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Collaboration

The. Collaboration. 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

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Collaboration

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  1. The Collaboration 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,… • ΩΛ= 0.73, Ωbaryon= 0.04, Ωnon-baryon= 0.23 in terms of the critical density Ω0= 1

  3. ￭ Evidence for Cold Dark Matter: The Galaxy → • Rotation curves: velocity as a function of radial distance from the center of Galaxy Fg = GMm/r2 = Fc = m (vrot)2/r Vrot = (GM/r)1/2 • Inside Galaxy kernel (spherical): M = 4/3 π r3 ρ→vrot ~ r • Outside Galaxy kernel: M = constant → vrot~ 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

  4. What is it ? • The neutralino – χof supersymmetry could be an adequate candidate: ■ Neutral (and spin ½) ■ Massive (10 GeV/c2 – 1 TeV/c2) ■ R-parity ((-1)3B + L + 2S) conserved → stable (LSP) ■ Interact weakly with ordinary matter

  5. Cold Dark Matter: Neutralinos • Neutralino are distributed in the halo of Galaxy with local density ρ~ 0.3 GeV/cm3 -- suppose neutralinos dominate dark matter in the halo • Each neutralino follows its own orbit around the center of the Galaxy • Maxwellian distribution for χvelocity in Galaxy • P(v) = (1/π<v2>)3/2 v2 exp(-v / <v2>) dv • v = χ velocity, <v> = average quadratic velocity • <v> related to rotation velocity of Sun around the center of Galaxy • <v2> = (3/2) vrot2 = (3/2) (220 ± 20)2 km/s • <v> ~ 270 km/s

  6. Expected count rate vmax dR/dER = NT(ρϰ/mϰ)∫ vf(v) dσ/dER(v,ER)dv ρϰ = local dark matter density = 0.3 GeV/cm3 Mϰ= neutralino mass Vmax = escape velocity (~600 km/s) ER = v2μ2χA (1 –cos θ*)/mA ;μχA = mχmA/(mχ + mA) f(v) = velocity distribution of CDM –ϰ NT = number of target nuclei = NA/A dσ/dER = neutralino-nucleus cross section (for 19F, isotropic in CM) = dσSI/dER + dσSD/dER vf(v) induces an annual effect (5 to 6%) vmin

  7. Observable rate

  8. R0 is the total rate assuming zero momentum transfer AT = atomic mass of the target atoms ρχ= mass density of neutralinos σ= neutralino cross section <νχ> = relative average neutralino velocity <ER> = mean recoil energy = 2MAM2χ/(MA+Mχ)2 <νχ2> F2(ER) = nuclear form factor ~ 1 for light nucleus (19F) and for small momentum transfer For σ ≈ 1 pb only a fraction of event per kg and per day

  9. The PICASSO detector • Use superheated liquid droplets (C3F8, C4F10… 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

  10. The Superheated Droplets

  11. Droplets diameter distribution

  12. Principle of Operation • When a C or F-nucleus recoils in the superheated medium, an energy ER 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

  13. The bubble will grow irreversibly if the energy deposited exceeds a critical energy Ec = (16π/3)σ3/(pi – pe)2 pi = internal pressure (vapour pressure in the bubble) pe=externaly applied pressure σ= the surface tensionσ(T) = σ0(Tc-T)/(Tc-T0) where Tc is the critical temperature of the gas, σ0 is the surface tension at a reference temperature T0, usually the boiling temperature Tb. Tb and Tc are depending on the gas mixture. Tb = -19.2 C, Tc = 92.6 C for a SBD-100 detector (loaded with a mixture of fluorocarbons: 50% C4F10 + 50% C3F8) Tb = -1.7 C, Tc = 113.3 C for SBD-1000 detectors (loaded with 100% C4F10)

  14. Bubble formation and explosion will occur when a minimum deposited energy, ERth, exceeds the threshold value Ec within a distance: lc = aRc, where the critical radius Rc given by Rc= 2 σ(T)/(pi - pe) If dE/dx is the mean energy deposited per unit distance→ the energy deposited along lc is Edep = dE/dx lc • The condition to trigger a liquid-to-vapour transition is Edep ≥ ERth Not all deposited energy will trigger a transition → efficiency factor η = Ec/ERth(2<η<6%)

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

  16. Detection of CDM with superheated liquids • 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/c2 up to 1 TeV/c2) • Recoil energy of a nucleus of Mass MN hit by χ with kinetic energy E = ½ Mχv2 scattered at angle θ (CM): ER = [MχMN/(Mχ+ MN)2] 2E (1 – cos θ) for Mχ~ 10 –1000GeV/c2 ( β~ 10 -3) gives recoil energy ER~ 0 → 100 keV i.e thesame recoil energyobtained from neutrons of low energy with freon-like droplets (C3F8, C4 F10, etc) – elastic scattering on 19F and 12C if En< 1 MeV

  17. Results for 200 keV Neutrons

  18. Results for 400 keV Neutrons

  19. Neutron Threshold Energies

  20. The probability that a recoil nucleus at an energy near threshold will generate an explosive droplet-Bubble transition is: • 0 if ENR (or Edep)< ENR,th • increases gradually up to1 ifENR (or Edep)> ENR,th • The probability is: P(Edep,ENR,th)=1 – exp(-b[Edep- ENR,th]/ ENR,th) bis to be determined experimentally

  21. Count Rates for 19F and 12C • For En < 500 keV, collisions with 19F and 12C are elastic and isotropic (dnN/dENR~ 1) →εN(En,T) = 1-ENth/En- (1-exp(-b[E-ENth(T)]/ENth(T))ENth(T)/bEn) • b, ENth(T), εN(En,T)are obtained from fitting the measured count rate (per sec) as a function of the neutron energy for various temperatures R(En,T) = Φ(En) [NAm/A] ∑iNiσin(En)εi(En,T) Φ(En) = the flux of neutrons of energy En NA = Avogadro number, m = active mass of the detector, A = molecular mass of the fluid Ni = atomic number density of species i in the liquid σin(En) = neutron cross section

  22. Fit gives an exponential temperature dependence for ENth (T) and b = 1.0 ± 0.1 (εN(En,T) obtained)

  23. • The minimum detectable recoil energy for 19F is extracted from ENth(T) The interaction of neutralino with the superheated carbo-fluorates is dominated by the spin-dependent cross section on19F EFR,th(T) = 0.19EFth = 1.55 102 (keV) exp[-(T- 20o)/5.78o] The phase transition probability as a function of the recoil energy deposited by a19F nucleus is At T = 40o C, EFR,th(T) = 4.87 keV (α = 1.0) → P(ER, EFR,th) = 1 – exp[-1.0(ER- 4.87 keV)/4.87 keV] Sensitivity curve shows detectors 80% efficient at 400C for ER≥35 keV and at 450C for ER ≥15 keV recoils

  24. Neutralino detection efficiency • Neutralino detection efficiency ε(Mχ,T) obtained from - Combining 19F recoil spectra from χ-interaction: dR/dER ≈ 0.75 (R0/<ER>)e -0.56ER/<ER> • The transition probability P(ER,ENR,th)=1 – exp(-[1.0±0.1][ER- ENR,th]/ ENR,th) with EFR,th(T) = 1.55 102 (keV) exp[-(T- 20o)/5.78o]

  25. The minimum detectable recoil energy for 19F is extracted from ENth(T) → sensitivity vs recoil energy

  26. Recoil Spectra of Neutralino

  27. Counting efficiency of neutralino

  28. Dark Matter Counting Efficiency Efficiency Mass (GeV)

  29. The Backgrounds

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

  31. α- background (measured from 6oC to 50oC) 241Am spiked 1 litre detectors ■ SBD-1000 ● SBD-100 Sensitivity for U/Th contamination !(mainly from CsCl) S ≡ reduced superheat Tb=boiling temp Tc=critical temp

  32. Sensitivity to  - and X-rays BD100 Efficiency curve fitted over more than 6 orders of magnitude by sigmoid function: T0 400 C,   0.90C max= 0.7  0.1% In plateau region droplets are fully efficient to MeV ’s and 5.9 keV X-rays

  33. SBD-1000 sensitivity to 

  34. 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

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

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

  37. Type of interaction of χ with ordinary matter • The elastic cross section of neutralino scattering off nuclei has the form: σA = 4 GF2 [MχMA/(Mχ+MA)]2 CA GF is the Fermi constant, Mχ and MA the mass of χ and detector nucleus Two types: coherent or spin independent (C) and spin dependent (SD) CA = CASI+ CASD i) Coherent: σA(C) ~ A2 >> for heavy nuclei (A > 50) CASI= (1/4π)[ Z fp + (A-Z)fn ]2 with fp and fn neutralino coupling to the nucleon

  38. ii) Spin Dependent: σA(SD) CASD = (8/π)[ ap <Sp> + an <Sn>]2 (J + 1)/J with <Sp> and <Sn> = expectation values of the p and n spin in the target nucleus ap and anneutralino coupling to the nucleon J is the total nuclear spin <Sp> and <Sn> are nuclear model dependent

  39. From the χ-nucleus cross section limit, σAlim , directly set by the experiment, limits on χ-proton (σplim (A) ) or χ-neutron (σnlim (A) ) cross sections, are given by assuming that all events are due to χ-proton and χ-neutron elastic scatterings in the nucleus: σplim (A) = σAlim (μp2/μA2) Cp/Cp(A) and σnlim (A) = σAlim (μn2/μA2) Cn/Cn(A) µp and µA are the χ-nucleon and χ-nucleus reduced masses (mass difference between neutron and proton is neglected) Cp(A) and Cn(A) are the proton and neutron contributions to the total enhancement factor of nucleus A Cp and Cn are the enhancement factors of proton and neutron themselves

  40. The ratio Rp≡Cp(F)/ Cp = 0.778 and Rn≡Cn(F)/ Cn = 0.0475 from the values <Sp> = 0.441 and <Sn> = -0.109 → A.F.Pacheco and D.D. Strottman, Phys. Rev. D40 (1989) 2131 Cp(F) and Cn(F) factors are related to ap and an couplings: Ci(F) = (8/π)ai2<Si>2 (J+1)/J

  41. Model dependence of enhancement factors Rp≡Cp(F)/ Cp Rn≡Cn(F)/ Cn

  42. Enhancement factors (favors 19F)[From Pacheco and Strottman]

  43. limit of σp = 1.3 pb for mχ= 29GeV/c2

  44. Limit of σn = 21.5 pb for mχ= 29GeV/c2

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

  46. If one takes into account: σplim(A)/σnlim(A) = Cp/Cn CAn/Cap = <Sn>2/ <Sp>2 One finds two lines: ap≤ - <Sn>/<Sp>an + (π/24GF2µp2σplim(A))1/2 ap≤ - <Sn>/<Sp>an -(π/24GF2µp2σplim(A))1/2 Note: CASD = K [ ap <Sp> + an <Sn>]2 Γ = B2 – 4AC = K24<Sp>2<Sn>2-K24<Sp>2<Sn>2=0

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