction of observation. Thus it cannot be mimicked by seasonal variations of the background.

76. Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS: Electron production during LSP-nucleus collisions During the neutralino-nucleus collisions, electrons may be kicked off the atom During the neutralino-nucleus collisions, electrons may be kicked off the atom Electrons can be identified easier than nuclear recoils (Needed: Low threshold, ~0.25keV, TPC detectors) Electrons can be identified easier than nuclear recoils (Needed: Low threshold, ~0.25keV, TPC detectors) The branching ratio for this process depends on the threshold energies and the LSP mass. 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. 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 Detection of hard X-rays also seams feasible

77. Physics of Masssive Neutrinos Milos 20-24/05/08 Conclusions: Experimental ambitions for Recoils

78. Physics of Masssive Neutrinos Milos 20-24/05/08 COMMON WISDOM!

79. Physics of Masssive Neutrinos Milos 20-24/05/08 nucleon cross sections extracted from the data. R<2.3 events for 52.5 Kg-d Dotted  E th =10 keV, thick  E th =0 keV 127 I (left) 73 Ge (right) (light WIMP)

80. Physics of Masssive Neutrinos Milos 20-24/05/08 nucleon cross sections extracted from the data. R<16 events per Kg-y Dotted  E th =10 keV, thick  E th =0 keV ( 19 F)

81. Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS: Excitation of the nucleus: Appears possible in the exotic models

82. Physics of Masssive Neutrinos Milos 20-24/05/08 Unfortunately, Not all available energy is exploitable! For ground to ground transitions For ground to ground transitions For Transitions to excited states For Transitions to excited states Sharply peaked at ξ=1 Sharply peaked at ξ=1

83. Physics of Masssive Neutrinos Milos 20-24/05/08 The recoil energy in keV for A=127 and Δ=50 keV. M χ =30 GeV, M χ =100 GeV, M χ =200 GeV, M χ =200 GeV, M χ =400 GeV.

84. Physics of Masssive Neutrinos Milos 20-24/05/08 The average excitation energy: A=127; Δ=50 keV (left), Δ=30 keV (right)

85. Physics of Masssive Neutrinos Milos 20-24/05/08 The directional event rate The event rate in directional experiments is: The event rate in directional experiments is: R dir =(κ/2π)R 0 [1+cos(α-α m π)] R dir =(κ/2π)R 0 [1+cos(α-α m π)] R 0 is the average usual (non-dir) rate R 0 is the average usual (non-dir) rate α the phase of the Earth (as usual) α the phase of the Earth (as usual) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ and α m depend only slightly on SUSY κ and α m depend only slightly on SUSY

86. Physics of Masssive Neutrinos Milos 20-24/05/08 The Directional rate t dir in the case of 127 I for wimp mass of 100 GeV M-B distribution m=1)

87. Physics of Masssive Neutrinos Milos 20-24/05/08 The Directional rate t dir in the case of 127 I for wimp mass of 100 GeV M-B distribution m=2)

88. Physics of Masssive Neutrinos Milos 20-24/05/08 The parameter κ vs the polar angle in the case of A=127, right for m χ =100 GeV(M-B distribution m=1)

89. Physics of Masssive Neutrinos Milos 20-24/05/08 The parameter κvs the polar angle in the case of A=127, right for m χ =100 GeV(M-B distribution m=2)

90. Physics of Masssive Neutrinos Milos 20-24/05/08 Directional Rate: Modulation vs Θ m wimp =100 GeV,dotted  Φ=π, fine  Φ=0, thick  Φ=π/2,3π/2 (m=1)

91. Physics of Masssive Neutrinos Milos 20-24/05/08 Directional Rate: Modulation vs Θ m wimp =100 GeV,dotted  Φ=π, fine  Φ=0, thick  Φ=π/2,3π/2 (m=2)

92. Physics of Masssive Neutrinos Milos 20-24/05/08 The event rate vs the polar angle (A=19, left), (A=127, right) for m χ =100 GeV and M-B distribution

93. Physics of Masssive Neutrinos Milos 20-24/05/08 The parameter κ vs the LSP mass: perpendicular to the sun’s velocity (left) and opposite to it (right)

94. Physics of Masssive Neutrinos Milos 20-24/05/08 A. SUSY MODELS WITH R-PARITY: The neutralino χ Standard model particles have R-parity=1 Standard model particles have R-parity=1 All SUSY particles have R-parity -1 All SUSY particles have R-parity -1 Lightest SUSY particle absolutely stable Lightest SUSY particle absolutely stable A linear combination of the 4 neutral fermions (two gauginos and two Higgsinos) i.e. A linear combination of the 4 neutral fermions (two gauginos and two Higgsinos) i.e.

95. Physics of Masssive Neutrinos Milos 20-24/05/08 From the quark level to the nucleon level (coherent)

96. Physics of Masssive Neutrinos Milos 20-24/05/08 The Differential cross section at the nuclear level. υ is the neutralino velocity and u stands essentially for the energy transfer Q: υ is the neutralino velocity and u stands essentially for the energy transfer Q: u=Q/Q 0, Q 0 =40A -4/3 MeV u=Q/Q 0, Q 0 =40A -4/3 MeV F(u): The nuclear form factor F(u): The nuclear form factor F 11 (u): The isovector spin response function F 11 (u): The isovector spin response function

97. Physics of Masssive Neutrinos Milos 20-24/05/08 Expressions for the nuclear cross section (continued) With With Σ S =σ p s (μ r /m p ) 2 A 2 (scalar interaction) Σ S =σ p s (μ r /m p ) 2 A 2 (scalar interaction) σ p s is the scalar proton-LSP cross section σ p s is the scalar proton-LSP cross section μ r is the LSP-nucleus reduced mass μ r is the LSP-nucleus reduced mass A is the nuclear mass A is the nuclear mass Σ Spin is the expression for the spin induced Σ Spin is the expression for the spin induced cross section (to be discussed later). cross section (to be discussed later).

98. Physics of Masssive Neutrinos Milos 20-24/05/08 The Relative (with respect to recoil) rate of ionization per electron vs: a) E threshold for m χ =100Gev (left) and b) m χ for E threshold = 0.2 keV (right)

99. Physics of Masssive Neutrinos Milos 20-24/05/08 Relative rate for inner electron hole production in the case of 132 Xe. n ℓ ε n ℓ (keV) (σ n ℓ /σ r ) L (σ n ℓ /σ r ) M (σ n ℓ /σ r ) H n ℓ ε n ℓ (keV) (σ n ℓ /σ r ) L (σ n ℓ /σ r ) M (σ n ℓ /σ r ) H is 34.56 0.034 0.221 0.255 is 34.56 0.034 0.221 0.255 2s 5.45 1.211 1.461 1.463 2s 5.45 1.211 1.461 1.463 2p 4.89 3.796 4.506 4.513 2p 4.89 3.796 4.506 4.513 WIMP masses indicated by subscript: WIMP masses indicated by subscript: L  30GeV, M  100GeV, H  300GeV L  30GeV, M  100GeV, H  300GeV

100. Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS-Transitions to excited states For neutralino transitions to excited states are possible in few odd A nuclei*. For neutralino transitions to excited states are possible in few odd A nuclei*. When allowed, are kinematically suppressed When allowed, are kinematically suppressed The branching ratio depends on the structure of the nucleus and the LSP mass 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 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 * For K-K WIMPS it is quite easy

101. Physics of Masssive Neutrinos Milos 20-24/05/08 II: Cosmological Evidence for dark matter The 3 main reasons for the Big Bang Scenario: The 3 main reasons for the Big Bang Scenario: The receding of Galaxies (red shift) (Hubble 1929) The receding of Galaxies (red shift) (Hubble 1929) The Microwave Background Radiation (CMBR – Penzias and Wilson 1964) The Microwave Background Radiation (CMBR – Penzias and Wilson 1964) The Big Bang Nucleosynthesis (BBN, 1946) The Big Bang Nucleosynthesis (BBN, 1946) All bear a signature of dark matter All bear a signature of dark matter (BBN also gave the first argument for CMBR, but nobody paid any attention)

102. Physics of Masssive Neutrinos Milos 20-24/05/08 Anisotropy in the CMBR (cont.)

103. Physics of Masssive Neutrinos Milos 20-24/05/08 IIc: Light curves : d L vs red shift z (Generalization of Hubble’s Law to Large Distances) Upper continuous Upper continuous Middle continuous Middle continuous Lower continuous Lower continuous Dashed- Dashed- Non accelerating Non accelerating universe universe

104. Physics of Masssive Neutrinos Milos 20-24/05/08 B1 Kaluza-Klein theories WIMP:B (1) K-K q (1) exchange-The axial current.

105. Physics of Masssive Neutrinos Milos 20-24/05/08 B2 WIMP is the ν (1). (continued) Ζ-Exchange Dominates.

106. Physics of Masssive Neutrinos Milos 20-24/05/08 Spin Contribution  Axial Current Going from quark to the nucleon level for the isovector component is standard (as in weak interactions): f 1 A (q)  f 1 A = g A f 1 A (q), g A =1.24 Going from quark to the nucleon level for the isovector component is standard (as in weak interactions): f 1 A (q)  f 1 A = g A f 1 A (q), g A =1.24 For the isoscalar this is not trivial. The naïve quark model fails badly (the proton spin crisis) f 0 A (q)  f 0 A = g 0 A f 0 A (q), g 0 A =0.1 For the isoscalar this is not trivial. The naïve quark model fails badly (the proton spin crisis) f 0 A (q)  f 0 A = g 0 A f 0 A (q), g 0 A =0.1

107. Physics of Masssive Neutrinos Milos 20-24/05/08 The relative differential Rate, (dR e /dT e )/R recoil, vs the electron energy T for electron production in LSP-nucleus (Moustakidis, Ejiri, JDV). The relative differential Rate, (dR e /dT e )/R recoil, vs the electron energy T for electron production in LSP-nucleus (Moustakidis, Ejiri, JDV).

108. Physics of Masssive Neutrinos Milos 20-24/05/08 Detection of hard X-rays (events relative to recoil) (continued) The interesting quantity is: The interesting quantity is: (σ K (K ij )/σ r )=(σ 1s /σ r ) b 1s B(K ij ) (σ K (K ij )/σ r )=(σ 1s /σ r ) b 1s B(K ij ) Where: Where: b n ℓ = Fluorecence ratio, K ij =K-ij branch b n ℓ = Fluorecence ratio, K ij =K-ij branch

109. Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS-Directional Rates Good signatures, but the experiments are hard (the DRIFT experiment cannot tell the sense of direction of recoil) Good signatures, but the experiments are hard (the DRIFT experiment cannot tell the sense of direction of recoil) Large asymmetries are predicted Large asymmetries are predicted The rates are suppressed by a factor κ/2π, κ<0.6 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 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 most favored direction κ is approximately 0.6 In the plane perpendicular to the sun’s velocity κ is approximately equal to 0.2 In the plane perpendicular to the sun’s velocity κ is approximately equal to 0.2

110. Physics of Masssive Neutrinos Milos 20-24/05/08 CONCLUSIONS- Modulation in Directional Experiments The Directional rates also exhibit modulation 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 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) 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)

111. Physics of Masssive Neutrinos Milos 20-24/05/08 A Scatter Plot (Non Universal) (Ceredeno, Gabrielli, Gomez and Munoz)

112. Physics of Masssive Neutrinos Milos 20-24/05/08 The event rate due to the spin Where f 0 A = a p +a n (isoscalar) and f 1 A = a p -a n (isovector) couplings at the nucleon level and Ω 0 (0), Ω 1 (0) the corresponding static spin matrix elements Where f 0 A = a p +a n (isoscalar) and f 1 A = a p -a n (isovector) couplings at the nucleon level and Ω 0 (0), Ω 1 (0) the corresponding static spin matrix elements The event rate is cast in the form: The event rate is cast in the form:

113. Physics of Masssive Neutrinos Milos 20-24/05/08 The factor f spin (A,m χ ) for A=127 (I) (The Dashed for threshold 10keV)

114. Physics of Masssive Neutrinos Milos 20-24/05/08 The factor f spin (A,m χ ) for A=19 (F) (The Dashed for threshold 10keV)

115. Physics of Masssive Neutrinos Milos 20-24/05/08 The constrained amplitude plane (a p,χ,a n,χ ) for the Α=127 system (arbitrary units), when they are relatively real.

116. Physics of Masssive Neutrinos Milos 20-24/05/08 The constrained (a p,χ,a n,χ ) plane: relative phase of the amplitudes δ=π/6 (-), δ=π/3 (-)and δ=π/2 (-)

117. Physics of Masssive Neutrinos Milos 20-24/05/08 The constrained (σ p,χ,σ n,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.

118. Physics of Masssive Neutrinos Milos 20-24/05/08 The constrained (σ p,χ,σ n,χ ) plane: relative phase of amplitudes δ=π/6 (-), δ=π/3 (-)and δ=π/2 (-)

119. Physics of Masssive Neutrinos Milos 20-24/05/08 The directional event rate The event rate in directional experiments is: The event rate in directional experiments is: R dir =(κ/2π)R 0 [1+cos(α-α m π)] R dir =(κ/2π)R 0 [1+cos(α-α m π)] R 0 is the average usual (non-dir) rate R 0 is the average usual (non-dir) rate α the phase of the Earth (as usual) α the phase of the Earth (as usual) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) α m is the shift in the phase of the Earth (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ/2π is the reduction factor (it depends on μ r and the direction of observation) κ and α m depend only slightly on SUSY κ and α m depend only slightly on SUSY

120. Physics of Masssive Neutrinos Milos 20-24/05/08 The Directional rate t dir in the case of 127 I for wimp mass of 100 GeV M-B distribution m=1)

121. Physics of Masssive Neutrinos Milos 20-24/05/08 The Directional rate t dir in the case of 127 I for wimp mass of 100 GeV M-B distribution m=2)

122. Physics of Masssive Neutrinos Milos 20-24/05/08 The parameter κ vs the polar angle in the case of A=127, right for m χ =100 GeV(M-B distribution n=1)

123. Physics of Masssive Neutrinos Milos 20-24/05/08 The parameter κvs the polar angle in the case of A=127, right for m χ =100 GeV(M-B distribution m=2)

124. Physics of Masssive Neutrinos Milos 20-24/05/08 Directional Rate: Modulation vs Θ m wimp =100 GeV,dotted  Φ=π, fine  Φ=0, thick  Φ=π/2,3π/2 (m=1)

125. Physics of Masssive Neutrinos Milos 20-24/05/08 Directional Rate: Modulation vs Θ m wimp =100 GeV,dotted  Φ=π, fine  Φ=0, thick  Φ=π/2,3π/2 (m=2)

126. Physics of Masssive Neutrinos Milos 20-24/05/08 The Differential Rate (Reminders)

127. Physics of Masssive Neutrinos Milos 20-24/05/08 The differential rate is proportional to the Function Ψ 0 (x); here n=1 (dotted  m WIMP 30GeV, thick  m WIMP 200GeV)

128. Physics of Masssive Neutrinos Milos 20-24/05/08 The differential rate is proportional to the Function Ψ 0 (x); here n=2 (dotted  m WIMP 30GeV, thick  m WIMP 200GeV) (dotted  m WIMP 30GeV, thick  m WIMP 200GeV)

129. Physics of Masssive Neutrinos Milos 20-24/05/08 The Differential Modulation Amplitude is proportional to H(x); Here n=1

130. Physics of Masssive Neutrinos Milos 20-24/05/08 The Modulation Amplitude H(x), n=2 Note a decrease by almost a factor of 5

131. Physics of Masssive Neutrinos Milos 20-24/05/08 Effect on Total Rates

132. Physics of Masssive Neutrinos Milos 20-24/05/08 Coupling of Dark Matter and Dark Energy (N. Tetradis, P.L. B 632 (2006) 463 Energy momentum tensor for DM Energy momentum tensor for DM diag(-ρ,p,p,p) with Eq. of state: p(r)=ρ(r) diag(-ρ,p,p,p) with Eq. of state: p(r)=ρ(r) Solution of Einstein Eqs  gravitational Potential Solution of Einstein Eqs  gravitational Potential such that: Φ ’ =(2/3)(1+κ 2 ) 1/r  such that: Φ ’ =(2/3)(1+κ 2 ) 1/r  matter rotational velocity:(υ 0 ) 2 =(2/3(1+κ 2 )) matter rotational velocity:(υ 0 ) 2 =(2/3(1+κ 2 ))  DM: MB ~ Exp[-υ 2 / (n υ 0 ) 2 ] ; n 2 =(1+κ 2 )  DM: MB ~ Exp[-υ 2 / (n υ 0 ) 2 ] ; n 2 =(1+κ 2 ) And escape velocity: And escape velocity: υ esc =2.84υ 0 (matter)  υ esc =2.84nυ 0 (DM) υ esc =2.84υ 0 (matter)  υ esc =2.84nυ 0 (DM) BEFORE WE EXPLOIT THIS EFFECT BEFORE WE EXPLOIT THIS EFFECT SOME REMINDERS ARE NEEDED SOME REMINDERS ARE NEEDED

133. Physics of Masssive Neutrinos Milos 20-24/05/08 Expression for the event rate Where: Where: m is the target mass m is the target mass ρ(0): the local WIMP density≈0.3 GeV/cm 3. ρ(0): the local WIMP density≈0.3 GeV/cm 3. σ S p,χ (σ spin p,χ ): the scalar (spin) WIMP-nucleon cross section. σ S p,χ (σ spin p,χ ): the scalar (spin) WIMP-nucleon cross section. It can be computed in a particle model. It can be computed in a particle model.

134. Physics of Masssive Neutrinos Milos 20-24/05/08 The Modulation Amplitude h for 127 I Q th =0  thick, Q th =5keV  fine Q th =10  dash; Eddington Theory

135. Physics of Masssive Neutrinos Milos 20-24/05/08 Conclusions: Experimental ambitions for Recoils

136. Physics of Masssive Neutrinos Milos 20-24/05/08 nucleon cross sections extracted from the data. R<2.3 events for 52.5 Kg-d Dotted  E th =10 keV, thick  E th =0 keV ( 19 F)

137. Physics of Masssive Neutrinos Milos 20-24/05/08 nucleon cross sections extracted from the data. R<2.3 events for 52.5 Kg-d Dotted  E th =10 keV, thick  E th =0 keV 127 I (left) 73 Ge (right)

138. Physics of Masssive Neutrinos Milos 20-24/05/08 The factor t for 127 I (coherent mode) Q th =0, 10 keV, Isothermal model (M-B), On top n=1, at the bottom n=2

139. Physics of Masssive Neutrinos Milos 20-24/05/08 The parameter t for 32 S Q th =0, Isothermal model (M-B), n=1 (Left), n=2 (right)

140. Physics of Masssive Neutrinos Milos 20-24/05/08 The parameter t for 32 S Q th =10 keV, Isothermal model (M-B), n=1 (Left), n=2 (right)

141. Physics of Masssive Neutrinos Milos 20-24/05/08 IIc: The angular power spectrum; θ =π/ ℓ black  WMAP3  ΛCDM red  WMAP1, orange  WMAP1+CBI

142. Physics of Masssive Neutrinos Milos 20-24/05/08 The dif. Rate; ξ=the cosine of the angle between the line of observation and the line of recoil (for the indicated polar angles).

143. Physics of Masssive Neutrinos Milos 20-24/05/08 Nuclear Recoil is after the WIMP- nucleus collision (WIMP: Weakly Interacting massive particle)

144. Physics of Masssive Neutrinos Milos 20-24/05/08 Cosmological Constraints in the (Ω,Λ) Plane (from S. Perlmutter)

145. Physics of Masssive Neutrinos Milos 20-24/05/08 Cosmological Constraints in the (Ω,Λ) Plane (From M. Kowalski et al, asrto-ph/08)

146. Physics of Masssive Neutrinos Milos 20-24/05/08 Slicing the Pie of the Cosmos WMAP3: Ω CDM =0.24±0.02, Ω Λ =0.72±0.04, Ω b =0.042±0.003 Confirming earlier data (Supernovae, WMAP1 etc):

147. Physics of Masssive Neutrinos Milos 20-24/05/08 Direct WIMP DETECTION - RECOIL

148. Physics of Masssive Neutrinos Milos 20-24/05/08 Current Limits on coherent proton cross section (astro-ph/0509259)

149. Physics of Masssive Neutrinos Milos 20-24/05/08 I:Measure v rs (r) and I(r); Assume ρ(r)=bI(r)  Φ(r,b)  v 2 lum (r,b)=r dΦ/dr  v 2 lum # v 2 rs

150. Physics of Masssive Neutrinos Milos 20-24/05/08 At still larger scales…

151. Physics of Masssive Neutrinos Milos 20-24/05/08 IIa: Luminosity-distance red shift Blue region: ΛCDM model WMAP3 prediction (68% CL) vs data

152. Physics of Masssive Neutrinos Milos 20-24/05/08 IIb: Relative abundance of elements in BBN η=10 -10  0.7  10 -31 g/cm -3 The relative The relative ( With respect ( With respect To hydrogen) To hydrogen) abundance abundance of elements of elements BBN (left) BBN (left) D/H=2.5x10 -5 D/H=2.5x10 -5 WMAP (right ) WMAP (right ) D/H=2.5x10 -5 D/H=2.5x10 -5 Notice the Notice the Ratio with Ratio with Respect Respect To the To the Critical Critical Density Density

153. Physics of Masssive Neutrinos Milos 20-24/05/08 IIc: Anisotropy in CMBR with WMAP3: astro-ph/0603449

154. Physics of Masssive Neutrinos Milos 20-24/05/08 IIc: The angular power spectrum Red line  best fit to ΛCDM; θ =π/ ℓ

155. Physics of Masssive Neutrinos Milos 20-24/05/08 The harmonic index ℓ as function of Ω m (Sanders, astro-ph/0402065). The dashed line  to WMAP data. Ω=1 is favored  Ω m ≈0.3

156. Physics of Masssive Neutrinos Milos 20-24/05/08 A typical Scatter Plot (Universal set of parameters) (Ceredeno, Gabrielli, Gomez and Munoz)

157. Physics of Masssive Neutrinos Milos 20-24/05/08 PRESENT VIEW OF THE COSMOS

158. Physics of Masssive Neutrinos Milos 20-24/05/08 Another view (ApPEC 19/10/06) Blue SUSY calculations (parameters on top)

159. Physics of Masssive Neutrinos Milos 20-24/05/08 nucleon cross sections extracted from the data. R<16 events per Kg-y Dotted  E th =10 keV, thick  E th =0 keV 127 I (left) 73 Ge (right) (mass: Log scale)

160. Physics of Masssive Neutrinos Milos 20-24/05/08 B1: K-B BOSON AS A WIMP for Δ=(m 2 /m 1 )-1=0.8

161. Physics of Masssive Neutrinos Milos 20-24/05/08 B2: R for K-K MAJORANA NEUTRINO (Higgs exchange, m h =500 GeV, Optimistic Structure of nucleon: Σ q f q =0.67)

162. Physics of Masssive Neutrinos Milos 20-24/05/08 B2: R for K-K MAJORANA NEUTRINO (Z-exchange) spin induced; 19 F

163. Physics of Masssive Neutrinos Milos 20-24/05/08 B2 : R for K-K MAJORANA NEUTRINO (Z-exchange) spin induced; 127 I