1. Collaboration The Université de Montréal: F. Aubin, M. Barnabé- Heider, M. Di Marco, P Doane, M.-H. Genest, R. Gornea, R. Guénette, C. Leroy, L., Lessard, J.P. Martin, U. Wichoski, V. Zacek Queens University: K. Clark, C. Krauss, A.J. Noble IEAP-Czech Technical University in Prague: S. Pospisil, J. Sodomka, I. Stekl University of Indiana, South Bend: E. Behnke, W. Feigherty, I. Levine, C. Muthusi Bubble Technology Industries: R. Noulty, S. Kanagalingam

2. Introduction ￭ Evidence for Cold dark matter (CDM): the Universe → Cosmic background radiation: WMAP,… Ω Λ = 0.73, Ω baryon = 0.04, Ω non-baryon = 0.23 in terms of the critical density Ω 0 = 1

4. ￭ Evidence for Cold Dark Matter: The Galaxy → Rotation curves: velocity as a function of radial distance from the center of Galaxy F g = GMm/r 2 = F c = m (v rot ) 2 /r V rot = (GM/r) 1/2 Inside Galaxy kernel (spherical): M = 4/3 π r 3 ρ → v rot ~ r Outside Galaxy kernel: M = constant → v rot ~ 1/√r Rotation curve measured (using Doppler shift) → v(r) = constant for large r → M~r => existence of enormous mass extending far beyond the visible region, invisible optically

6. What is it ? The neutralino – χ of supersymmetry could be an adequate candidate: ■ Neutral (and spin ½) ■ Massive (10 GeV/c 2 – 1 TeV/c 2 ) ■ R-parity ((-1) 3B + L + 2S ) conserved → stable (LSP) ■ Interact weakly with ordinary matter

7. Cold Dark Matter: Neutralinos Neutralino are distributed in the halo of Galaxy with local density ρ ~ 0.3 GeV/cm 3 -- suppose neutralinos dominate dark matter in the halo Each neutralino follows its own orbit around the center of the Galaxy Maxwellian distribution for χ velocity in Galaxy –P(v) = (1/π ) 3/2 v 2 exp(-v / ) dv –v = χ velocity, = average quadratic velocity – related to rotation velocity of Sun around the center of Galaxy – = (3/2) v rot 2 = (3/2) (220 ± 20) 2 km/s – ~ 270 km/s

8. Expected count rate dR/dE R = N T (ρ ϰ /m ϰ )∫ vf(v) dσ/dE R (v,E R )dv ρ ϰ = local dark matter density = 0.3 GeV/cm 3 M ϰ = neutralino mass V max = escape velocity (~600 km/s) E R = v 2 μ 2 χA (1 –cos θ*)/m A ; μ χA = m χ m A /(m χ + m A ) f(v) = velocity distribution of CDM –ϰ N T = number of target nuclei = N A /A dσ/dE R = neutralino-nucleus cross section (for 19 F, isotropic in CM) = dσ SI /dE R + dσ SD /dE R vf(v) induces an annual effect (5 to 6%) v min v max

9. Observable rate

10. R 0 is the total rate assuming zero momentum transfer A T = atomic mass of the target atoms ρ χ = mass density of neutralinos σ= neutralino cross section = relative average neutralino velocity = mean recoil energy = 2M A M 2 χ /(M A +M χ ) 2 F 2 (E R ) = nuclear form factor ~ 1 for light nucleus ( 19 F) and for small momentum transfer For σ ≈ 1 pb only a fraction of event per kg and per day

11. The PICASSO detector Use superheated liquid droplets (C 3 F 8, C 4 F 10 … active medium) Droplets (at temperature T > Tb) dispersed in an aqueous solution subsequently polymerized (+ heavy salt (CsCl) to equalize densities of droplets-solution) By applying an adequate pressure, the boiling temperature can be raised→ allowing the emulsion to be kept in a liquid state. Under this external pressure, the detectors are insensitive to radiation. By removing the external pressure, the liquid becomes sensitive to radiation. Bubble formation occurs through liquid-to-vapour phase transitions, triggered by the energy deposited by nuclear recoil Bubble can be recompressed into droplet after each run

12. The Superheated Droplets

13. Droplets diameter distribution

14. Principle of Operation When a C or F-nucleus recoils in the superheated medium, an energy E R is deposited through ionization process in the liquid WIMPS are detected through the energy deposited by recoiling struck nuclei A fraction of that energy is transformed into heat A droplet starts to grow because of the evaporation initiated by that heat; as it grows, the bubble does work against the external pressure and against the surface tension of the liquid

15. The bubble will grow irreversibly if the energy deposited exceeds a critical energy E c = (16π/3)σ 3 /(p i – p e ) 2 p i = internal pressure (vapour pressure in the bubble) p e = externaly applied pressure σ = the surface tension σ(T) = σ 0 (T c -T)/(T c -T 0 ) where T c is the critical temperature of the gas, σ 0 is the surface tension at a reference temperature T 0, usually the boiling temperature Tb. Tb and T c are depending on the gas mixture. T b = -19.2 C, T c = 92.6 C for a SBD-100 detector (loaded with a mixture of fluorocarbons: 50% C 4 F 10 + 50% C 3 F 8 ) T b = -1.7 C, T c = 113.3 C for SBD-1000 detectors (loaded with 100% C 4 F 10 )

16. Bubble formation and explosion will occur when a minimum deposited energy, E Rth, exceeds the threshold value E c within a distance: l c = aR c, where the critical radius R c given by R c = 2 σ(T)/(p i - p e ) If dE/dx is the mean energy deposited per unit distance→ the energy deposited along l c is E dep = dE/dx l c The condition to trigger a liquid-to-vapour transition is E dep ≥ E Rth Not all deposited energy will trigger a transition → efficiency factor η = E c /E Rth (2<η<6%)

17. Piezoelectric sensor Frequency spectrum Droplet burst A 1-litre Picasso Detector

18. Nuclear recoil thresholds can be obtained in the same range for neutrons of low energy (e.g. from few keV up to a few 100s keV) & massive neutralinos (10 GeV/c 2 up to 1 TeV/c 2 ) Recoil energy of a nucleus of Mass M N hit by χ with kinetic energy E = ½ Mχ v 2 scattered at angle θ (CM): E R = [M χ M N /(M χ + M N ) 2 ] 2E (1 – cos θ) for M χ ~ 10 –1000 GeV/c 2 ( β ~ 10 -3 ) gives recoil energy E R ~ 0 → 100 keV i.e the same recoil energy obtained from neutrons of low energy with freon-like droplets (C 3 F 8, C 4 F 10, etc) – elastic scattering on 19 F and 12 C if E n < 1 MeV Detection of CDM with superheated liquids

19. Results for 200 keV Neutrons

20. Results for 400 keV Neutrons

21. Neutron Threshold Energies

22. The probability that a recoil nucleus at an energy near threshold will generate an explosive droplet-Bubble transition is: –0 if E N R (or E dep ) < E N R,th –increases gradually up to 1 if E N R (or E dep ) > E N R,th The probability is: P(E dep,E N R,th )= 1 – exp(-b[E dep - E N R,th ]/ E N R,th ) b is to be determined experimentally

23. For E n < 500 keV, collisions with 19 F and 12 C are elastic and isotropic (dn N /dE N R ~ 1) → ε N (E n,T) = 1-E N th /E n - (1-exp(-b[E-E N th (T)]/E N th (T))E N th (T)/bE n ) b, E N th (T), ε N (E n,T) are obtained from fitting the measured count rate (per sec) as a function of the neutron energy for various temperatures R(E n,T) = Φ(E n ) [N A m/A] ∑ i N i σ i n (E n )ε i (E n,T) Φ(E n ) = the flux of neutrons of energy E n N A = Avogadro number, m = active mass of the detector, A = molecular mass of the fluid N i = atomic number density of species i in the liquid σ i n (E n ) = neutron cross section Count Rates for 19 F and 12 C

24. Fit gives an exponential temperature dependence for E N th (T) and b = 1.0 ± 0.1 (ε N (E n,T) obtained)

25. The minimum detectable recoil energy for 19 F is extracted from E N th (T) The interaction of neutralino with the superheated carbo- fluorates is dominated by the spin-dependent cross section on 19 F E F R,th (T) = 0.19E F th = 1.55 10 2 (keV) exp[-(T- 20 o )/5.78 o ] The phase transition probability as a function of the recoil energy deposited by a 19 F nucleus is At T = 40 o C, E F R,th (T) = 4.87 keV (α = 1.0) → P(E R, E F R,th ) = 1 – exp[-1.0(E R - 4.87 keV)/4.87 keV] Sensitivity curve shows detectors 80% efficient at 40 0 C for E R ≥35 keV and at 45 0 C for E R ≥15 keV recoils

26. Neutralino detection efficiency Neutralino detection efficiency ε(M χ,T) obtained from - Combining 19F recoil spectra from χ-interaction : dR/dE R ≈ 0.75 (R 0 / )e -0.56E R / -The transition probability P(E R,E N R,th )= 1 – exp(-[1.0±0.1][E R - E N R,th ]/ E N R,th ) with E F R,th (T) = 1.55 10 2 (keV) exp[-(T- 20 o )/5.78 o ]

27. The minimum detectable recoil energy for 19 F is extracted from E N th (T) → sensitivity vs recoil energy

28. Recoil Spectra of Neutralino

29. Counting efficiency of neutralino

30. Dark Matter Counting Efficiency Efficiency Mass (GeV)

31. The Backgrounds

32. background count rate as a function of the detector fabrication date [ from no purification before fabrication until all ingredients were purified]

33. α- background (measured from 6 o C to 50 o C) 241 Am spiked 1 litre detectors ■ SBD-1000 ● SBD-100 Sensitivity for U/Th contamination !(mainly from CsCl) S ≡ reduced superheat T b =boiling temp T c =critical temp

34. Sensitivity to  - and X-rays BD100 Efficiency curve fitted over more than 6 orders of magnitude by sigmoid function: T 0  40 0 C,   0.9 0 C  max = 0.7  0.1% In plateau region droplets are fully efficient to MeV  ’s and 5.9 keV X-rays

35. SBD-1000 sensitivity to 

36. PICASSO at SNO Detectors installed at SNO consisted of 3 1-litre detectors produced at BTI with containers specially designed for the setup at SNO (low radon emanation). Since the Fall of 2002 Picasso has a setup in the water purification gallery of the SNO underground facility at a depth of 6,800 feet ~20g of active mass Main advantage of SNO: very low particle background

37. Present Picasso Installation at SNO Picasso detectors are in here!

39. Neutralino response efficiency (T)  - response recoil spectra

40. Type of interaction of χ with ordinary matter The elastic cross section of neutralino scattering off nuclei has the form: σ A = 4 G F 2 [M χ M A /(M χ +M A )] 2 C A G F is the Fermi constant, M χ and M A the mass of χ and detector nucleus Two types: coherent or spin independent (C) and spin dependent (SD) C A = C A SI + C A SD i) Coherent: σ A (C) ~ A 2 >> for heavy nuclei (A > 50) C A SI = (1/4π)[ Z f p + (A-Z)f n ] 2 with f p and f n neutralino coupling to the nucleon

41. ii) Spin Dependent: σ A (SD) C A SD = (8/π)[ a p + a n ] 2 (J + 1)/J with and = expectation values of the p and n spin in the target nucleus a p and a n neutralino coupling to the nucleon J is the total nuclear spin and are nuclear model dependent

42. From the χ-nucleus cross section limit, σ A lim, directly set by the experiment, limits on χ-proton (σ p lim (A) ) or χ- neutron (σ n lim (A) ) cross sections, are given by assuming that all events are due to χ-proton and χ-neutron elastic scatterings in the nucleus: σ p lim (A) = σ A lim (μ p 2 /μ A 2 ) C p /C p(A) and σ n lim (A) = σ A lim (μ n 2 /μ A 2 ) C n /C n(A) µ p and µ A are the χ-nucleon and χ-nucleus reduced masses (mass difference between neutron and proton is neglected) C p(A) and C n(A) are the proton and neutron contributions to the total enhancement factor of nucleus A C p and C n are the enhancement factors of proton and neutron themselves

43. The ratio R p ≡ C p(F) / C p = 0.778 and R n ≡C n(F) / C n = 0.0475 from the values = 0.441 and = -0.109 → A.F.Pacheco and D.D. Strottman, Phys. Rev. D40 (1989) 2131 C p(F) and C n(F) factors are related to a p and a n couplings: C i(F) = (8/π)a i 2 2 (J+1)/J

44. Model dependence of enhancement factors R p ≡ C p(F) / C p R n ≡C n(F) / C n R p R n Ref. 0.441 -0.109 0.778 0.0475 Pacheco Strottman 0.368 -0.001 0.542 1x10 -6 EOGM g A /g V =1.25 0.415 -0.047 0.689 0.0088EOGM g A /g V =1.00 0.4751 -0.0087 0.903 0.0003Divari et al. PRC61(2000) 054612-1

45. Enhancement factors (favors 19 F) [ From Pacheco and Strottman] Nucleus J C p(A) /C p C n(A) /C n 19 F 1/2 0.441 -0.109 7.78x10 -1 4.75x10 -2 23 Na 3/2 0.248 0.020 1.37x10 -1 8.89x10 -4 27 Al 5/2 -0.343 0.030 2.20x10 -1 1.68x10 -3 29 Si 1/2 -0.002 0.130 1.60x10 -5 6.76x10 -2 35 Cl 3/2 -0.083 0.004 1.53x10 -2 3.56x10 -5 73 Ge 9/2 0.030 0.378 1.47x10 -3 2.33x10 -1 127 I 5/2 0.309 0.075 1.78x10 -1 1.05x10 -2 129 Xe 1/2 0.028 0.359 3.14x10 -3 5.16x10 -1 131 Xe 3/2 -0.009 -0.227 1.80x10 -4 1.15x10 -1

47. limit of σ p = 1.3 pb for mχ= 29GeV/c 2

48. Limit of σ n = 21.5 pb for mχ= 29GeV/c 2

49. a p -a n plane From the χ-proton and χ-neutron elastic scattering cross section limits one finds the allowed region in the a p -a n plane from the condition: relative sign inside the square determined by the sign of / In our experiment, a p and a n are constrained, in the a p -a n plane, to be inside a band defined by two parallel lines of slope - / = 0.247. ( = 0.441 and = -0.109) :

50. If one takes into account: σ p lim(A) /σ n lim(A) = C p /C n C A n /C a p = 2 / 2 One finds two lines: a p ≤ - / a n + (π/24G F 2 µ p 2 σ p lim(A) ) 1/2 a p ≤ - / a n - (π/24G F 2 µ p 2 σ p lim(A) ) 1/2 Note: C A SD = K [ a p + a n ] 2 Γ = B 2 – 4AC = K 2 4 2 2 -K 2 4 2 2 =0

51. Example σ χp = 1 pb (= σ p lim(F) ) and Mχ = 50 GeV/c 2 Which corresponds to σ χF = 160 pb ► σ χn = 16.4 pb (= σ n lim(F) ) ► two exclusion boundary limits: a p = 1.71 + 0.25 a n and a p = -1.71 + 0.25 a n

53. 4.5 L Detector Modules: 32 Total net detector volume: ~ 150 L Total active mass (C4F10): ~ 2 kg (each detector loaded with 60 g of active mass bubble size around 80-100 µm) Acoustic channels: 288 (9 channels per detector) 8 independent TPCS To be installed at the same site (SNO underground Lab) Data taking starts in November 2005 Expected exposure: ~280 Kg∙day (Six- month period) PICASSO NEXT PHASE

55. PICASSO 2006

56. PICASSO shows that the superheated droplet technique works. Data from 3 detectors with 19.4±1.0 g of active mass ( 19 F) installed underground at SNO for an exposure of 1.98 ±0.19 kgd. No positive evidence for χ induced nuclear recoil Upper limit of 1.3 pb for σ χp and 21.5 pb for σ χ n for m χ = 29 GeV/c 2 next step: 2 kg active mass by early 2006 (32 modules of 4.5 litres each, Expected exposure: ~280 Kg∙day (Six-month period)) clean room facility for production of larger modules ready at Montreal (LADD) purification work to reduce alpha- background ongoing envisage 10 kg to 100 kg during 2005/6 → best limit to be achieved (could reach ϰ detection zone) Conclusions