First limits on nuclear recoil events from the ZEPLIN I galactic dark matter detector

Astroparticle Physics 23 (2005) 444–462

www.elsevier.com/locate/astropart

First limits on nuclear recoil events from the ZEPLIN Igalactic dark matter detector

UK Dark Matter Collaboration

G.J. Alner , H. Araujo , G.J. Arnb a

a b ison a, J.C. Barton d,z, A. Bewick b,C. Bungau , B. Camanzi , M.J. Carson c, D. Davidge b, J.V.Dawson b,G.J. Davies b, J.C. Davies c, T. Durkin a, T. Gamble c, S.P. Hart a,

R.J. Hollingworth c, G.J. Homer a, A.S. Howard b, I. Ivaniouchenkov a,b,W.G. Jones b, M.K. Joshi b, V.A. Kudryavtsev c, T.B. Lawson c, V. Lebedenko b,J.D. Lewin a, P.K. Lightfoot c, I. Liubarsky b, M.J. Lehner c,1, R. Luscher a,b,J.E. McMillan c, B. Morgan c, A. Nicholls a, G. Nicklin c, S.M. Paling c,

R.M. Preece a, J.W. Roberts a,c, M. Robinson c, J.J. Quenby b, N.J.T. Smith a,*,P.F. Smith a, N.J.C. Spooner c, T.J. Sumner b, D.R. Tovey c

a Particle Physics Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, UKb Blackett Laboratory, Imperial College London, London SW7 2BZ, UK

c Department of Physics and Astronomy, University of Sheffield, Hounsfield Road, Sheffield S3 7RH, UKd Department of Physics, University of London Queen Mary, London E1 4NS, UK

Received 14 June 2004; received in revised form 1 February 2005; accepted 5 February 2005

Available online 16 March 2005

Abstract

We report first results from the ZEPLIN I dark matter detector, based on measurement of scintillation pulse shapes

in a liquid xenon target of 3.2 kg fiducial mass. Neutron calibration shows nuclear recoil pulses to have a time con-

stant ffi 0.5 that of gamma and beta background events. The detector is located in the 2800 mwe depth UK BoulbyMine, and is surrounded by a liquid scintillator Compton veto and passive lead shielding. Three runs totaling

293 kg d fiducial exposure yielded data consistent with a single population of background pulses, with no significant

0927-6505/$ - see front matter � 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.astropartphys.2005.02.004

* Corresponding author. Tel.: +44 1235 445151; fax: +44 1234 446733.

E-mail address: [email protected] (N.J.T. Smith).z Deceased.1 Present address: U. Pennsylvania, Philadelphia, PA 19104, USA.

mailto:[email protected]

G.J. Alner et al. / Astroparticle Physics 23 (2005) 444–462 445

low energy population of shorter pulses. From the 90% confidence limit on the latter a limit is derived on the spin-inde-

pendent WIMP-nucleon cross-section versus particle mass with a minimum at 1.1 · 10�6 pb.� 2005 Elsevier B.V. All rights reserved.

PACS: 29.40.Mc; 14.80.Ly; 23.60.+e; 95.35.+d; 95.30.Cq

Keywords: Dark matter; WIMPs; Scintillation detectors; Liquid xenon; Pulse shape analysis

1. Introduction

Galaxies and clusters are dominated by non-

luminous matter. Recent astrophysical evidence

has shown with increasing precision that the

majority of the dark matter in the universe is

non-baryonic [1–3]. Experiments are in progress

in a number of world underground sites to search

for signals which would result from weakly inter-

acting massive particles colliding with nuclei in tar-gets of ordinary matter.

For dark matter particles in the mass range 10–

1000 GeV, and galactic velocities �107 cm/s, suchcollisions would result in a continuous spectrum

of nuclear recoils mostly below 100 keV. For the

hypothetical neutralino of supersymmetry theory,

typical predicted rates are 1–10�4 events/kg/d

which, for coherent scalar couplings (/A2), corre-sponds to WIMP-nucleon cross-sections in the

region 10�6–10�10 picobarns. These events must

be distinguished from the much higher back-

ground of gamma and beta events from surround-

ing materials or radioactive impurities in the target

itself. This can be achieved by exploiting differ-

ences between nuclear and electron recoil signals

in scintillation, ionisation, or phonon processes,or some combination of these [4].

The efficiency of this discrimination can be cal-

ibrated using a neutron source to produce elastic

nuclear recoils. Since neutron interactions cannot

be individually distinguished from the hypothetical

dark matter events, it is necessary to minimise neu-

tron background in the experiment by means of

shielding or veto techniques, and by undergroundoperation to reduce neutrons from cosmic ray

muons by many orders of magnitude.

The UK-based programme is located in the

2800 mwe vertical depth Boulby Salt Mine, where

results have been reported previously from the

NaIAD detectors based on pulse time constant dif-

ferences in scintillating NaI crystals [5]. Here wepresent results from the ZEPLIN I experiment,

using a target of 5 kg liquid xenon (3.2 kg fiducial)

which shows a larger discrimination between elec-

tron and nuclear recoils. No dark matter signal

has been detected in�293 kg d data. This improvessubstantially on our previous spin-independent

WIMP-proton cross-section limits from NaI detec-

tors, setting a 90% confidence limit with a mini-mum at 1.1 · 10�6 pb for aWIMPmass of 50 GeV.

2. Liquid xenon and the ZEPLIN programme

A summary of the basic excitation mechanisms

in liquid xenon, with detailed references to earlier

studies of these, has been given in Ref. [6]. Thereare two principal mechanisms:

Process P1: Production of a molecular excited

state Xe�2 in singlet and triplet states which decay

back to the ground state with time constants

�3 ns (singlet) and �27 ns (triplet), emitting thecharacteristic 175 nm scintillation photons.

Process P2: Production of Xeþ2 which recom-

bines with a free thermal electron, again formingXe�2 which decays as in P1 but with an overall time

constant governed by the recombination process.

For electron collisions with no applied fields the

light is emitted 25% from P1 and 75% from P2 fall-

ing exponentially with a time constant �30–40 nsin small scale tests [6,7]. For alpha particle colli-

sions the time profile is dominated by the two

exponential decays in P1, averaging to a time con-stant 15–20 ns.

The factor of 2–3 difference in scintillation pulse

time constants between scintillation signals pro-

duced by electrons and alpha particles is attributed

to the higher density ionisation track left by alpha

446 G.J. Alner et al. / Astroparticle Physics 23 (2005) 444–462

particles which promotes faster recombination and

hence shortens the timescale for photon emission

from P2. A similar behaviour is expected for the

high density tracks left by nuclear recoil, and this

is confirmed by neutron calibrations. This differ-ence in pulse times is the basis of the ZEPLIN I

detector described in this paper.More powerful dis-

crimination can be achieved by using both the scin-

tillation and ionisation processes in P2, extracting

the ionisation to produce both a primary scintilla-

tion signal, and a secondary proportional scintilla-

tion signal for each event [8,9]. This provides the

basis of two larger and more complex detec-tors, ZEPLIN II and ZEPLIN III, currently under

construction as a continuation of this programme

[10].

3. ZEPLIN I detector design

The principal features of the detector are shownin Fig. 1. The target consists of a total mass �5 kgliquid xenon, with a fiducial mass 3.2 kg. This is

contained in a 15 cm diameter copper vessel

viewed from the top through quartz windows by

three 8 cm quartz-window ETL 9265Q photomul-

Fig. 1. Arrangement of ZEPLIN I detector (centre), veto and shield

neutron shielding was added over the top Pb shielding.

tipliers (PMTs). The vessel is lined internally with

5 mm thick diffuse PTFE reflector. The PMT con-

nections pass through housings forming part of an

outer copper vacuum chamber. The viewing win-

dows are mounted on 4 cm long �turrets�, linedinternally with Al reflector. The purpose of the tur-

rets is to provide active shielding zones to reject

low energy gammas (and also neutrons) from

residual U/Th activity in the PMTs.

Higher energy gammas producing low energy

deposits in the target by small angle Compton

scattering are registered with an estimated 90%

efficiency (from a Monte Carlo simulation) in thesurrounding 30 cm thick liquid scintillator coinci-

dence veto for an energy threshold 100 keV. Out-

side this is a 25 cm thick lead shield to attenuate

external gammas. The liquid scintillator also serves

as a neutron moderator/absorber, and a high pur-

ity passive gamma shield. For each interaction in

the liquid xenon, scintillation light reaching the

three PMTs produces photoelectron (pe) signalswhich are integrated and digitised at 1 ns intervals.

Initial runs used a DAQ system based on a GPIB-

controlled 8-bit LeCroy LC475 oscilloscope, later

runs using a PCI-based Acquiris DC270 digi-

tiser. For both DAQ systems the trigger was pro-

ing for runs 1 and 2. For run 3, a 10 cm layer of hydrocarbon


vided by a threefold coincidence using CAEN

N417 discriminators set at single-pe levels. A sep-

arate digitiser channel was used for the summed

signals from the 10 veto PMTs.

The chamber is cooled by an IGC PFC330�Polycold� refrigerator, and Xe gas is progressivelycondensed into the chamber through a Messer–

Griessheim �Oxisorb� purifier. A stainless steel

dump vessel stores the evaporated Xe in the event

of refrigeration failure. Full practical and opera-

tional details of the complete system will be de-

scribed in a separate paper. This paper discusses

only those topics relevant to the estimation of darkmatter signal limits.

4. Time constant and pulse selection

Prior to underground operation the system was

characterised by tests in a surface laboratory. Using

gamma sources 57Co and 137Cs located outside thechamber, the energy calibration was found to be in

the range 1.5–2.5 pe (total) per keV for gammas

from 57Co interacting in the lowest part of the vessel

(position dependence being discussed in Section 5).

This figure varied with cooldown cycle, possibly

due to variations in xenon purity (see Section 7).

Since the dark matter limit depends entirely on

events with energies below 10 keV, the correspond-ing pulses contained pe numbers npe < 15–25 and,

in integrated form have a stepped appearance due

1

10

100

1000

1 1

even

ts/n

s

Fig. 2. Example of observed time constant distribution of undergrou

energy range 7–10 keV, showing also the fit using Eq. (2) (dashed line).

using gamma-ray sources. Nuclear recoil events would be observable

distribution.

to the separated arrival times of the photoelectrons

[29]. Although the parent xenon light emission

pulse profile is approximately double-exponential,

it is sufficient for discrimination purposes to char-

acterise each pulse by a single �measured� parametersm, defined as the time interval between the 5% and90% levels of the maximum amplitude.

Of course sm is not a physically meaningfulparameter; for events with npe 6 10 this procedure

returns a value of sm corresponding to the timedelay between first and last photoelectrons. How-

ever the value of sm is effective as a discriminationfactor, even for events in which there would be toofew photoelectrons to identify a double-exponen-

tial shape, as will be shown below. For each event

the pulse amplitude and sm are first derived for theindividual pulses from each photomultiplier and

used to apply event selection criteria detailed

below. Once selected a single value of sm is derivedfrom the summed signals from all three photomul-

tipliers for each event, and this is used for all thesubsequent data analysis. A resulting distribution

in sm is shown in Fig. 2. The shape of this distribu-tion is purely determined by the stochastic arrival

time distributions for events with small number

of photoelectrons and how this translates into

values of sm. The value of sm at the peak of the dis-tribution has a physical associated with the charac-

teristic parent time constants of the emissionprocess. The width of the distribution depends

on the mean number of photoelectrons available

0 100

τm (ns)

nd data pulses (diamond points) from a gamma-ray source for

Distributions of identical shape are observed in laboratory tests

as a second population of events on the left hand tail of the


for the measurement. Hence the width depends on

energy and photon yield.

To eliminate noise pulses and also local PMT

background events in the �turret regions� the fol-lowing pulse acceptance criteria were imposed:

(i) �trigger cut�: requirement of at least one pe ineach of the three PMTs.

(ii) �turret cut�: rejection of events with morethan 67% of npe in one PMT.

(iii) �noise cut�: rejection of events for which, inany single PMT, sm < 10 ns and npe > 2.5.

(The latter criterion being set by inspection of a

population of fast noise events, with near identical

time constant, apparently being generated by the

photomultipliers themselves.)

These cuts result in some loss of genuine events,

and the resulting efficiency factors, obtained as a

function of npe from simulations and data, are dis-

cussed in Appendix A and tabulated in Section 8.Note that the above three efficiency factors are

not independent; cut (i) already removing most

of events (ii) and (iii) at low energies, so that effi-

ciencies estimated for these represent the addi-

tional reduction needed after (i) has been applied.

5. Energy calibration and quenching factor

To convert the observed pulse height (in mV or

photoelectrons) to electron equivalent energy for

each event we calibrate with one or more gamma

sources of known energy. We used 57Co

(122 keV) and 137Cs (660 keV) sources placed un-

der the xenon vessel. The 137Cs source gave a mea-

sured light yield 25% lower than the 57Co. Sinceprevious laboratory work [7] had shown a re-

sponse linear with energy, this difference is due

to a position-dependent light collection, the

122 keV gammas penetrating only a few mm into

the bottom of the xenon volume, while the

662 keV gammas deposited energy (by Compton

scattering and absorption) throughout the cham-

ber volume. To take account of this, an estimateof the position-dependent light collection was

made by simulating the chamber geometry in a

ray-tracing program. We denote the variable npe

keV�1 (or mV/keV) by L(r,z) where z is the height

from the lowest point of the chamber and r is the

radius measured from the central axis. The results

were used to determine a position-dependent ratio

g(r,z) = L(r,z)/L(0,0) linking the light yield fromeach point to the value L(0,0) at the bottom of

the chamber, determined by the 57Co calibration.

This was verified by simulating the Xe vessel and137Cs or 60Co sources in a gamma-tracking Monte

Carlo with the energy deposited at each scattering

point (r,z) reduced by the fraction g(r,z). The

resulting spectrum showed the 662 keV peak to

be displaced downwards by 25 ± 3%, consistentwith the observed reduction in light output. For

a 60Co source, irradiating the whole volume uni-

formly, the downward displacement of the peak

was 30 ± 3%.

The fraction g(r,z) was then summed over the

chamber volume V to obtain the total dV/dg as a

function of g and then re-expressed as a matrix

ML(m,n) which converts a spectrum of spatiallyuniform events (binned in energy by assuming a

constant reference light yield L(0,0)) into a cor-

rected spectrum distributed over energy bins

En < Em. This �rebinning matrix� is included, alongwith the analogous energy resolution matrix, in the

final stage of the analysis detailed in Section 9. The

systematic error for this procedure is discussed in

Appendix A.The above energy calibration applies to electron

recoils from photoelectric absorption or Compton

scattering of gammas. Electron recoils from beta

decay (e.g. from local radioactive contamination)

are assumed to produce pulses similar in shape

and time constant, as confirmed for the case of

scintillation pulses in NaI [11]. However, in the case

of nuclear recoils, the visible (electron-equivalent)energy Ev is related to the true recoil energy ER by

ER ¼ Ev=fXeðERÞ ð1Þwhere fXe(ER) is the nuclear recoil efficiency or �qu-enching factor�, which may be energy dependent.Measurements of fXe have been made using

both neutron sources and beams for recoil energiesdown to �40 keV. Our published neutron beammeasurements [12] give fXe = 0.22 ± 0.02 in the re-

coil energy range 60–70 keV and 0.22 ± 0.04 as a

weighted average of four measurements between

Fig. 3. Examples of neutron calibration of ZEPLIN I, showing fits to the neutron and gamma populations. Energy ranges correspond

to L(0,0) defined in Section 5. (Top) Tagged Am–Be source, observed energy range 20–30 keV. Minimum-v2 ratio

rnc ¼ s0n=s0c ¼ 0.64� 0.04. (Centre) Ambient neutrons and low intensity 60Co gammas, observed energy range 3–7 keV. Minimum-v2 ratio rnc ¼ s0n=s0c ¼ 0.42� 0.07. (Lower) Low threshold Am–Be run, observed energy range 3-8 keV. Minimum-v2 ratiornc ¼ s0n=s0c ¼ 0.44� 0.09.


40 and 60 keV. These are in reasonable agreementwith [13] but lower than values obtained in a sim-

ilar energy range by the Rome group of

fXe = 0.45 ± 0.12 using a neutron generator, and

fXe = 0.65 ± 0.10 using an Am–Be source [14].

The latter result from the Rome group relied on

a Monte Carlo simulation fitted to the measured

nuclear recoil spectrum and treating the quenching

factor as a free parameter. The same technique hasbeen applied to the ZEPLIN I tagged Am–Be data

used in the top plot of Fig. 3 between 15 and70 keV electron-equivalent energies. This gives a

value of fXe = 0.25 ± 0.05 averaged over a recoil

energy range 60–280 keV.

The above measurements provide the quench-

ing factor at �40 keV recoil energy (�8 keVelectron-equivalent) but do not extend to our

experimental threshold of 10 keV recoil energy

(2 keV electron-equivalent). Theoretical discus-sions [15] do not suggest a definite behaviour of


the quenching with energy. An increase of the

quenching factor towards low energies has been

seen in neutron beam measurements on solid scin-

tillators [16,17] with CsI showing a factor 2 in-

crease in quenching factor with decreasing energydown to 12 keV. In the absence of definitive mea-

surements in liquid xenon we assume a constant

value fXe = 0.22 for the 10–50 keV nuclear recoil

energy range of this experiment to calculate our

upper limit. In Appendix A we show how the

upper limit is affected for other values of fXe.

6. Time constant distribution and nuclear recoil

calibration

Due to statistical fluctuations in optical photon

production and collection times, and in the single

pe response of the photomultipliers, a set of pulses

with a given total amplitude will show a spread of

values of sm, even if the underlying distributionhas a single well-defined time-constant value. A

typical distribution of data events taken under-

ground, with measured energy deposition between

7 and 10 keV, is shown in Fig. 2. It is useful to para-

meterise the distribution shape, and for energies

above about 7 keV the differential event number

distribution dN/dsm is well-fitted by a generalisedgamma density distribution in the �rate� parameterx = 1/sm:

ð1=NTÞdN=dsm ¼ Gðx; a; bÞ¼ ð1=baCðaÞÞxa�1 expð�x=bÞ ð2Þ

where NT is the total number of events in the

distribution.It is more physically transparent to rewrite G

as a function H of the two alternative parameters

s0/sm, w:

Hðs0=sm;wÞ � Gðs0=sm; 1þ 1=w;wÞ ð3Þwhere s0 is now the peak of the distribution and wis a single parameter characterising the width.Both s0 and w are allowed to vary with energy.For w this is particularly important as we noted

earlier that the width of the distribution arises

purely from the statistical limitation on how accu-

rately a time constant can be derived given the

number of photoelectrons available for the mea-

surement. For energies <5 keV the distribution is

modified at small sm by the effective response timeof the PMTs, giving a steeper tail. This can be ade-

quately fitted by the empirical multiplying correc-tion factor:

KðsmÞ ¼ ½1� expð�sm=spÞj�½1þ expð�sm=sqÞk�ð4Þ

where sp = 9 ns, sq = 15 ns, j = 4, k = 8, determinedby fitting to Compton calibration data. Since the

fitted s0 increases with energy, the correction (4)is close to unity except at low energy where it accu-

rately models the increased slope of the distribu-

tion at short times. Thus a function which fits

the data at all energies is the product of (3) and (4):

ð1=NTÞdN=dsm ¼ CKðsmÞHðs0=sm;wÞ¼ Hmodðsm; s0=sm;wÞ ð5Þ

where C is a renormalising constant to maintain

the integral of (4) at unity. The above fitting func-

tions are arbitrary, chosen to provide a parame-

terisation of the gamma background and a

model for the hypothetical signal shape. Note,however, that the subsequent Poisson limit analy-

sis uses the observed discrete data points, as dis-

cussed in Section 9 below.

Prior to underground operation the detector

was calibrated with a gamma-tagged Am–Be neu-

tron source to obtain the time constant ratio

between nuclear recoils and gammas. Some low-

rate 60Co calibration data contained also a low en-ergy population of events from ambient neutrons.

Examples of spectra are shown in Fig. 3. The addi-

tional population resulting from the neutrons can

be observed in comparison to the underground

data in Fig. 2: indeed none of the underground

runs, at any given energy interval, showed such a

population. During the neutron source runs, the

neutron tagging (using a CsI crystal to detectthe simultaneous 4.44 MeV gamma) suppresses

the trigger rate by a factor �102, making the ambi-ent neutron population negligible. Minimum v2 fitsfor several energy intervals were obtained assum-

ing two populations of the shape (5), thus yielding

for each case a best fit time constant ratio

rnc ¼ s0n=s0c . In a given energy range the two pop-


ulations have equal width parameters w, consistent

with the expected dependence of w on the number

of photoelectrons and not on the originating parti-

cle. The analysis presented in this paper is based

on these surface calibrations, owing to technical is-sues preventing a more extended underground

neutron calibration. The best fits to the data

showed a decrease of rnc with energy, from ffi0.6at 20–30 keV to values 0.42–0.44 in the energy

range 3–8 keV relevant to the dark matter limits.2

Although the presence of ambient neutrons in a

low-gamma rate observation is not in itself surpris-

ing and is perfectly consistent with both rateexpectations and measured rnc , we prefer to rely

more heavily on the specific and unambiguous

Am–Be source calibrations. This gives rnc ¼0.44� 0.09. A rigorous analysis treatment wouldtake this ratio forward as a probability distribu-

tion to be convolved through the various equa-

tions. The result of this is that a 90% confidence

limit on the final result corresponds to adoptinga single value of rnc ¼ 0.50. Hence for the purposesof clarity in the following analysis we restrict

s0n=s0c to the constant value rnc ¼ 0.5 below

10 keV. In Appendix A we discuss how the calcu-

lated upper limits depends on rnc in a systematic

way. Finally we note that simulations show that

multiple neutron scattering in these calibration

runs affects only 20% of the events, and this wouldchange the variation drnc=dE by 8%, i.e. has noeffect for the assumption of a constant value of rnc .

7. Underground data runs

Following the surface laboratory calibrations,

the detector was transferred to the Boulby under-ground laboratory and assembled inside the

Compton veto and lead shield. After several test

cooldowns, stable operating conditions were

achieved in three continuous periods of data tak-

ing, also showing a progressive improvement in

the light output, probably from improved xenon

2 These values are not in disagreement with those in [12] for

two reasons. Firstly, sm, as calculated in this present work is notthe same as the definition in [12] and secondly the values in [12]

are averaged over a wide energy range 6–30 keV.

purification procedure during filling. Basic param-

eters of the three runs are shown in Table 1. The

variation of pe/keV with cooldown cycle is consis-

tent with changes in the light scattering/attenua-

tion length as the xenon purity improves. Thepeak in the pulse time constant distributions re-

mains stable within 10% from run-to-run and no

changes can be detected in the relative light yield

throughout the detector volume. The variation in

absolute light yield is automatically accounted

for in the analysis procedure.

For analysis purposes a 2 keV threshold energy

is used for all three runs. Several factors affect theobserved energy resolution, which remained in the

range DE(rms)/E = 1.19 ± 0.02(E/1 keV)�1/2 overall three runs. Energy calibration was obtained

using a 57Co source inserted below the chamber,

giving a distinctive peak through the 5 mm Cu

containing vessel. This was confirmed every day

and provided the reference value L(0,0) discussed

in Section 5.For each digitised pulse the mean time sm (de-

fined in Section 4) was computed and binned in

1 ns intervals, while the corresponding apparent

energy (i.e. the mV amplitude multiplied by mean

pe/mV and divided by L(0,0)) was binned in 1 keV

intervals, the total data set now reduced to a two-

dimensional array in time constant and apparent

energy. The correction required to take accountof the position dependence of L, described by the

energy rebinning matrix M(m,n) derived as dis-

cussed in Section 5, is included in the final limit

analysis in Section 9 below.

8. Analysis stage 1: mean signal estimate and

upper limits on nuclear recoil events

Since the hypothetical dark matter recoil spec-

trum would vary smoothly with energy, it is conve-

nient to group the 1 keV energy bins into

somewhat larger intervals. Taking account of the

higher dark matter sensitivity at low energy, and

the inverse variation of distribution width with

energy, an appropriate set of intervals was chosento be 2–3 keV, 3–5 keV, 5–7 keV, 7–10 keV,

10–15 keV, and thence in 5 keV intervals. Only

(observed) energies up to 10 keV (ffi50 keV recoil

Table 1

Summary of run lengths, energy calibration, and energy threshold

Run length (days) 57Co energy calibration pe/keV (3 PMTs) Trigger threshold (keV electron equivalent)

Run 1 25.4 1.5 2.0

Run 2 49.9 1.8 1.7

Run 3 16.2 2.5 1.2


energy) contribute significantly to the limits in this

experiment, so that only the first four of these

energy intervals are analysed. From the sm-distri-butions in these energy intervals we will estimate

the most probable signal value and the 90% confi-

dence upper limit.

We demonstrate first that the most probable

nuclear recoil signal is consistent with zero. Thisis done by comparing the data sm-distributionswith a distribution of Compton electron recoils

from Compton scattering. As discussed above,

electrons from beta decay (expected from 85Kr in

the xenon or other radioactive contamination)

should show the same distribution as Compton

electrons [11]. In addition, the neutron background

from U/Th in rock and detector is estimated (froma Monte Carlo simulation of the detector in the

Boulby cavern) to be in the region 0.1 events/d,

an order of magnitude below the experimental sen-

sitivity derived below. Events in the data set which

are in coincidence with events in the surrounding

Compton veto form a pure electron recoil data

set which had been intended to provide this com-

parison. However, the vetoed data comprised only25% of the total, the background being dominated

by internal radioactivity, so although there was

agreement between the non-vetoed and vetoed data

sets better statistics were needed. We therefore in-

cluded prior to run 3 a two-day high statistics

Compton calibration run, using a 60Co source.

We adopt the simple test shown in Fig. 4, which

illustrates that a small signal population of shortermean time constant will always reduce the initial

slope d ln(N)/dsm of the left hand branch of thesm-distributions. The variation of this slope withsignal event number can be determined quantita-

tively by adding hypothetical signal distributions

with the assumed value rnc ¼ s0n=s0c ¼ 0.5, the re-sults being shown in Fig. 5. The initial slopes for

the sm-distributions of the data runs were deter-

mined numerically by using the event numbers

for the two 1 ns bins (i.e. following the first occu-

pied sm-bin). Remarkably, these measured initiallogarithmic slopes lie in a narrow range showing

no significant dependence on either energy, light

output or number of events in the distribution.

For the four energy ranges 2–3 keV, 3–5 keV, 5–

7 keV, 7–10 keV the (12) slope values of d ln(N)/dsm for the three data runs were in the range1.1 < d ln(N)/dsm < 1.6 ± 0.3, with an average

value 1.36 ± 0.11 (Fig. 5). Comparison shows (a)

that the initial slopes of Compton calibration and

data sm-distributions do not differ significantlyand (b) that using the variation with event number

shown, the central value signal estimate lies in the

range Nc = �1 ± 4 events (for each energy inter-val). We thus establish that the mean signal is con-

sistent with zero, or with a possible positive value

small compared with the typical Poisson upper lim-

its of 15–30 events per energy bin which will next be

derived. Note that the error bar on Nc relates only

to the mean signal estimate and is not used in the

subsequent more precise Poisson limit analysis.

We define the 90% Poisson upper limit as themean signal which could be present but, through

a statistical downward fluctuation, has a 10% prob-

ability of reaching the observed value or lower [18].

Using the time constant ratio rnc ¼ 0.5 and the dis-tribution shape of Eqs. (3)–(5), prior numerical

investigation showed the statistically most sensitive

region of the data to be at the start of the left

branch of the sm-distributions (as illustrated inFig. 4), specifically at the first occupied time bin

or the preceding unoccupied bin (which would

acquire events in the presence of a significant sig-

nal). We therefore adopt the procedure of obtain-

ing a Poisson upper limit on the fraction of the

integrated distribution at this point, then determin-

ing the size of signal distribution which would

match this upper limit.

0.0

0.5

1.0

1.5

2.0

-10 0 10 20

Number of added recoil events in single energy bin

initi

al s

lope

d ln

(N)/

dtm

mean initial slope of data distributions

mean initial slope of Compton calibration

effect of adding nuclear recoil events

Fig. 5. Changes in initial slope of time constant distribution for gamma calibration, resulting from the addition of simulated recoil

signals with time constant ratio 0.5. The graph applies to each one of the energy ranges 2–3 keV, 3–5 keV, 5–7 keV, 7–10 keV. Also

shown is the mean initial slope of the data distributions, consistent with the gamma calibration for zero added signal, the error bars

allowing a positive value <4 events. Thus the central value of the signal can be taken as zero in the subsequent determination of Poisson

upper limits.

1

10

100

1000

1 10 100τm (ns)

even

ts/n

s

nuclear recoil signal 40 events

electron recoil background

16000 events

change of initial slope

Fig. 4. Illustration showing effect of adding to a distribution of electron recoil events a relatively small nuclear recoil signal with time

constant ratio 0.5. The initial logarithmic slope dln(N)/dsm is decreased, by an amount shown quantitatively in Fig. 5.


We first define, for a given energy range, the

integral of the data distribution D(sm), (norma-lised to ND events) between zero and a selected

point sm = sA

NDIDð0; sAÞ ¼Z sA

0

DðsmÞdsm

¼XsA

0

DðsmÞDsmðDsm ¼ 1 nsÞ ð6Þ

Similarly we define, for a hypothetical signal NSevents given by Eq. (5), the integral:

NSISð0; sAÞ ¼Z sA

0

N SHmodðsm; rnc s0=sm;wÞdsm

ð7Þand define the background (for zero mean signal)

as the fit of (5) to the data distribution

NDIBð0; sAÞ ¼Z sA

0

NDHmodðsms0=sm;wÞdsm ð8Þ

For the Poisson upper limit in the presence ofbackground we use the Feldman–Cousins unified

values [19] for the 90% upper confidence limit


PF-C(nobs,nb) which is tabulated as a function of an

observed number of events nobs and mean back-

ground number of events nb. In our case nobs is

given by Eq. (6) and nb by Eq. (8). The 90%

confidence limit for that fraction fA of the inte-grated signal up to the point sm = sA is thus givenby:

fANS ¼ NSISð0sAÞ ¼ PF–Cðnobs; nbÞ¼ PF–C½NDIDð0; sAÞ;NDIBð0; sAÞ� ð9Þ

and, in the absence of a nuclear recoil population,

the (integral) nobs and (smoothed) nb will be statis-tically equal for any choice of sA.Fig. 6 illustrates the general shape of the result-

ing Poisson upper limit versus s, together with thesignal integral (7), the 90% confidence limit occur-

ring where the two curves meet tangentially, at

point A in Fig. 6. The optimum choice of sA coin-cides with the pre-specified value discussed above

(thus avoiding optimisation bias [20]). If ID is stillzero at sA (i.e. sm-bins unoccupied up to sA) thebackground fit nevertheless has a fractional value

in the range 0 < nb < 1 (corresponding to the

non-zero probability of observing an event with

further running) and the limits for this situation

Fig. 6. Notation for Poissonian analysis point. Light dashed curve: i

form of Poisson (Feldman–Cousins) upper limit versus sm. Continuouincreased until it touches the Poisson limit at point A, defining sm = sfANS at point A.

are covered by the first row PF-C(0,nb) of the Feld-

man–Cousins tables [19].

The 90% signal upper limits obtained for the

four energy ranges <10 keV, for each of the data

runs, are shown in Table 2 (only the first three en-ergy ranges contributing significantly to the final

limits). This table also shows the estimated efficien-

cies for the cuts in Section 4, and the fraction fA of

the signal integral at sA. The statistical event limitsshould be divided by these efficiencies to obtain the

true event limits. However, because of the trivial

identity

rate ¼ ðevents=efficiencyÞ=time¼ events=ðefficiency� timeÞ ð10Þ

it is more convenient, for the subsequent purpose

of combining data sets, to leave the absolute event

limits unchanged, and apply all of the efficiency

factors to the running time. This gives a reduced

effective running time teff for each energy bin ineach data set. We show in Table 2 both the experi-

mental running time for the total signal limit NS,

and the efficiency-reduced running time teff corre-

sponding to the Poisson event limit at the analysis

point sA. As a cross-check on the event limits,

ntegral of data versus sm (Eq. (6)). Thick dashed curve: typics curve: hypothetical signal integral (Eq. (7)). The signal value

A. The corresponding total signal is then NS and has the valu

al

is

e

Table 2

Summary of 90% confidence limits and efficiency-adjusted running times for each energy range in each data run

Trigger efficiency

(Appendix A)

Turret efficiency

(Appendix A)

Noise cut efficiency

(Appendix A)

90% upper signal

limit NS

True run

time (days)

Total exptl

efficiency

Signal

fraction

fA at sA

Total

efficiency at sA

Effective

run time

teff at sA (days)

Run 1

2–3 keV 0.12 1.00 0.97 38 25.4 0.12 0.09 0.011 0.28

3–5 keV 0.45 0.94 0.72 32 25.4 0.30 0.10 0.030 0.77

5–7 keV 0.77 0.95 0.59 23 25.4 0.42 0.17 0.071 1.86

7–10 keV 0.94 0.97 0.71 17 25.4 0.65 0.12 0.078 1.97

Run 2

2–3 keV 0.28 0.96 0.90 37 49.9 0.24 0.10 0.024 1.20

3–5 keV 0.61 0.95 0.58 36 49.9 0.34 0.11 0.037 1.85

5–7 keV 0.88 0.97 0.62 19 49.9 0.53 0.11 0.058 2.90

7–10 keV 0.99 1.00 0.88 14 49.9 0.87 0.15 0.131 6.52

Run 3

2–3 keV 0.45 0.94 0.62 19 16.2 0.26 0.12 0.031 0.50

3–5 keV 0.82 0.96 0.62 19 16.2 0.49 0.11 0.054 0.87

5–7 keV 0.97 0.99 0.83 13 16.2 0.80 0.17 0.136 2.20

7–10 keV 1.00 1.00 0.93 16 16.2 0.93 0.22 0.205 3.32

In all cases the Feldman–Cousins 90% lower limit is zero.

Note 1: Trigger efficiency estimated by (a) statistical simulation of trigger criterion, assuming 50% detection loss of first pe in each PMT and (b) low rate 60Co calibration,

and fits to low energy data runs––see Appendix A.

Note 2: Turret cut efficiency estimated by statistical simulation of turret cut condition.

Note 3: Noise cut efficiency is supplementary to the trigger cut (also removing low-E noise) and estimated by (a) neutron calibration data, before and after cut, to

determine surviving fraction of neutron population as a function of p.e. number and time constant and (b) statistical simulation confirming that this supplementary

efficiency rises to unity for both large and small number of p.e. in pulse.

G.J.Alneretal./Astro

particle

Physics

23(2005)444–462

455

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1 10 100

E(obs) keV

num

ber

per

1 k

eV b

in SSS111

SSS222

LLL222

LLL111

FFF111

Fig. 7. Event numbers for run 2. S1: Observed spectrum before veto or cuts. The decrease towards lower energy is mainly due to

triggering efficiency, but may also have a small contribution from a 85Kr beta-decay component. S2: Residual data after all cuts. F1: Fit

without trigger efficiency (including rising 85Kr component). L1: Nuclear recoil upper limit on observed data prior to efficiency

correction. L2: Increased nuclear recoil upper limit after efficiency corrections of Section 3 (light and resolution matricesML andMR

incorporated at later stage).


simulated signals with rnc ¼ 0.5 were added

numerically to the gamma calibration data at the

levels NS of Table 2, to confirm that the 90% Pois-

son lower limit (as tabulated in [19]) then becomes

non-zero. To illustrate the magnitudes involved,

Fig. 7 shows the observed electron recoil back-

ground for run 2 before and after cuts, together

with the Poisson upper limits as a function of en-ergy, showing the effect of the trigger efficiency

on observed background and limits. Note that at

the lower energies the smaller number of photo-

electrons result in a larger width to the time

distributions and a lower trigger efficiency, for

which the above procedures automatically yield

lower ‘‘effective run times’’ for those lower energy

bins. This is offset by the greater contribution ofthese lower energy bins to the dark matter limit,

Table 3

Combining Poisson limits for runs 1, 2 and 3

Bin

label, m

Energy

range, keV

(nobs,nb) values ðP

nobs;P

nbÞ FP

Run 1 Run 2 Run 3

1 2–3 (1,0.9) (2,2.2) (0,0.2) (3,3.3) 4

2 3–5 (1,0.9) (2,2.0) (0,0.4) (3,3.3) 4

3 5–7 (2,1.9) (0,0.4) (0,0.3) (2,2.6) 3

4 7–10 (0,0.4) (0,0.3) (1,0.7) (1,1.4) 3

so that the net effect is that all four energy

ranges make similar contributions to the final

result.

We next amalgamate the results for runs 1, 2,

and 3 to make a single combined limit for each en-

ergy range. This can be done by summing, for each

energy range, the three values of (nobs,nb) and

determining a combined Poisson upper limitPF–C½

Pnobs

Pnb� for events at the analysis point

sA and a combined running time tc ¼P

teff (takenfrom the final column of Table 2). For limit set-

ting, simple summation of event limits for the

three runs is a conservative procedure because it

gives equal weight to each (and hence over-weights

the poorest result, raising the overall limit). The

resulting combined values for the four energy binsare summarised in Table 3.

ANS ðevents < sAÞ ¼F–Cð

Pnobs;

PnbÞ

tc ¼P

teff ,days

Recoil rate

limit, events/d

Total event

limit for

91.5 days

.2 1.98 2.12 194

.2 3.49 1.20 110

.4 6.96 0.49 45

.0 11.81 0.26 24


9. Analysis stage 2: Calculation of dark matter

cross-section limits

The preceding event rate limits are now com-

pared with a theoretical dark matter spectrum inorder to estimate an overall limit on the dark mat-

ter event rate, and hence a cross-section limit. For

a flux of particles of massMD (GeV) incident on a

nucleus of atomic number A, producing a recoil

energy ER (keV), the differential event rate R

(events/kg/d) is given by [21]

dR=dER ¼ ðc1R0=E0rÞ� expð�c2ER=E0rÞF 2ðER;AÞ ð11Þ

where E0 (keV)=0.5 · 106MD(v0/c)2, v0=220 km/s,

r = 4MDMT/(MD +MT)2, MT = 0.932A, and F

2 is

a nuclear form factor correction. For a detector

at rest with respect to an isotropic Maxwellian

dark matter flux, c1 = c2 = 1, while motionthrough the Galaxy gives average fitted values

c1 = 0.75, c2 = 0.56, with a small annual modula-

tion tabulated in [21].

R0 (events/kg/d) is defined as the total rate for a

stationary Earth, and is related to the total nuclear

cross-section rA by

R0=r ¼ DrAðpbÞ=l2A ð12Þ

where lA =MDMT/(MD +MT) is the reduced

mass of the colliding particles and D is a numericalfactor equal to 94.3 [21] for an assumed dark mat-

ter density 0.3 GeV/cm3. ER is related to the exper-

imentally observed energy by (1) and, as discussed

in Section 5, we take fXe = 0.22.

It is customary to express the final limits in

terms of the equivalent WIMP-nucleon cross-sec-

tion rW–N. This is related to rA, in the case of aspin-independent nuclear interaction, by

rW–N ðpbÞ ¼ ðl1=lAÞ2ð1=A2ÞrA ðpbÞ ð13Þ

where l1 (�0.925 GeV) is the reduced mass forA = 1. Hence, from (12)

rW–N ðpbÞ � 9.1� 10�3ð1=AÞ2ðR0=rÞ ð14ÞWe calculate only the spin-independent limits in

this paper. The procedures for determining the

spin-dependent WIMP-neutron and WIMP-pro-

ton cross-sections are given in [22].

The nuclear form factor correction F2(ER,A) is

a function of qrA, the dimensionless product of

momentum transfer q (fm�1) = 0.00692(AER)0.5

(using h/2p = 197.3 MeV fm) and nuclear radiusrA, with rXe = 5.6 fm. For a spin-independentinteraction F2 has the following form [23] using

the Bessel function j1:

F 2ðqrAÞ ¼ ½3j1ðqrAÞ=qrA�2exp½�ðqsÞ2�; s ¼ 0.9 fm

ð15Þ

Limits on the quantity R0/r, and hence rA via (12),can now be set by comparing (11) with the event

rate limits obtained in Section 8. To do this, we

re-write (11) in terms of a finite range of visible

energy Ev1, Ev2, also replacing ER by Ev/fXe:

DRðEv1;Ev2Þ ¼ ðR0=rÞZ Ev2

Ev1

ðc1=E0Þ

� expð�c2Ev=fXeE0rÞF 2ðqrAÞdEv=fXeð16Þ

which we abbreviate to:

DRðEv1;Ev2Þ ¼ ðR0=rÞK theoryðEv1;Ev2;MDÞ ð17Þwhere Ktheory is obtained by evaluating the integral

(16) numerically for specific dark matter particle

masses in the range 10 GeV <MD < 1000 GeV.

To relate (17) to observations, the vector of theo-

retical integrals Ktheory must be redistributed to

take account of both finite energy resolution and

the position-dependent light yield. As discussedin Section 5, the latter was expressed as a rebinning

matrix ML(n,m) where n, m, are integer labels for

the successive energy bins. An analogous energy

resolution matrix MR(n,m) was calculated by

assuming a gaussian energy spread r = ±k(E)0.5

with the measured value k = 1.2. The vector of cor-

rected values

KcðmÞ ¼ MRðn;mÞMLðn;mÞK theoryðnÞ ð18Þthen provides the corrected RHS of (17) to match

the experimental limits on the LHS. Again using

(10) to re-express rate in terms of event numbers

and noting that R is defined per kg of target,

(17) finally becomes, for MXe kg liquid xenon:

fAðmÞN SðmÞ ¼ MXetcðmÞðR0=rÞKcðm;MDÞ ð19Þ

where NS(m) and tc(m) are obtained from Table 3.

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1 10 100 1000 10000

Mass (GeV)

WIM

P-n

ucle

on c

ross

sec

tion

(pb

)

.

Fig. 8. Exclusion plot for spin-independent WIMP-nucleon cross-section versus particle mass (90% confidence) from 293 kg d

(fiducial) running of ZEPLIN I and based on standard halo parameters. The plot also requires assumptions about the xenon time

constant ratio between nuclear and electron recoils and the quenching factor behaviour with energy. Due to the lack of high precision

experimental data on these parameters below a recoil energy of 40 keV, we include a systematic study of the consequences to changes in

their assumed values on the WIMP-nucleon cross-section in Appendix A.


From (19) we can obtain at 90% confidence lim-

its for (R0/r) as a function ofMD for each of the m

energy ranges in Table 3. To obtain a combined

limit from all energy ranges, we use the conserva-

tive procedure adopted for combining data runs

in Table 3––i.e. to sum over m the observed and

background values, converting these to a single

Feldman–Cousins limit for the total energy rangeused. This is equated to the sum over m of the

RHS terms in (19) which have the common factor

(R0/r) and hence provide an overall limit on (R0/r)

as a function of MD. As a final step the spin-inde-

pendent cross-section rW-N(pb) is obtained from(R0/r) using (14), for each WIMP mass MD. The

resulting limit plot is shown in Fig. 8. We empha-

sise that this limit is valid under the followingassumptions:

• energy-independent quenching factor P0.22,• an energy independent time constant ratio

60.5,

• a volume-average light loss 630%.

Whilst all these assumptions are consistent with

our calibration data, there are unfortunately no di-

rect experimental data currently available to con-

firm the first assumption for recoil energies below

40 keV, nor independent confirmation of the sec-ond assumption below 40 keV. Because of this

we derive the sensitivity of the limit to these

parameters in Appendix A.

10. Conclusions and future improvements

At the present time, considerable interest lies inreaching sensitivities matching the predictions of

supersymmetry theory for a neutralino of mass

in the range 30–300 GeV and spin-independent

cross-section rW–N in the range 10�5–10�10 pb.

In addition, there is interest in the interpretation

of a seasonal modulation reported by the DAMA

group [24,27] in the overall counting rate in a so-

dium iodide array. The result reported in thispaper thus appears to disfavour particles with


scalar elastic interactions as an explanation of the

Rome modulation effect, though it does not ex-

clude a spin-dependent interaction which could

be significantly different for Na and Xe nuclei, or

interactions dominated by inelastic scattering.Expansion of the DAMA region is possible with

a wider range of halo parameters [25] most of these

also lowering the limit in Fig. 8 by a similar

amount. Other experiments reporting progres-

sively improving limits in this region are the

CDMS [26] and EDELWEISS [27] low tempera-

ture detectors, and the IGEX Ge detector [28].

The results of this first run are encouraging alsofrom the viewpoint of utilising liquid Xe in the

more sensitive experiments under construction,

ZEPLIN II and ZEPLIN III, based on a larger

target mass and discrimination by two-phase pro-

portional scintillation [9,10]. Practical tests on pro-

totype systems for these detectors indicate that

individual event discrimination should be possible,

offering the prospect of major improvements insensitivity using target masses up to 1000 kg or

more.

Acknowledgments

This workwas funded by the Particle Physics and

AstronomyResearchCouncil. Thanks are due toD.Akimov (ITEP) for discussions and advice on

xenon purification. We gratefully acknowledge the

provision of facilities and services in the Boulby

Mine by Cleveland Potash Ltd., and the substantial

assistance from the BoulbyMine Staff, in particular

A. Williams, T. Coleman, R. Lockerbie and G.

Clarke. We thank V.W. Edwards, G. Pullinger

and E.G. Capocci for their technical support, E.J.Daw and A.S. Murphy for useful discussions. P.F.

Smith acknowledges an Individual Emeritus

Research Grant from the Leverhulme Trust.

Appendix A. Discussion of systematic errors

A.1. Trigger efficiency (see Section 4)

The pulse acceptance condition, of at least one

photoelectron in each of the three photomulti-

pliers, results in the acceptance of a fraction

g(npe) < 1 of the total events, which is a functionof the number of photoelectrons npe. This can be

calculated statistically and depends also on the

fluctuation in the PMT gain and on the presenceof baseline noise, which has the effect of losing

approximately 50% of the first photoelectrons in

each of the photomultipliers. The resulting values

of g(npe) as a function of npe can be obtained bya statistical simulation and are shown by the dia-

mond points in Fig. 9. These were also consistent,

to within ±10%, with a fit to the longest data run

(run 2), assuming a flat spectrum together with acomponent from a 85Kr beta decay spectrum. Bet-

ter experimental confirmation was provided by a

subsequent low-rate 60Co calibration of the ZE-

PLIN I system, shown by the histogram in Fig.

9. This gave slightly higher efficiency values than

the diamond points of the simulation, but the lat-

ter values were retained to provide a conservative

margin.

A.2. Turret cut and noise cut efficiencies (see

Section 4)

The removal of pulses giving >67% of photo-

electrons in one PMT, and hence most likely to

be PMT background, results in a small loss of gen-

uine events, which can be estimated accurately as afunction of photoelectron number by a statistical

simulation. Similarly, the noise cut (defined in Sec-

tion 4) designed to remove fast noise pulses seen

predominantly in one PMT, removes also some

genuine events, which can be estimated by a statis-

tical simulation. The simulations results have been

compared to the neutron calibration data, for

which the fitted population of neutrons can becompared before and after the noise cut. The ratio

of these neutron numbers for different energy

ranges provides values for the efficiency of the

noise cut for nuclear recoil events as a function

of npe. The uncertainty in the efficiency calcula-

tions was estimated as 10%, based on the compar-

ison with data as discussed above, which gives a

10% uncertainty in the final limit.For both the turret cut and the noise cut, the

efficiency is supplementary to the trigger cut,

which itself already removes some of the unwanted

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 2 4 6 8 10 12 14 16

number of photoelectrons

effi

cien

cy (

reta

ined

eve

nts

/to

tal)

trigger efficiency simulation

trigger efficiency measurement

total efficiency(trigger + turret +

noise cuts)

Fig. 9. Summary of efficiency factors versus number of photelectrons. (Solid points) Trigger efficiency simulation for 50% loss of first

photoelectron in each PMT. (Histogram) Measured trigger efficiency. (Open circles) Total efficiency including trigger, turret, and PMT

noise cut.


events. The resulting total efficiency factor, i.e. the

combined efficiency of the trigger, turret and noisecuts, is shown as a function of npe by the open cir-

cles in Fig. 9. Using the pe/keV values in Table 1,

the energy-binned efficiencies in Table 2 are ob-

tained by converting the energy ranges to a range

of npe and averaging the efficiency values in each

range.

A.3. Quenching factor (see Section 5)

Measurements of the efficiency of nuclear recoil

relative to electron recoil have been made for a

number of scintillators, including liquid xenon,

using neutron sources and neutron beams, but in

general not down to the recoil energy range appro-

priate for dark matter detection. The measure-

ments of Ref. [12] for liquid xenon give a meanvalue 0.22 ± 0.04 for the range 40–60 keV recoil

energy. The value of about 0.18 for the quenching

factor was found in Ref. [13] for Xe recoils above

40 keV. It is technically more difficult to reach the

10 keV level corresponding to the energy threshold

of this experiment and no measurements have been

made at this energy. Comparison to the Lindhard

model, which predicts a decrease of ionisation with

decreasing energy, may not be appropriate here,since neutron beam measurements of quenching

factor for the scintillators NaI, CaF2 [16] and in

particular CsI [17] show a constant or increasing

scintillation efficiency with decreasing energy.

For the case of liquid xenon (and also liquid

argon) the scintillation mechanisms are different,

but similar behaviour of dE/dx with E for nuclei

and electrons in liquid Xe, NaI and CsI [6] maysuggest a similar increase (or a constant value)

for the quenching factor in Xe, NaI and CsI.

It is therefore legitimate to assume a constant

value of 0.22 below 10 keV visible energy for the

purpose of limit calculations. Table 4 shows the ef-

fect on the limit of lower and higher values of fXe(including the DAMA measured values in the

region �0.45–0.65 [14]).

A.4. Time constant ratio (see Section 6)

Measurements of the time constant ratio

rnc ¼ sn=sc by exposing the ZEPLIN I detector to

ambient and laboratory neutron sources showed

a decrease from the value 0.64 ± 0.04 at 20 keV

Table 4

Effect of systematic variations with remaining parameters unchanged, expressed as a percentage of the limit with basic value

1.1 · 10�6 pb

Quenching factor 0.18 0.22 0.26 0.36 0.46 0.60

Minimum of limit curve relative to the basic value 1.1 · 10�6 pb 124 100 83 66 52 48

Form of time constant ratio Am–Be neutrons

only giving

rnc ð90%Þ ¼ 0.50

Am–Be + ambient

neutrons, rnc ¼ 0.50 @10 keV to rnc ¼ 0.40 @2 keV

Volume average light collection PAV 65% 70% 75% 65% 70% 75%

Minimum of limit curve relative to the basic value 1.1 · 10�6 pb (for fXe = 0.22) 107 100 92 76 70 65


to the value 0.43 ± 0.06 at 3–7 keV electron-equiv-

alent energy if both ambient neutron data as well

as Am–Be data are used as shown in Fig. 3. The

use of rnc ¼ 0.5 for a 90% confidence level was jus-tified on the basis of only using the Am–Be data. If

instead the central (minimum-v2) values were used,suggesting a possible linear decrease of rnc from

�0.6 at P20 keV to �0.4 at 2 keV, a repeat ofthe complete analysis gives a limit lower by a fac-

tor 1.4 (see Table 4). Conversely, to illustrate the

effect of a systematic increase in the time constant

ratio, we note that a 10% increase in the value of

rnc ¼ 0.5 yields a limit of 1.8E�6 pb.

A.5. Light response matrix (see Section 5)

The variable light collection from the xenon ves-

sel is included in the final analysis by the rebinning

matrix ML(n,m), also combined with the energy

resolution matrix MR(n,m) as detailed in Section

9. The construction of the matrix requires the light

collection probability distribution dP(g)/dg where

g is the fraction of light collected, in turn obtained

by summation of the contributions from all parts ofthe chamber volume. This is estimated by a ray-

tracing simulation, which requires an assumption

about the reflectivity rw of the PTFE inner walls

of the vessel. However, because of the simple func-

tional form of dP(g)/dg (zero at g = 0 and 1, vary-

ing smoothly with a single maximum) it can be

characterized with sufficient accuracy by a single

parameter, which in turn is related to the volumeaverage value PAV = �dP(g)/dg/�dP(g) with �dP(g)normalized to 1. Thus variation of the internal

reflectivity rw will, to a close approximation, simply

change the average value PAV. The latter can be

measured experimentally and characterizes the

function dP(g)/dg from which the complete matrix

ML(n,m) can be obtained. Calibration with a60Co

source (which uniformly irradiates the whole

chamber volume) showed a 30 ± 3% reduction in

the position of the peak. This has been monitored

and remains constant throughout the surface tests

and underground runs. Accordingly ML(n,m) andthe corresponding limit was determined for

PAV = 65%, 70%, 75%. The results are shown in

Table 4, PAV = 70% being the most probable.

A.6. Attenuation length and light output

Using ray-tracing simulations, we find that an

improvement in attenuation length would accountentirely for the increase in light collection between

the different runs, while having only a second

order effect (<a few %) on the ratios of light collec-

tion from different parts of the chamber. Thus,

changes in attenuation length will not significantly

alter the rebinning matrix ML(n,m) or the average

PAV (discussed in (e)). This is consistent with the

fact that PAV is not observed to change signifi-cantly between runs.

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First limits on nuclear recoil events from the ZEPLIN I galactic dark matter detector

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Transcript of First limits on nuclear recoil events from the ZEPLIN I galactic dark matter detector