Searching for WIMPs by the annual modulation signature

2 April 1998

Ž .Physics Letters B 424 1998 195–201

Searching for WIMPs by the annual modulation signature

R. Bernabei a, P. Belli a, F. Montecchia a, W. Di Nicolantonio b, A. Incicchitti b,D. Prosperi b, C. Bacci c, C.J. Dai d, L.K. Ding d, H.H. Kuang d, J.M. Ma d

a Dip. di Fisica, UniÕersita’ di Roma ‘‘Tor Vergata’’ and INFN, sez. Roma2, I-00133 Rome, Italyb Dip. di Fisica, UniÕersita’ di Roma ‘‘La Sapienza’’ and INFN, sez. Roma, I-00185 Rome, Italy

c Dip. di Fisica, UniÕersita’ di Roma III and INFN, sez. Roma, I-00185 Rome, Italyd IHEP, Chinese Academy, P.O. Box 918r3, Beijing 100039, China

Received 14 November 1997Editor: K. Winter

Abstract

Ž .A set of preliminary test data, collected with large mass highly radiopure NaI Tl detectors, has been analysed by amaximum likelihood method to search for the WIMP annual modulation signature. q 1998 Published by Elsevier ScienceB.V.

1. Introduction

In this paper the maximum likelihood method hasbeen applied to a preliminary data set collected with

Ž .large-mass highly-radiopure NaI Tl detectors, in or-der to study the possible presence of an annualmodulation of the WIMP rate in the target-detectorset-up. Standard assumptions for the WIMP modelhave been considered in the following.

The annual modulation of the WIMP rate on atarget-detector is induced by the Earth’s motion

w xaround the Sun 1,2 . In fact, the expected recoilenergy spectrum depends on the WIMP velocitydistribution and on the Earth’s velocity in the galac-

Ž .tic frame, Õ t . It varies along the year according tor

the expression:

Õ t sV qV cosg cosv ty t ; 1Ž . Ž . Ž .r Sun Earth 0

here V s232 kmrs is the Sun’s velocity withSun

respect to the halo; V s30 kmrs is the Earth’sEarth

orbital velocity around the Sun on a plane with

inclination gs608 respect to the galactic one; fur-thermore, vs2prT with Ts1 year and t ,2nd

0Ž .June when the Earth’s speed is at maximum . The

WIMP velocity distribution in the galactic halo frameis considered to be a Maxwellian distribution with Õ0

Ž .(parameter defined as 2r3 Õ and a cut-offŽ . r.m .s.

velocity equal to the escape velocity of the Galaxy.The Earth’s velocity can be conveniently expressed

Ž . Ž . Žin unit of Õ : h t sÕ t rÕ sh qDhcosv ty0 r 0 0.t , being h s1.05 the yearly average of h and0 0

Dhs0.07. Since Dh<h , the signal rate in the0

k-th energy interval is accurately given by the firstorder Taylor approximation:

ESkw xS h t sS h q Dhcosv ty tŽ . Ž .k k 0 0Eh h0

sS qS cosv ty t , 2Ž . Ž .0,k m ,k 0

being the contribution from the highest order termsless than 0.1%. It is important to note that the Sm ,k

0370-2693r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved.Ž .PII S0370-2693 98 00172-5

( )R. Bernabei et al.rPhysics Letters B 424 1998 195–201196

contributions can be not only positive, but also nega-tive or zero, due to the expected energy distributionprofiles in June and in December within a finite

w xenergy window 3 . Therefore, the highest sensitivitywill be obtained considering the smallest energy binsallowed by the available statistics and a whole year

w xstatistics 4 .Although the modulation effect is expected to be

small, a suitable large-mass, low-radioactive set-upwith an efficient stability monitoring would point outits presence. In fact, a correlation analysis can allowto extract even a small periodic component, super-posed with a larger time independent signal and a

w xbackground 2 . In addition, with the present technol-ogy, the annual modulation remains the main signa-ture of a possible WIMP signal 1.

Finally, let us remark that the safest strategy is tocompare results on exclusion plot and modulationobtained within the same experiment. In particular,the comparison of exclusion plots obtained by differ-ent experiments requires a consistent use of astro-

Ž .physical local density, velocities and nuclearŽ .physics matrix elements, spin factors, form factors

Žparameters. Also the instrumental effects energythreshold, noise rejection capability, detector resolu-

.tions and quenching factors have to be always ade-quately introduced. Moreover, for different target-de-tectors further uncertainties could also arise becauseof the needed rescaling from the cross section of the

Ždifferent target-nuclei to s the WIMP-proton elas-p.tic cross-section and because of possible different

unknown or underestimated systematic errors.

2. The experimental data

The data considered here have been collected withŽ .nine 9.70 kg NaI Tl detectors, part of the 115.5 kg

Ž .higly radiopure NaI Tl set-up now running at the

1 We comment, in particular, that a pulse shape discrimination– even under the assumption of an ‘‘ideal’’ electromagneticbackground rejection – cannot account alone for a WIMP signa-ture. In fact, e.g. the neutrons and the internal end-range a ’sinduce signals indistinguishable from WIMP induced recoils andcannot be estimated and subtracted in any reliable manner at theneeded precision.

w xGran Sasso Laboratory 4 . The detectors were en-closed in a low radioactivity copper box inserted in alow radioactivity shield made by 10 cm of copperand 15 cm of lead; the lead was surrounded by 1.5mm Cd foils and about 10 cm of polyethylene. Anitrogen atmosphere is maintained inside the copperbox by a continuous flux of high purity nitrogen gasfrom bottles long stored deeply underground. A de-

w xtailed description of the detectors can be found in 5 .We recall, in particular, that each detector is viewedby two low-background EMI photomultipliers work-ing in coincidence at single photoelectron threshold;

w x2 keV is the software energy threshold 5 . Weremark that a 2 keV pulse corresponds in our case to

Ž .11–15 photoelectrons depending on the detector ,well distinguishable from PMT noise by using thepulse information recorded over 3250 ns by a LecroyTransient Digitizer. In fact, the ‘‘physical’’ pulseshave a time distribution with a decay time hundredsof ns, while the PMT noise is present in form of fastsignals.

A statistics of 4549.0 kg=day is available for theannual modulation studies: 3363.8 kg=day in thewinter time and 1185.2 kg=day in the summerperiod. It is distributed along the year in the follow-

Ž .ing way: y1Fcosv t y t Fy0.334 in winteri 0Ž .time and 0.932Fcosv t y t F0.996 in summeri 0

time. It is evident that part of the time of a similarexperiment – mainly at its beginning – is devoted toperiodical needed studies on calibrations, detector

Fig. 1. Energy distributions measured by the nine detectors.

( )R. Bernabei et al.rPhysics Letters B 424 1998 195–201 197

Ž .Fig. 2. Example of behaviours of some parameters. From top to bottom: external radon see text ; operating temperature; HP N flux in the2

Cu box containing the detectors.

features and qualification; in particular, during theŽlonger winter period corresponding to the whole

.quoted cosine range , several periods have been alsodevoted to these purposes. Obviously the used analy-sis method properly takes into account both thecollected low energy statistics and the cosine rangein which it has been taken. All the available lowenergy data collected in the two periods have beenconsidered. In Fig. 1 the measured energy distribu-tions are shown. They are given – as in all theprevious experimental papers on Dark Matter searchŽ .although generally not explicitly quoted – in keVelectron equivalent, the detectors being always cali-brated with g sources. The quenching factors for Naand I have been properly measured inducing nuclearrecoils in the whole sensitive volume by neutronelastic scattering and they are, respectively, 0.30 and

w x 20.09 5,6

2 For the sake of comparison, we recall that the measuredquenching factors of other nuclei in the most widely used target-

w xdetectors are listed in Table 1 of Ref. 7 with the exception of thetarget-bolometers for which systematic measurements on the dif-ferent types – accounting also for the response of the bulk of thedetectors – are not yet available.

Note that here we do not adopt any pulse shapeŽ .analysis PSA technique to reject electromagnetic

Ž w x. .background see 5,6 . In fact: i the PSA has – in.any case – a statistical nature; ii in case it givesŽupper limits on the WIMP signal as it is generally

.the case , its results cannot be used for the annual.modulation analysis; iii the annual modulation anal-

ysis acts itself as a very efficient background rejec-tion. In any case, as it will be shown in Fig. 4, theresult presented here is well compatible with the

w xupper limits obtained in Ref. 5 by using also thesedetectors and PSA.

As regards the data taking considered here – inŽ .addition to the controls on calibration see later –

also other parameters determining the stability of theexperimental apparatus have been monitored. Amongthem let us remember the level of external environ-mental radon, the HP N flux and the overpressure2

of the Cu box in which the detectors are, the temper-ature, the total and single crystal rates over the single

Žphotoelectron threshold i.e. from noise to.‘‘infinity’’ . In Fig. 2 examples of the behaviour of

some of these parameters in the long term are shown.In particular the stability control profited of the

210 Pb peak at 46.5 keV present at level of a few


210 ŽFig. 3. Typical spectrum showing the Pb peak at 46.5 keV see.text .

cpdrkg, mainly due to a surface contamination byenvironmental radon during the first period of thecrystals storage underground; both the peak positionand the resolution have been controlled binning to-

Ž .gether the data every ,7 days see Fig. 3 . ThisŽallowed an intrinsic monitoring of the threshold we

recall that scintillators are not affected by micro-.phonic noise as ionizing and bolometer detectors

Žand of the calibration stability e.g. PMT gain and.electronic line stability .

In the following, we will further summarize themain features of the experiment allowing the control

.of possible systematics: a data have been takenŽfirstly in winter and, then, in summer time therefore

possible positive effects cannot be accounted by. .isotope decay ; b the threshold, the PMT gain and

electronic line stability have been verified both bythe features of 210 Pb calibration peak and by moni-

.toring the rates; c the operating temperature hasbeen controlled and the environmental temperaturein the installation is not influenced by external sea-

.sonal variations, being conditioned; d the stability inthe 12–20 keV energy region allowed to verify thatno appreciable variation of neutron, of electromag-netic background and of environmental conditionswere present, although it is not clear how all of themcould vary with the same period and phase of a

.possible WIMP signal; e the external environmental

radon has been recorded, although two levels ofŽsealing in supronyl maintained in HP N long stored2

.underground isolate the shield containing the Cu.box in which the detectors are enclosed; f the HP N2

flux in the Cu box and its overpressure have beenmonitored.

Further ‘‘off-line’’ controls having the goal toverify the absence of significant systematics will bediscussed in Section 4.

Finally, we stress that possible systematics isstrongly dependent on the quality of an experiment,therefore its nature and level is generally very differ-ent from one experiment to another. On the otherhand, in the annual modulation case – if present –systematics can either simulate the presence of anunexisting signal or cancel the presence of a realone; therefore, an a priori decision on the role of itspossible ‘‘generic’’ presence would be arbitrary.

3. The maximum likelihood method and the questfor a candidate

To determine the cross section and the mass of apossible WIMP candidate, a time correlation analysisof all the data – properly considering the timeoccurrence and energy of each event – has beenperformed.

The experimental data collected by a j-th detectorof mass M are considered as grouped in 1-day timej

bins and in DEs1 keV energy bins; the number ofthe events in the i-th day and k-th energy bin, N ,i jk

will follow a poissonian statistics with mean valueŽ Žgiven by m s b q S q S cos v t yi jk jk 0, k m , k i

..t M Dt DEe , where a time independent back-0 j i jk

ground contribution, b , has been included in addi-jk

tion to the dark matter signal searched for. Here Dti

represents the detector running time during the i-thŽ .day DtF1 day and e represents the analysis cutjk

w xefficiency 5 . The maximum likelihood function is:mNi jkym i jki jkLsP e . The usual procedure to obtaini jk N !i jk

the best fit value of the free parameters is to mini-Ž .mize the function: ysy2ln L yconst. Consider-

ing the data collected with all the 9 crystals at thesame time and in all the energy bins, we can writeysS y .i jk i jk


Table 1S values obtained by the maximum likelihood methodm ,k

Energy Sm ,kŽ . Ž .keV cpdrkgrkeV

2– 3 0.023"0.0373– 4 0.017"0.0304– 5 0.036"0.0275– 6 0.042"0.0216– 7 0.038"0.0227– 8 0.003"0.0238– 9 0.050"0.0249–10 0.065"0.025

10–11 0.032"0.02611–12 0.053"0.02712–13 0.015"0.02813–14 0.017"0.02914–15 0.023"0.03015–16 y0.045"0.02916–17 0.008"0.03017–18 y0.031"0.02918–19 0.002"0.03119–20 0.016"0.030

As a first step, to allow a direct simple compari-son of the sensitivity reached here with those of

w xprevious experiments 3,8 , we have independentlyminimized the single y sS y values with re-k i j i jk

Žspect to the corresponding S and to all the b qm ,k jk.S contributions. The obtained S values are0, k m ,k

shown in Table 1; it is evident the relevance ofincreasing the collected statistics.

To obtain a first qualitative view from Table 1,we can initially point our attention e.g. on the 2–12

ŽkeV energy bin where a signal contribution can a. ² : Žpriori be expected , where S s 0.037"2 – 12m

.0.008 cpdrkgrkeV and on the one between 12–20ŽkeV where no significant signal contribution can a

. ² : Žpriori be expected , where S s 0.000"12 – 20m.0.010 cpdrkgrkeV. The first value qualitatively

supports the presence of a possible modulation, re-quiring therefore a suitable statistical analysis of thedata to verify if it can be in total or in part ascribedto a possible WIMP presence, or it can not. Thesecond value well supports the absence of an overallsystematics significantly exceeding the statistical er-ror in the interesting energy region.

w xWe stress that here and in 4,9 the achieved resultŽ .see later is not linked to this qualitative descriptionŽ ² : .that is, it is not linked to any S value , but2 – 12m

to the application of the maximum likelihood method( )on all the aÕailable data 2–20 keV described in the

following. An unbiased statistical analysis on all theavailable data at the same time has been then per-formed; this analysis will be presented in Section 4and its results will be quantified by C.L. and x 2

values.The maximum likelihood method is well suitable

to test if the modulated effect qualitatively describedŽ .above can or not be accounted by a WIMP with

cross section and mass allowed for instance for thew x Ž .neutralino 10 , assuming a Spin-Independent SI

interaction and, if it can, at which C.L. In particular,we refer our results to the quantity js , where jp

r y3WI MPs , r s0.3 GeV cm and to s , WIMP cross0 pr0

section on proton. For this purpose, we note that S0, k

and S can be written – pointing out their depen-m ,k

dence on js and the WIMP mass M – in the formp wX Ž . X Ž .S sjs S M and S sjs S M respec-0, k p 0,k w m ,k p m ,k w

X Ž . X Ž .tively. The S M and S M values can be0, k w m ,k ww x Žcalculated according to 5 e.g. besselian form fac-

.tor, js1, etc. . The js and M values in the bestp w

agreement with the experimental data have beenobtained by minimizing here the y function – usingall the events with their energy and time occurrence– with respect to the free parameters: js , M andp w

bX s. A two-step minimization strategy allowed us tojk

handle this large number of parameters. In fact, by aŽ .preliminary y minimization the b qS s fjk 0,k jk

values have been determined and then, by a subse-quent one, also the js and M values. In this lastp w

Ž .step, the conditions M G25 GeV and b qSw jk 0,kf Xjk Ž .Xs f if js F or b qS sjs S other-jk p jk 0,k p 0,kS0 ,k

wise are required, to take into account both theresults achieved at accelerators for SUSY particlesand the obtained values for the unmodulated term.

The minimum value of the y function has beenŽ q 36 .found for M s 59 GeV and js sw y 19 p

Ž q0.1. y51.0 10 pb.y0.4

4. Consistency checks and statistical evaluations

To verify the consistency of this result, M hasw

been fixed and both js and the modulation periodp

T have been considered as free parameters, obtainingŽ q0.4.still the previous value for js and Ts 1.3p y0.3


years, a period compatible with a yearly modulation.Then, both M and T have been fixed, while jsw p

and the phase t have been considered as free pa-0

rameters, obtaining the already found js value andpŽ q49. ndt s 140 days, a phase compatible with ,20 y43Ž .June ,153-th day in the year 1996 . The uncertain-

ties quoted for T and t are due to the limited0

available statistics and to the particular periods ofdata taking.

It is evident that the verification of the period andphase by the maximum likelihood method limits thepossible systematics to those effects able to inducean annual modulation with 1 year period and ,2nd

june phase. This will be even a stronger constraintŽwhen almost whole years data taking periodical

calibrations and others are obviously needed in any.case will be considered.

Finally, a suitable analysis of the maximum likeli-Ž . Ž .hood ratio, lsL H rL H , has been performed0 1

Žto test the goodness of the null hypothesis H ab-0.sence of modulation with respect to the H hypoth-1

Žesis presence of modulation according to the given.M and js . From the definition of the y functionw p

we obtain lsew yŽH1.yyŽH0 .xr2; clearly 0FlF1. Al value close to 1 will imply absence of modulation,while a l value close to 0 will support the presenceof modulation with the given M and js . Tow p

perfom a quantitative statistical test, one can use theŽ .variable y2lnl which is asymptotically distributed

2 Žas a x high values of y2lnl will support pres-. 2ence of modulation . At 90% C.L. the upper tail x0

is equal to 2.7 for 1 degree of freedom; in our casey2lnls3.14)x 2. Therefore the hypothesis of no0

modulation can be rejected in favour of the hypothe-sis of modulation with the given M and js atw p

90% C.L. 3. At this point the agreement between H1

and the experimental data has been analysed by a x 2

test comparing the obtained S of Table 1 with them ,k

expected values; a probability of 6%, to have – onlybecause of statistical fluctuations – a x 2 valuehigher than we found, has been calculated. Thisprobability is mainly limited by the S valuesm ,k

3 We remark that this C.L. found in the overall analysis alreadyŽaccounts for the single crystal response remember the method

.features and the L function definition , that is for ‘‘possiblemodulation’’ spread over the crystals.

between 8 and 12 keV, which show up to ,2s

fluctuations from the expected ones 4. It is, there-fore, evident the relevance of data now under analy-sis with a statistics about 7 times larger than thepresent one.

We note that here the – widely considered –w xHelm SI form factor has been used for iodine 11 ; in

any case, no relevant effects – within the presenterrors – on the quoted M and js were observedw p

w xwhen adopting different SI form factors 12 .Ž .Moreover, we have also analyzed the NaI Tl data

with the procedure described above, to test the hy-pothesis of a modulation effect due to a spin-depen-

Ž .dent SD coupled WIMP. The calculation has beenw xperformed according to 5 , but using here for iodine

w xthe recently published Ressel SD form factor 13 .The y function is obviously different from the SIcase, mainly because of the different behaviour ofthe form factor with the transferred momentum. Inthis case, no minimum of the y function has beenfound satisfying the condition d yrdM sd yrdsw p

s0 in the Wimp mass region exceeding the limitsset at accelerators.

We recall – at this point – that preliminary resultson searches for the annual modulation signature havebeen also obtained by using a liquid Xenon scintilla-

Ž . w xtor statistics of 408.2 kg=day 3 and the CanfrancŽ . Ž . w xNaI Tl detectors statistics of 1342.8 kg=day 8 .

This last experiment had a poorer sensitivity than theprevious one and, to a larger extent, than the presentone, mainly because of the higher background rate.Also these experiments considered only the two ex-treme periods. In spite of our initial considerations,to obtain a comparison, we have examined the Xenon

w xresult of Ref. 3 . In this case we have performed astandard best fit on the S values, constraining Mm ,k w

by the accelerator limits and js by the morepŽ .stringent results obtained with the NaI Tl detector

w x5 . An indication for M ,60 GeV and js ,0.5Pw p

10y5 pb – values compatible with those obtainedabove – has been found, but with extremely poor

4 To have a qualitative view one can overimpose the S curvem ,k

calculated using the found M and js values on the S ofw p m ,k

Table 1; it is evident that the calculated curve is fully under theS points and the deviations are quantitatively represented bym ,k

the poor value for the C.L.


Fig. 4. Plane js versus M : the region allowed by this prelimi-p wŽ .nary analysis at 90% C.L. see text is shown. The best upper limit

contour for spin independent interaction, obtained so far, is super-w ximposed 5,13 ; the blank area is excluded at the given C.L., while

the shaded one represents the values for M and js notw p

explored till now.

C.L.; this could be ascribed to the reduced statisticsŽ .a factor ,11 smaller than the present one andsensitivity available there.

In Fig. 4 the region allowed at 90% C.L. – for aSI coupled candidate – by the obtained js and Mp w

values is shown; the best upper limit contour for SIw xinteraction obtained so far 5,14 is superimposed.

The shaded region represents the values for M andw

js neither excluded by the present analysis nor byp

the exclusion plot. It has been noted that this regionis well embedded in the Minimal Supersymmetric

Ž .Standard Model MSSM estimates for neutralinow x10,15 .

5. Conclusions

We can comment that the present statistical evi-dence, although in the usual range considered in rareevent searches, it is not very stringent. Only verylarge exposure would allow to reach a firm conclu-

sion; similar exposures will be obtained in nearfuture by our experiment, which is continuouslyrunning.

Considering both the difficulty of this kind ofsearches and the relevance of a positive result, acautious attitude is mandatory. We can conclude thatthis is a bare status report on first experimental data;however, it singles out a possible region – with

w xinteresting features 15 – which we are now furthercarefully investigating with much larger statisticsand in improved conditions. In particular a statisticsof about 20000 kg=day is already under analysis.

Acknowledgements

We gratefully acknowledge Prof. S. d’Angelo formany helpful discussions. We wish to thank Mr. A.Bussolotti and G. Ranelli for their technical help andthe LNGS staff for support.

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Searching for WIMPs by the annual modulation signature