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

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

￭ 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

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

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

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

Observable rate

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

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

The Superheated Droplets

Droplets diameter distribution

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

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 = C, T c = 92.6 C for a SBD-100 detector (loaded with a mixture of fluorocarbons: 50% C 4 F % C 3 F 8 ) T b = -1.7 C, T c = C for SBD-1000 detectors (loaded with 100% C 4 F 10 )

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%)

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

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 ~ ) 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

Results for 200 keV Neutrons

Results for 400 keV Neutrons

Neutron Threshold Energies

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

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

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

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 = (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 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

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) = (keV) exp[-(T- 20 o )/5.78 o ]

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

Recoil Spectra of Neutralino

Counting efficiency of neutralino

Dark Matter Counting Efficiency Efficiency Mass (GeV)

The Backgrounds

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

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

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

SBD-1000 sensitivity to 

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

Present Picasso Installation at SNO Picasso detectors are in here!

Neutralino response efficiency (T)  - response recoil spectra

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

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

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

The ratio R p ≡ C p(F) / C p = and R n ≡C n(F) / C n = from the values = and = → 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

Model dependence of enhancement factors R p ≡ C p(F) / C p R n ≡C n(F) / C n R p R n Ref Pacheco Strottman x10 -6 EOGM g A /g V = EOGM g A /g V = Divari et al. PRC61(2000)

Enhancement factors (favors 19 F) [ From Pacheco and Strottman] Nucleus J C p(A) /C p C n(A) /C n 19 F 1/ x x Na 3/ x x Al 5/ x x Si 1/ x x Cl 3/ x x Ge 9/ x x I 5/ x x Xe 1/ x x Xe 3/ x x10 -1

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

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

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 - / = ( = and = ) :

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 K =0

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 = a n and a p = a n

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 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

PICASSO 2006

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