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,…

• ΩΛ= 0.73, Ω baryon= 0.04, Ωnon-baryon= 0.23

in terms of the critical density Ω0= 1

￭ 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

• What is it ?

• The neutralino – χ of 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

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 χ velocity 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) vrot

2 = (3/2) (220 ± 20)2 km/s– <v> ~ 270 km/s

Expected count ratedR/dER = NT(ρϰ/mϰ)∫ vf(v) dσ/dER(v,ER)dv ρϰ = local dark matter density = 0.3 GeV/cm3

Mϰ = neutralino massVmax = escape velocity (~600 km/s)ER = v2 μ2

χA (1 –cos θ*)/mA ; μχA = mχmA/(mχ + mA)f(v) = velocity distribution of CDM –ϰNT = 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

vmax

Observable rate

skmforccforcc

eEFERcdEdR

spectrumcoil

ectorthetospecificTEEP

dEdEdRTEEPTMR

E

E

EEcR

RR

RThR

RescERRThRobs

RR

/24456.075.001

)(/

Re

det))(,(

),(/))(,(),,(

21

21

/201

0

2

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 <νχ

2>

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

)230)(

3.0)((403)( 13

110

kmsGeVcmpbMAdkgcountsR

T

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

The Superheated Droplets

Droplets diameter distribution

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

• 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 tension σ(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)

• 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%)

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/c2 up to 1 TeV/c2)

• Recoil energy of a nucleus of Mass MN hit by χ with kinetic energy E = ½ Mχ v2 scattered at angle θ (CM):

ER = [MχMN/(Mχ + MN)2] 2E (1 – cos θ)

for Mχ ~ 10 –1000 GeV/c2 ( β ~ 10 -3 )

gives recoil energy ER ~ 0 → 100 keV

i.e the same recoil energy obtained from neutrons of low energy with freon-like droplets (C3F8, C4 F10, etc) – elastic scattering on 19F and 12C if En < 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 EN

R (or Edep) < ENR,th

– increases gradually up to 1 if ENR (or Edep) > EN

R,th

• The probability is:

P(Edep,ENR,th)= 1 – exp(-b[Edep- EN

R,th]/ ENR,th)

b is to be determined experimentally

• For En < 500 keV, collisions with 19F and 12C are elastic and isotropic (dnN/dEN

R~ 1)

→ εN(En,T) = 1-ENth/En- (1-exp(-b[E-EN

th(T)]/ENth(T))EN

th(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] ∑i Niσin(En)εi(En,T)

Φ(En) = the flux of neutrons of energy EnNA = Avogadro number, m = active mass of the detector, A = molecular mass of the fluidNi = atomic number density of species i in the liquidσi

n(En) = neutron cross section

Count Rates for 19F and 12C

Fit gives an exponential temperature dependence for EN

th (T) and b = 1.0 ± 0.1 (εN(En,T) obtained)

• The minimum detectable recoil energy for 19F is extracted from EN

th(T) The interaction of neutralino with the superheated carbo-fluorates is

dominated by the spin-dependent cross section on19F EF

R,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 a 19F nucleus is

At T = 40o C, EFR,th(T) = 4.87 keV (α = 1.0)

→ P(ER, EF

R,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

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- EN

R,th]/ ENR,th)

with

EFR,th(T) = 1.55 102 (keV) exp[-(T- 20o)/5.78o]

RR

RThR dEdEdRTEEP

RTM ))(,(175.0),( 0

0

The minimum detectable recoil energy for 19F is extracted from EN

th(T) → sensitivity vs recoil energy

Recoil Spectra of Neutralino

Counting efficiency of neutralino

Dark Matter Counting EfficiencyEf

ficie

ncy

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 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

Sensitivity to - and X-rays

BD100

Efficiency curve fitted over more than 6 orders of magnitude by sigmoid function:

)exp(1 0

max)(

TTT

T0 400 C, 0.90Cmax= 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

vMTM

constdgR F

),(.)( 11

efficiency (T) 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: σA = 4 GF

2 [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 + CA

SD

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

• 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 an neutralino coupling to the nucleon

J is the total nuclear spin

<Sp> and <Sn> are nuclear model dependent

• From the χ-nucleus cross section limit, σA lim , directly set by the experiment, limits on χ-proton (σp

lim (A) ) or χ-neutron (σn lim (A) ) cross sections, are given by assuming that all events are due to χ-proton and χ-neutron elastic scatterings in the nucleus:

σp

lim (A) = σA lim (μp2/μA

2) Cp/Cp(A)

and σnlim (A) = σA lim (μn

2/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

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

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

<Sp> <Sn> Rp Rn Ref. 0.441 -0.109 0.778

0.0475PachecoStrottman

0.368 -0.001 0.542 1x10-6 EOGMgA/gV=1.25

0.415 -0.047 0.689 0.0088

EOGMgA/gV=1.00

0.4751

-0.0087

0.903 0.0003

Divari et al.PRC61(2000) 054612-1

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

Nucleus J <Sp> <Sn> Cp(A)/Cp Cn(A)/Cn

19F 1/2 0.441 -0.109 7.78x10-1

4.75x10-2

23Na 3/2 0.248 0.020 1.37x10-1

8.89x10-4

27Al 5/2 -0.343 0.030 2.20x10-1

1.68x10-3

29Si 1/2 -0.002 0.130 1.60x10-5

6.76x10-2

35Cl 3/2 -0.083 0.004 1.53x10-2

3.56x10-5

73Ge 9/2 0.030 0.378 1.47x10-3

2.33x10-1

127I 5/2 0.309 0.075 1.78x10-1

1.05x10-2

129Xe 1/2 0.028 0.359 3.14x10-3

5.16x10-1

131Xe 3/2 -0.009 -0.227 1.80x10-4

1.15x10-1

limit of σp = 1.3 pb for mχ= 29GeV/c2

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

ap-an planeFrom 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)

2

2

22

2

)lim()lim( 24

p

pp

pFA

n

nA

p

p

mmmm

Gaa

• If one takes into account: σp

lim(A)/σnlim(A) = Cp/Cn CA

n/Cap

= <Sn>2/ <Sp>2

One finds two lines:

ap ≤ - <Sn>/<Sp>an + (π/24GF2µp

2σplim(A))1/2

ap ≤ - <Sn>/<Sp>an - (π/24GF2µp

2σplim(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

Example

σχp = 1 pb (= σp lim(F)) and Mχ = 50 GeV/c2

Which corresponds to σχF = 160 pb

► σχn = 16.4 pb (= σn lim(F))

►two exclusion boundary limits:

ap = 1.71 + 0.25 an

and

ap = -1.71 + 0.25 an

• 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

PICASSO2006

• PICASSO shows that the superheated droplet technique works.

•Data from 3 detectors with 19.4±1.0 g of active mass (19F) 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 σχp and 21.5 pb for σχn for m χ = 29 GeV/c2

• 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