Direct dark matter search in XMASS-I

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Physics

Letters

B

www.elsevier.com/locate/physletb

A

direct

dark

matter

search

in

XMASS-I

XMASS

Collaboration



K. Abe

a

,

e

_,

_{K. Hiraide}

a

,

e

_,

_{K. Ichimura}

a

,

e

_,

_{Y. Kishimoto}

a

,

e

_,

_{K. Kobayashi}

a

,

e

_,

_{M. Kobayashi}

a

_,

S. Moriyama

a

,

e

,

M. Nakahata

a

,

e

,

T. Norita

a

,

H. Ogawa

a

,

e

,

1

,

K. Sato

a

,

H. Sekiya

a

,

e

,

O. Takachio

a

,

A. Takeda

a

,

e

,

S. Tasaka

a

,

M. Yamashita

a

,

e

,

B.S. Yang

a

,

e

,

2

,

N.Y. Kim

b

,

Y.D. Kim

b

,

Y. Itow

c

,

f

,

K. Kanzawa

c

,

R. Kegasa

c

,

K. Masuda

c

,

H. Takiya

c

,

K. Fushimi

d

,

3

,

G. Kanzaki

d

,

K. Martens

e

,

Y. Suzuki

e

,

B.D. Xu

e

,

R. Fujita

g

,

K. Hosokawa

g

,

4

,

K. Miuchi

g

,

N. Oka

g

,

Y. Takeuchi

g

,

e

,

Y.H. Kim

h

,

b

,

K.B. Lee

h

,

M.K. Lee

h

,

Y. Fukuda

i

,

M. Miyasaka

j

,

K. Nishijima

j

,

S. Nakamura

k

a_{KamiokaObservatory,InstituteforCosmicRayResearch,theUniversityofTokyo,Higashi-Mozumi,Kamioka,Hida,Gifu,506-1205,Japan} b_{Centerfor UndergroundPhysics,InstituteforBasicScience,70Yuseong-daero1689-gil,Yuseong-gu,Daejeon,305-811,SouthKorea} c_{InstituteforSpace-EarthEnvironmentalResearch,NagoyaUniversity,Nagoya,Aichi464-8601,Japan}

d_{InstituteofSocio-ArtsandSciences,TheUniversityofTokushima,1-1MinamijosanjimachoTokushimacity,Tokushima,770-8502,Japan} e_{KavliInstituteforthePhysicsandMathematicsoftheUniverse(WPI),theUniversityofTokyo,Kashiwa,Chiba,277-8582,Japan}

f_{Kobayashi-MaskawaInstitutefortheOriginofParticlesandtheUniverse,NagoyaUniversity,Furo-cho,Chikusa-ku,Nagoya,Aichi,464-8602,Japan} g_{DepartmentofPhysics,KobeUniversity,Kobe,Hyogo657-8501,Japan}

h_{KoreaResearchInstituteofStandardsandScience,Daejeon305-340,SouthKorea} i_{DepartmentofPhysics,MiyagiUniversityofEducation,Sendai,Miyagi980-0845,Japan} j_{DepartmentofPhysics,TokaiUniversity,Hiratsuka,Kanagawa259-1292,Japan}

k_{DepartmentofPhysics,FacultyofEngineering,YokohamaNationalUniversity,Yokohama,Kanagawa240-8501,Japan}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received9April2018

Receivedinrevisedform17August2018 Accepted12October2018

Availableonline5December2018 Editor:M.Doser

Keywords:

Darkmatter Lowbackground Liquidxenon

A search for dark matter using an underground single-phase liquid xenon detector was conducted at the Kamioka Observatory in Japan, particularly for Weakly Interacting Massive Particles (WIMPs). We have used 705.9 live days of data in a fiducial volume containing 97 kg of liquid xenon at the center of the detector. The event rate in the fiducial volume after the data reduction was (4.2 ±0.2)×

10−3_day−1_kg−1_keV−1

ee at 5 keVee, with a signal efficiency of 20%. All the remaining events are consistent

with our background evaluation, mostly of the “mis-reconstructed events” originated from 210_{Pb in the}

copper plates lining the detector’s inner surface. The obtained upper limit on a spin-independent WIMP-nucleon cross section was 2.2 ×10−44_cm2 _{for a WIMP mass of 60 GeV/c}2 _{at the 90% confidence level,}

which was the most stringent limit among results from single-phase liquid xenon detectors.

©2018 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3_.

 _{E-mailaddress:xmass.publications6@km.icrr.u-tokyo.ac.jp.}

1 _{NowatDepartmentofPhysics,NihonUniversity,1-8Kanda,Chiyoda-ku,Tokyo,} 101-8308,Japan.

2 _{NowatCenterforAxionandPrecisionPhysicsResearch,InstituteforBasic} Sci-ence,Daejeon34051,SouthKorea.

3 _{NowatDepartmentofPhysics,TokushimaUniversity,2-1MinamiJosanjimacho} Tokushimacity,Tokushima,770-8506,Japan.

4 _{NowatResearchCenterforNeutrinoScience,TohokuUniversity,Sendai,Miyagi} 980-8578,Japan.

1. Introduction

The existence ofdark matter (DM)inthe universe isinferred frommanycosmologicalandastrophysical observations[1,2].The nature of DM’s particle content, on the other hand, is still un-known.AnumberofDMdirectdetectionexperimentsaimto ob-serveDMinteractingwithnucleiintheirtargetmaterials,resulting innuclearrecoils[3].XMASS,asoneofthedirectdetection exper-iments,searchesforWeaklyInteractingMassiveParticles(WIMPs), one ofthe well-motivated DMcandidates [4–6], aswell asother DMcandidatessuchassuper-WIMPs[7].

https://doi.org/10.1016/j.physletb.2018.10.070

0370-2693/©2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

Consideringthe latest experimental constraintson the WIMP-nucleon cross section, requirements for the detectors to have a large target mass, ultra-low background (BG), and a low energy threshold,are growing inimportance. Experimentsusing a noble liquid(xenonorargon)targetareattheforefrontofcurrentWIMP searches [8–12] as they satisfy these requirements, with some achievingultra-low BGby particle identification. Particle identifi-cationsinthenobleliquiddetectorarerealizedbyscintillationin the gasphase seen in dual-phase detectors [8–10] and by decay timeseeninliquidargondetectors[11,12].

XMASS-Iisasingle-phaseliquidxenon(LXe)detectordesigned torealizealowBGleveloflessthan10−4day−1kg−1keV−_ee1 with afiducialmassof100kg andan energythresholdofa fewkeVee

[13,14]. A single-phase detector has a simple geometry;a

mini-mum requirement is the target and surrounding PMTs. The

de-tector design ofXMASSpursues this simplicityasa potential for

a scaling-up, low BG with a minimum detector component, and

alow energythresholdwitha large photo-coverage.Anotherkey ideato achievelow BGwiththe single-phaseLXe detectorwhich doesnothaveadecentparticleidentificationisshieldingof

γ

-rays from outside material with a large-Z material xenon itself (self-shielding).Since thepropertiesofDMarestillunknown,searches withvariousexperimental configurations are importantforresult reproducibilityandvalidation.

Thispaperpresents theresultsof aWIMP search inthe fidu-cial volume ofthe XMASS-I detector. The amount of BGand its systematic error were evaluated from a detailed detector simu-lation verified on a range of different detector calibrations. The WIMPsignalwassearchedbyfittingtheobservedenergyspectrum withthesumofevaluated BGandthesignal. The abundancesof radioactiveisotopes(RIs)assumedintheBGpredictionwere inde-pendentlymeasured withdedicatedequipmentorestimatedfrom theXMASS-Idataitself.

2. TheXMASS-Idetectorandthesimulations

The XMASS-I detector [15] in the Kamioka Observatory is lo-catedunderground atadepth of2700meterwaterequivalent. It consists of a water-Cherenkov outer detector(OD) anda single-phaseLXe innerdetector(ID). TheOD isa cylindricalwatertank with a diameter of 10 m and a height of 11m and contains ul-trapurewaterreadby7220-inchphotomultipliertubes(PMTs).It servesasashieldagainstfastneutronsandexternal

γ

-raysaswell asanactive muonveto[15].The 222Rn contentinthewaterwas continuously monitoredandkeptlessthan 10mBq/m3 exceptfor onetime whereitwent upto

∼

150mBq/m3 duetoatrouble in thewaterpurificationsystem.

ThestructureoftheIDisshowninFig.1-(a).Allits structural elementsincludingthevacuumvessel,LXecontainmentvessel,and PMTholderaremadeofoxygenfreehighconductivitycopper.The

photocathodes of the 642 low radioactivity Hamamatsu R10789

PMTscover 62.4% ofthepentakis-dodecahedral ID’sinner surface which is

∼

40cm from its center (hereafter HamamatsuR10789 PMTsarecalledPMTs).ThequantumefficiencyofthePMTsatthe LXe scintillation wavelength (

∼

175nm [17]) is 30% on average. The LXe contained in the active volume bounded by the copper andthephotocathodeshasatotalmassof832kg.

Fig.

1

-(b)showsthestructurebelowtheIDsurfacealongacut indicatedasthelineA

−

AontherightsideofFig.

1

-(a).Duringthe

XMASS-I commissioningphase we found that thealuminum seal

betweenthePMTs’quartzwindowsandtheirmetalbodiescontain theupstream portion ofthe238_{Udecaychain and}210_{Pb[15]. To}

mitigate this, we refurbished the detectorin 2013and installed: A) acopperringaroundeachPMTs’window/metalbodytransition todisplacemostoftheLXeandblock scintillationlight emerging

Fig. 1. (a)ThestructureoftheIDontheleftandaninsideviewofitsinnersurface ontheright(green:photocathode,yellow:copperplate).Notshownarethecopper blocksfillingthevolumeoutsidethePMTholdertodisplaceLXeuptothesurface oftheliquidphase.(b)Crosssectionalviewofthestructurebelowtheinnersurface alongtheA–Alineinpanel(a).(c)Copperplatearoundtheboundary.

from the vicinity of thisseal, and B) copper plateswith cutouts forthePMTphotocathodeareastocoverthegapsbetween neigh-boringPMTs’copperrings. Wealsovapor-deposited aluminumon theside ofthePMTwindowtoprevent scintillationlight emitted attheinevitablegapbetweentheringandthePMTfromentering

the PMT window and the sensitive detector volume. The copper

plates,eachcoveringatriangleinthepentakis-dodecahedralID in-nersurface,haveoverlappinglipsalongtwooftheirthreeedgesas shownontheleftsideofFig.1-(c);alongthethirdedgehowever, there is no overlapbetween thetwo neighboring platesas illus-tratedontherightsideofFig.1-(c). Thecopperrings,plates,and holderswereelectro-polishedandthePMTwindowswerewashed withnitricacidtoreducethe210Pbontheirsurfaces.

The signalsfrom the PMTs were recorded using CAENV1751

waveform digitizers witha samplingrateof 1GHz. An ID trigger was issued ifatleastfourofthe PMTs detectedsignals dropping belowa thresholdof

−

5mV within200ns,whichcorresponds to 0.2photoelectrons(PE).Inthefollowing,suchasignal willbe re-ferred toasa hit.Onlythe PMTsignalsaroundthe regionbelow athresholdof

−

3mV werestored.Thewaveformswereintegrated to calculatethe numberof PE ineach PMTby correcting forthe time-dependent gainandtheeffectofdoublePEemissionby sin-glephotonsofLXescintillation[16].Then,thenumbersofPEfrom allthePMTswithina500nswindowaroundthetriggertimewere summeduptoobtainthetotalnumberofPEofanevent.Thegains ofthePMTswerecontinuouslymonitoredbymeasuringasinglePE withablueLEDembeddedintheinnersurfaceofthedetector. En-ergycalibrationsbetween5

.

9keV and2

.

6MeV wereconductedvia

theinsertionof55_Fe,109_Cd,241_Am,57_Co,and137_{Cssourcesalong}

theverticalaxisintothedetector’ssensitivevolume,andbysetting

60_Coand232_{Thsourcesoutsidethevacuumvessel.Thetime}

vari-ationoftheenergyscalewastracedviairradiationwith60_Coand

the insertion of 57Co every week and every other week, respec-tively.The measuredvariation of thePE yield during datataking periodwasbetween13.0and14

.

8PE/keV for122keV gamma-ray. Thisvariationwas foundto beduetothe variationofabsorption lengthof 4.4–30 mwhile thescatteringlength was stable within 52–53 cm.The detectorresponse tothe nuclearrecoils,especially thescintillationdecaytime constants,measuredbyirradiatingthe detectorwithneutronsfroma252Cfsourcesetoutsidethevacuum vessel[18].

AGEANT4 [19] basedMonteCarlo(MC)simulationforXMASS wasdeveloped.Thedetectorgeometryandmaterialsandtheir re-spectiveradioisotope activitiesareincludedintheMCsimulation. TheMCsimulationcovers: (i)The generationofscintillation pho-tons considering the energy dependence and the nature of the depositingparticleand(ii)thetracingofeachscintillationphoton consideringtheopticalpropertiesofallthecomponentsincontact with the LXe and the properties of the LXe itself. The scintilla-tionefficiencyfornuclearrecoils(

Leff

)isconsideredintheprocess of (i).Thenon-linearityofthescintillationefficiencyforelectronic eventswas takeninto account using a non-linearity modelfrom [20] with a further correction based on our gamma-ray calibra-tions. An angle dependent reflection, and absorption atthe PMT photocathode,aswellasother aspects ofthePMT, togetherwith thedataacquisitionresponse,arealsoconsidered.Themodelwas verifiedbyreproducingbasicdistributionssuchasobservedPE dis-tributionsandreconstructedenergiesandpositions[21].

3. Eventselection

The data used in this analysis was accumulated between

November 2013andMarch 2016. 10 days fromthe neutron

cal-ibration and periods with data acquisition problems were

re-moved from the data set. Then periods which have more than

one 10-minutes’-average rateout of5

σ

from themean value or withmore than 40 triggers in any second were eliminated. The total live time was 705.9 days. All ID triggers without a muon veto(ODtrigger) are considered asevents.A cuton eventswith astandard deviationofhit timingsgreater than100ns ora time differencefrom theprevious eventofless than10ms, isused to removenoiseeventscausedbyPMTafterpulsestypicallyO(

μ

s)to O(ms)afterahighenergyevent.Waveformsoscillatingaroundthe pedestallevel areremoved aselectronic noise.Cherenkovevents, primarilygeneratedby

β

-raysfrom40KinthePMTphotocathodes, areremovedbyeliminatingeventswith(thenumberofhitswithin thefirst 20ns)

/

(the totalnumber ofhitsin theevent)

>

0.6 for eventswith

<

200PE.Thecombinationofabovecutsisreferredto asthe“standardcut”hereafter.

Aneventvertexanditsdistancefromthecenterofthe detec-tor,R,isreconstructedforeachevent.Twodifferentreconstruction methodsexist,one based ontiming [22] andthe other basedon the PE distribution [15]. These methods are referred to as R

(

T

)

, andR

(

P E

)

,respectively.

R

(

T

)

was calculated by comparing the observed and the ex-pectedtimingdistributionsofallPMTsbasedonamaximum like-lihood method. Intrinsic timing differences among all the PMTs wereadjusted withcalibration datafromthe57Cosourcelocated at R

=

0cm. The expected timing distributions at each position throughoutthe detectorvolume are calculated usingMC simula-tions. Because the time (

∼

10ns) in whichthe scintillation light crossthe sensitive volume is not much larger than the scintilla-tiontimeconstant(

τ

∼

27ns ormore)oreventransittimespread

Fig. 2. (Top)NumbersofPEdistributionsofdataaftereachreductionstep.Seethe textfor details.(Bottom) Thereconstructedenergydistributionofthefinaldata sample.

of our PMT (2

.

4ns in standard deviation), the position resolu-tion of R

(

T

)

is

∼

16cm at R

=

0cm and not as good as that of R

(

P E

)

. However, requiring R

(

T

) <

38 cm still eliminates some surface eventsthat are mis-reconstructedby thePE-based recon-struction;therefore,weuseaso-calledR

(

T

)

cutat38cm.

R

(

P E

)

is also reconstructed using a maximum likelihood method.Thelikelihood iscalculatedatseveralpositions through-out the detectorvolume by comparing theobserved andthe ex-pectednumberofPE ofallthePMTs,wheretheexpectednumber isderived fromMC simulations forreferencepositions ona grid. The position resolution of the R

(

P E

)

evaluated by the MC sim-ulations for an electron equivalent energy (keVee) of 5keVee is

∼

5

.

1cm at R

=

20cm.Afiducialvolume containing97kg of LXe was established by requiring R

(

P E

) <

20 cm decided by MC so that the self-shielding is effective. The observed PE is converted tokeVeeincorporatingall the

γ

-raycalibrationsdescribedin

sec-tion 2 and considering the non-linearity of the energy scale. To evaluate the performance of the reconstruction for low-energy events,a novelmethodtosimulatelow-energyeventsusinghigher energycalibration data,called “PEthinning”, was developed.The waveformsineachPMTaredecomposedintosinglePEpulses[23] andthesplitpulsesarerandomlythinnedtosimulatelow-energy eventhits. Thismethodwasusedtoevaluatethesystematicerror of the R

(

P E

)

reconstruction for the BG MC simulations in Sec-tion5andthatofthedetectionefficiencyinSection6.

The top ofFig. 2 showsthe PE distributions ofthe data after each reduction step. The final data sample is obtainedby apply-ing the standard andthe R

(

T

)

cut andthe R

(

P E

)

selection.The reconstructedenergyisestimatedfromtheobservedtotalnumber ofPEusingMCsimulationsforthepositiondependencecorrection. The positiondependenceofexpectednumberofPE atR

=

20cm fromthe detectorcenterisabout 6%.This correction isvalidated by source calibrations from Z

= −

40cm to

+

40cm by1cm step [15].ThebottomofFig.2showsthereconstructedenergy distribu-tionofthefinaldatasample.Thedecreaseintherateoftheevents withenergy

<

5keVeereflectsthelowefficiencyofthe R

(

P E

)

4. RadioactiveBGinXMASS-I

TheassumedradioactiveBGinXMASS-Iwasclassifiedaseither (1) RIs in the LXe, (2) 210_{Pb in the detector’s inner surfaces, or}

(3) RIsintheXMASSdetectormaterials.TheseBGswereestimated using the energy region of no contribution from WIMP-induced event. Also a subset of full data was used for the estimation of (2)and(3)toavoidthearbitrarybias.

(1)TheRIsof222Rn,85Kr,39Arand14CdissolvedintheLXeare retainedasBGeventsafterthefiducialvolumecut. Weestimated theseconcentrationsusingall705.9daysofdata.The222_Rn

activ-itywasobtainedbylookingfor214Bi–214Pocoincidencesidentified bythe 164

μ

s half-lifeof214_{Pointhe fullvolumeofthe ID,with}

onlythestandardcutappliedfor214_Biandonlythe

_α

_{-ray events}

selectedfor214Po. The

α

-ray eventswere selectedbasedontheir shorter scintillation decay time of less than 32ns. The selection efficiencywasestimatedtobe100% byMC.85_{Krwasidentified}

us-ingthe

β

–

γ

coincidencethatoccursinitsdecaywithabranching ratioof0

.

434% andahalf-lifeof1

.

015

μ

s with36

.

8% selection effi-ciency.Theconcentrationof222_RninLXeis10

_.

₃

_±

₀

_.

₂

_μ

_Bq/kgand

the concentration of 85Kr is0

.

30

±

0

.

05

μ

Bq/kgcorresponding to 6

.

5ppt ofkrypton.The39Arand14Cconcentrationswereevaluated by fittingthe R

(

P E

)

<

30cm spectrum above 30keVee [24]. This

appears to be justified because the energy region 30–250 keVee

should have nearly no contribution frompossible WIMP-induced nuclearrecoils andtheother RIs ((2) 210_{Pbcontamination inthe}

detector’s surface and (3) RIs in the components other than the LXeandtheinnersurfacematerial,discussedinthefollowing).

(2)The210_{Pbcontaminationatthedetectorsurfacewas}

evalu-atedbasedonastudyofthe

α

-rayeventsextractedfrom15days of data (asubset ofthe 705.9-day data sample in thisanalysis), usingthefullvolumeoftheIDand

α

-rayeventselection.The ac-tivity of 210_{Pb inside the copper plates which face the ID were}

evaluated using the

α

-ray PE spectrum of their preceding 210Po decaystogetherwiththeeventparameter“maximumPE/totalPE” (the ratioofthemaximumnumberofPE onasingle PMTtothe totalnumberofPE inthe event).Thisparameter’svalue depends on the location of the event. Fig. 3 shows the maximum PE/to-tal PE distribution asa function ofthe number ofPE. BGevents from 222_Rn, 218_{Po, and} 214_{Po are identified by their energy ((A)}

in Fig. 3). The values of the maximum PE/total PE are large for eventsoriginatingfromthePMT’squartzwindowsurface((B)and (C)inFig.3)becausethescintillationlightconcentratesonthe cor-responding PMT.The value of themaximum PE/total PE is small foreventsfromthecoppersurface.The

α

-rays from210Poonthe coppersurface depositlarger energy(D)compared tothose from

210_{Pocontaminatingtheinsideofthecopperplate(E).The}

satura-tionofthePMTslimitsthemaximumPEandaffectsthemaximum PE/totalPE.The shapeoftheBGMC simulationsreproduce these distinctive distributions. The

α

-ray events below thedashed line inFig.3areidentifiedasthe210Podecayswhichareusedto eval-uatethe210_{Pbconcentrationonthecoppersurface,andinsidethe}

copperplate.Theefficiencyofthecoppersurfaceandinsideofthe copperplateare27

.

5% and0

.

8%,respectively.Thesevaluesare es-timatedbytheBGMC.

The estimated concentration of 210_{Pb inside the copper plate}

is 25

±

5 mBq/kg. This is consistent with the estimated value of 17–40 mBq/kg from a measurement using our low BG

α

-ray counter[25].Theactivitiesintheringandtheholderareestimated fromthiscopperplate’sbulkactivitybyscalingtotheirrespective masses. Similarly, 210Pb concentrationson thePMT’squartz win-dowsurfaceandonthecoppersurface areobtainedfrom(B)and (C),and(D),respectively.

(3)TheRIsinthecomponentsotherthantheLXeandtheinner surface materialwere evaluatedvia fitstothe PEspectrum using

Fig. 3. Theα-rayeventdistributionbetweenthenumberofPEandtheratioofthe maximumPEonasinglePMTtothetotalnumberofPE(maximumPE/totalPE) for15daysofdata.Theclusterscanbeexplainedas:(A)222_Rn,218_Po,and214_Po inLXe,(B)210_{PoonthePMTquartzsurface,(C)}210_{PoonthePMTquartzsurface} atthebacksideoftheplate,(D)210_{Poonthecopperplatesurface,and(E)}210_Po contaminatedinthecopperplate.Thereddottedlineindicatestheseparation cri-teriaoftheα-rayeventsonthecopperfromotherevents.Inordertoinclude214_Po events,acutoneventswithatimedifferencefromthepreviouseventoflessthan 10ms isnotappliedforthisfigure.

Fig. 4. (Top)NumberofPEspectrafor15daysofdataandtheMCsimulationsinfull volume.Theblacklinerepresentsthedata.EachcolorhistogramisadifferentBGRI. Onebincorrespondsto400PE.ThecontributionsfromLXeand210_Pbonsurface, copperplateandringaresosmallthattheyarenotvisibleintheplot.(Bottom) TheratiooftheMCspectrum(bestfit)tothedataisshownasaredpoint.Thebar ontheredpointsindicatesthestatisticalerror.Theblueandgreenregionsindicate theuncertaintyintheradioactivityandthePEscalewith1σand2σ.

the same15daysofdata andMC simulations, butwithonly the standard cutapplied,i.e., usingthefull volumeoftheID.A large part of thisdata originates from

β

-rays and

γ

-rays entering the IDfromthedetectormaterials,withtheeventsreconstructed out-sidethefiducialvolume.238_U,235_U,232_Th,40_K,60_Coand210_Pbare

considered asRI candidates. All detectorcomponents, except for thecopperandtheLXe,wereassayedwithhighpuritygermanium (HPGe)detectorsandtheresultsofthesemeasurementswereused asinitial valuesandtheir uncertainties asconstraintsforthefull volumespectrumfit.Theenergyspectrumabove

∼

400PE wasfit todeterminetheactivitiesoftheRIs.ThesystematicerroroftheRI activitywasestimatedconsideringtheuncertainties oftheenergy scale, the geometryandthe initial assumption ofRIs. The fitting

Table 1

Summaryoftheradioactivityinthedetector.Thelistisorganizedfollowingthethreetypesof estimationmethods.InternalRIsinLXeareestimatedfromcoincidences(222_Rn,85_Kr)and spec-trumfitting(14_C,39_{Ar).Theactivitiesofthecopperplateanddetectorsurfacesareestimated} fromα-rayspectra.Theactivitiesof210_{Pbinthecopperringandtheholderareestimatedfrom} thecopperplate’sactivitybyscalingtotheirrespectivemasses.TheactivitiesofthePMTand thedetectorvesselmaterial,exceptfor210_{Pbintheholder,areestimatedbyfittingdata.Initial} valuesanderrorsofthefitweredeterminedbytheHPGedetectormeasurements.

Location of RI RI Activity[mBq/detector] initialvalueofthefit

Activity[mBq/detector] the bestfitvalue

LXe 222_{Rn – 8.53±0.16} 85_{Kr – 0} .25±0.04 39_{Ar – 0} .65±0.04 14_{C – 0.19±0.01}

Copper plate and ring 210_{Pb – (6.0±1.0)×10}2

Copper surface 210_{Pb – 0.7±0.1}

PMT quartz surface 210_{Pb – 6.4±0.1} PMT

(except aluminum seal andquartzsurface)

238_{U (1.5±0.2)×10}3 _{(2.0±0.2)×10}3 232_{Th (1.2±0.2)×10}3 _{(1.1±0.3)×10}3 60_{Co (1.9±0.1)×10}3 _{(1.6±0.2)×10}3 40_{K (5.8±1.4)×10}3 _{(9.6±1.7)×10}3 210_{Pb (1.3±0.6)×10}5 _{(2.2±0.7)×10}5 PMT aluminum seal 238_{U (1.5±0.4)×10}3 _{(9.0±4.1)×10}2 235_{U (6.8±1.8)×10}1 _{(4.1±1.8)×10}1 232_{Th (9.6±1.8)×10}1 _{(5.5±2.2)×10}1 210_{Pb (2.9±1.2)×10}3 _{(3.4±1.2)×10}3 Detectorvessel,

holderandfiller

238_{U (1.8±0.7)×10}3 _{(9.0±7.6)×10}2 232_{Th (6.4±0.7)×10}3 _{(6.4±3.2)×10}3 60_{Co (2.3±0.1)×10}2 _{(3.0±1.9)×10}2

210_{Pb – (3.8±0.5)×10}4

wasrepeatedbychangingeachoftheseconditions,andthemean andtheerrorofeachRIactivitywereobtainedfromthe distribu-tionoftheseindependentfittingresults.Fig.4showsacomparison of the 15-day full volume spectrum and the expected BG spec-trumcorresponding to the best-fit above 400PE.The thick black linerepresentsthedata,andthestackedcoloredspectrarepresent thevariousRIcontributionsdetailedintheupperpanelofthe fig-ure.ThesixcolorsindicatethedifferentBGsources.As expected, the

γ

-rays fromthe PMTs are foundto be thelargest BGsource inthefull volume data.Theratioof thebestfit MC spectrumto the15-daydata withthe uncertaintyoftheradioactivityandthe PEscaleisdisplayedinthelowerpanelofFig.4.Thediscrepancy appearsaround20000PE bythechangeofaspectrumslopeanda systematicalshiftaccordingtothe energyscaleerrorof+₋1₂%. The horizontalaxis in Fig. 4 is the observed number of PE;the cor-respondingkeVee scale inthe centerof thedetector isshownat

thetopofthefigure.Fig.5showsthePEspectraofboththedata (black)andthe best-fitMC simulation(magenta) includingthose for (1)–(3) above in the full volume for PE

<

400. The gray re-gionindicatestheMCsimulations withoutcontributions fromthe

PMTaluminumseal. Below400PE,thedominantBGcomes from

the PMTaluminum seal. Its origin is small amounts of scintilla-tionlightemergingfromacrackbetweenthealuminumsealand thequartzwindowthatwasformedwhenthequartz waspressed onto the metal body of the PMT in the manufacturing process. The greenarea outlines theuncertainty rangeattributedto limi-tationsinourknowledgeofcertaindetails inthegeometryofthe PMTaluminum seal.The PE distribution is sensitive tothe exact shapeofthe crackmentioned above.The shape ofthecrackwas studied using a microscope after carefully cutting a PMT to ob-tainacross-sectionalview.TheoverallcontributionfromthePMT aluminumsealhoweverbecomesverysmallafterthefiducial vol-umecutisappliedbecausetheseeventsareeasilyrecognizedfrom their squeezed pattern, whichlimitsthis uncertainty’simpact on oursystematics.Overall,Fig.5showsthatourBGmodel,whichis

Fig. 5. FullvolumePEdistribution.Theblacklineindicatesthe705.9daysofdata. Themagenta lineis sumofthecontributions totheBG MCsimulations ofthe activitiesinTable1.Thegreenregioncoverstheuncertaintyfrommodelingthe aluminumgeometry.ThegrayregionshowstheBGMCsimulationswithout contri-butionsfromthePMTaluminumseal.

basedonthevariousfitstodataasdescribedabove,iscompatible withtheobservedspectruminourfinal705.9-daysample.

Thecontributions ofotherBGsources suchas(

α

,n)reactions in the detector materials [26], cosmogenic RIs, 220_{Rn, and solar}

neutrinos together with 136Xe 2

ν

ββ

in the LXe [27] were also evaluated and found to be negligibly small in the energy range discussed here. Table 1 showsthe fit results forthe RI activities usedinthefollowingdiscussion.

5. BGeventsinthefiducialvolumeandtheirsystematicerrors

ABGMCsimulationwiththesamelivetimeandoptical param-eterevolutionasinthe705.9daysofdatawasgeneratedbasedon theRI contributionsevaluated intheprevious section.The

statis-Fig. 6. (Top)BG estimateforthefiducialvolume.Thecoloredstackedhistograms showthevariouscontributionstothisestimate.Thehatchedareaindicatesthatthe BGgeneratingpositionisonthesurfaceofthedetector.Theerroronthebluesum ofallcontributionsisthestatisticalerrorofthisestimate.(Bottom)Energy spec-trumwithsystematicerrorevaluationofourBGestimate.ThebluelineistheBG estimatewiththegreenregioncoveringitssystematicandstatisticalerrorsadded inquadrature;thesystematicerrordominates.

ticalerroroftheMCsimulationsissufficientlysmallcomparedto the systematicerror, whichis discussed later inthis section. For each RI MC was generatedseparately in an amountreflecting its estimatedactivityconsidering its naturaldecay.The top ofFig. 6

showstheenergydistributionoftheBGsimulationsaftertheevent selectiondescribedinSection3.Thehorizontalaxisshowsthe re-constructedenergy.The dominantcontributioncomesfrom210Pb insidethecopperplateandringandtheRIs inthePMTs.The es-timatedrateoftheseeventsareO

(

10−3

₎

_day−1_kg−1_keV−1

ee around

5 keVee.Therearetwosurface locationscausingtheseevents.One

isthecopper platessurface.Anotheristhenon-overlapping edge ofthecopperplateswhere

γ

sfromRIsinthePMTsand

β

sinside the copper ring cause low level light leakage into the detector’s sensitive volume. In both cases, the scintillation photons do not directlyenterthenearby PMTsandthereforearemostly detected byPMTs farfromtheactual eventlocation.Thusthe PE distribu-tioncomestoresemblethat ofafiducialvolumeeventleadingto theeventbeingreconstructedinsidethefiducialvolume,therefore werefer tothem as“mis-reconstructed events”.Theseevents oc-curfrequentlybelowa reconstructedenergyof30 keVee.InFig.6

theircontributionisshownasthehatched portionofthetop fig-ure.

Table 2 shows a list of the systematic errors for the event rateintheBGMCsimulations.Thesystematicerrorsforthe fidu-cialvolumeareestimatedbychangingthedetectorgeometry,the detectorresponse, and the LXeproperties in the BGMC simula-tionswithinreasonablebounds.Thesethreecategoriesarebroken downintoatotalofnineindividualitems.Thesystematicerrorof eachitemisevaluatedseparately,regardedasindependentofeach other.Inthispaper,we evaluatedtheBGanditssystematicerror using the BGMC simulation verified by various calibration data. The calibration data withthe

γ

-rays from outsideare also used forapartofthesystematicerror.

The uncertainty of the detector geometry makes the largest contributionandisbrokendownintoitems(1)–(5)inTable2.The dominantitemistheuncertaintyinthegapwidthalongtheedge whichdoesnot overlapandisdenoted“(1)Plate gap”(shown in Fig. 1-(c)). The uncertainty in the average gap size is estimated to be between30 and140

μ

m afterconsidering the manufactur-ing andassembling accuracy ofthe copper plates andrings. The probability ofmis-reconstruction was evaluatedusingMC forgap

Table 2

ListofthesystematicerroronthetotaleventrateintheBGMCsimulations. Neg-ligiblevaluesareindicatedasablankentry.Thecontentsarecategorizedaccording totheuncertaintyofthedetectorgeometry(a)for(1)–(5),thesystematicerrorsfor thedetectorresponse(b)for(6)–(8)andthesystematicerrorsrelatedtotheLXe properties(c)for(9).

Contents Systematic error

2–15 keVee 15–30 keVee (1) Plate gap +6.2/−22.8% +1.9/−6.9% (2) Ring roughness +6.6/−7.0% +2.0/−2.1% (3) Copper reflectivity +5.2/−0.0% +2.5/−0.0% (4) Plate floating +0.0/−4.6% +0.0/−1.4% (5) PMT aluminum seal +0.7/−0.7% – (6) Reconstruction +3.0/−6.2% – (7) Timing response +4.6/−8.5% +0.4/−5.3% (8) Dead PMT +10.3/−0.0% +45.2/−0.0% (9) LXe optical property +0.7/−6.7% +1.5/−1.1%

widthof 85

μ

masnominal, 30

μ

masminimum, and140

μ

mas maximum, andit turned out that the probability increasedwith thelargergapwidth.

“(2) Ring roughness” is closely related to the “(1) Plate gap” problem: The closest surfaces below the copper platesare those ofthecopperrings.Thecopperrings’surfaceroughnesswas mea-suredto be30

μ

m.To assesstheimpactofpartial obscurationof scintillationlightfrom

β

-raysemergingfromrecessesinthisrough surface,we evaluatedourMCfor210_{Bieventsonthecopperring.}

Weconsidertwocases:1)all

β

-raysintheLXeassumingthecase that the surface condition is completely flat and2) only

β

-rays’ kinetic energymore than 250keV inthe LXe assuming the real-isticsurface roughnesscondition (a250-keV electronwouldhave rangeof30

μ

m inLXe).Theresultingmis-reconstruction probabil-ityisevaluatedwithintheseextremes,withtheaverageofthetwo casesbeingadoptedasthenominalvalue.

“(3)Copperreflectivity”affectstheamountoflightreachingthe IDfrombelowthecopperplatesandthereforeagainthe probabil-ityofmis-reconstruction.Theabsolutevalueaswellasthe uncer-taintyofthereflectivityareestimatedfrom46.5-keV

γ

-rayevents emitted from 210Pbdecay atthe detectorsurface, and are found tobe 0

.

25

±

0

.

05.Theprobability ofmis-reconstructionwas eval-uated fora reflectivityof0.25asnominal,0.20 asminimum,and 0.30 asmaximum only forevents nearthe detectorsurface. The probability increased ifthereflectivity departed from0.25which wasassumedinthereconstruction.

Anothersourceofuncertaintyisthatthecopperplatesarenot always pressedsnuglyagainstthecopperringseverywhere, espe-ciallyalongtheplateboundaries.Themaximumdistancebetween theringsandtheplatesmayreachupto 600

μ

m.Thismaximum distanceisestimatedfromthePEspectrumtogetherwiththe max-imum PE/total PE distribution of our external 60_Co

_γ

_{-ray source}

calibration by comparison with MC. The resulting uncertainty is referredtoas“(4)Platefloating”andaffectstheprobabilityof mis-reconstruction forthe eventsfrominsidethegap.Theprobability ofmis-reconstructionisevaluatedfor30

μ

masnominaland mini-mumfloatingdistanceand600

μ

masamaximumfloatingdistance betweenthecopperringsandtheplates.

The last item related to the detector geometry is the uncer-tainty in the actual shape of the “(5) PMT aluminum seal”. As previouslydiscussedattheendofSection4,theshapeofthe alu-minum crack affects the light leakage fromthe

α

-ray and

β

-ray emissions under the copper plate, which often results in events beingmis-reconstructed insidethe fiducialvolume.The probabil-ityofmis-reconstructedeventsisevaluatedusingtheuncertainty fromthealuminumseal modelingshowninFig.5onlyforevents nearthecrackinthealuminumseal.

Thesystematicerrorsinthedetectorresponsearethoserelated tophotoelectroncountingandtiming.Theperformanceof“(6) Re-construction” includes the algorithmand the energydependence ofthereconstruction,andisevaluatedfromMC simulations.This systematicerror hastwo components. One componentrelates to thepositionreconstructionandwasevaluatedbychangingthe un-derlyingMC generatedPE mapswhilewatchingtheeffectonthe reconstruction.Theothercomponentistheenergydependenceof themis-reconstructionprobability.Itwasevaluatedusing46.5-keV

γ

-ray events emitted from 210Pb decays at the detector surface. A data and a MC sample are obtained by selecting events with smallmaximumPE/totalPEratiosinthe330to370PErangefrom dataandBGMC(210_{Pbinplatebulk),respectively.Withthesetwo}

sampleslower energiesare probedby “PEthinning”,where thin-ninglowerstheevents’PElevels tolevelsequivalentto2–5 keVee

and5–10 keVeeandthedifferencesinmis-reconstruction

probabil-itybetween data and MC for theseenergy ranges become

∼

2%

and

∼

8%,respectively.

Theuncertaintyofthe“(7) Timingresponse” changesthe effi-ciencyof the eventselection,especially the “Cherenkovcut” and the“R(T)cut”.Thesetwotypesoftiming-relatedsystematicerrors are discussed below. The uncertainties in the scintillation signal decaytimeandthePMTjitterareestimatedfromtheinnersource calibrationdata[23].Therangeofthedecaytimeisprobedwithin

±

1

.

5ns from the nominal value with both narrow andwide jit-terdistributions followingRef. [23].The changeinthe numberof remainingevents isevaluated fromcombinationsof thesetiming ranges.Anothertiming issue,thetiming responsenearthe detec-torsurface, leads to a discrepancy betweenthedata andXMASS MCsimulations.Itmanifestsitselfindifferingdistributionsforthe “Cherenkov cut” parameter in the data and the MC simulations. Thedatatakenwithourexternal60_Co

_γ

_{-raysourcecontains}

_γ

_-ray

eventswherethe

γ

-rayisconvertedundertheinnerplatesurface. Thechange ineventnumbers inthe final sample isevaluated to beapproximately

−

10% for2–10 keVee.

Finally,it wasfoundthat deadPMTs(currently10out of642) lead to mis-reconstruction of events occurring right in front of suchPMTs: “(8)Dead PMT”.Theattribution ofmis-reconstructed eventstodeadPMTs isconfirmedby analyticallymaskingnormal PMTsandwatchingtheeffectontheeventdistribution.Wefound thatthesemis-reconstructedeventstendtomoveinthedirection ofthelineconnectingthatPMTandthedetectorcenter,andthat the probability of entering the fiducial volume is determined by thedistancetothelineandenergy.Thistypeofmis-reconstruction

was also confirmed by the BGMC simulation. However, we find

adifferenceintheprobabilityofmis-reconstructionbetweendata andthesimulationsastheenergydecreased,especially

<

30keVee.

Theresultingdifference betweenthedataandBGMCsimulations wasevaluatedasthesystematicuncertainty.

“(9)LXe optical property” reflects our knowledge of the opti-calparameters. Theoptical parametersinthe MCsimulations are tunedto followtheregular inner source calibrations.There isno constrainton eitherthe absorptionorthescatteringlengthwhen tuning the MC simulations. The mis-reconstruction ratedepends on theseoptical parameters, and the resulting systematic uncer-taintyofmis-reconstructioneventsisevaluated bycomparingthe results with different values of these parameters in the BG MC simulations.

In addition, we studied the systematics of our assumptions about the scintillation light yield and the spatial distribution of

206_{Pb nuclear recoils from} 210_{Pb decays in the detector surface.}

We found that these uncertainties are negligible in ouranalysis. ThebottomofFig.6 showsour BGestimate aftereventselection withallthesesystematicuncertaintiesaddedinquadrature.

Fig. 7. (Top)Dataspectrum(filleddots)withthestatisticalerror,BGestimate(thick andblueintheonlinecolorhistogram)withthe1σerrorfromthebestfitshownas ashaded(greenincoloronline)band,andtheWIMPMCexpectationfor60 GeV/c2 withenergyregionbetween2 keVeeand30 keVee.A2.2×10−44cm2crosssection at the90%CLisshownas thedotted(redincoloronline) histogram.(Bottom) Overallefficiencyfor60 GeV/c2_{WIMPsafterapplyingthestandardcut,the R}

(T) cut,andtheR(P E)selectionwithstatisticalandsystematicerrors.

Throughout thisstudy,the mis-reconstruction of events origi-nating from the surface of the detector was found to make the dominantcontributionwithlargesystematicuncertainties,andthe detailedmechanismsofthemis-reconstructionwerealsorevealed. Inordertoovercomethismis-reconstructionproblem,anewtype

of PMT (Hamamatsu R13111) which has a dome-shaped

photo-cathode has been developed. The dome-type PMT has a better

sensitivitytodetectscintillationphotonsfromthesideofthePMT and thus would help to reduce the mis-reconstruction by elimi-nating theblind spotsonthe detectorsurface[28].The studyon themis-reconstructioninthispaperwouldbeapplicableforfuture large-scalesinglephasedarkmatterdetectors.

6. DMsearchinthefiducialvolume

A WIMP DM search for the 705.9 day fiducial volume data

usingourBGestimate wasperformed.WIMP-nucleonelastic

scat-tering events were simulated (WIMP MC simulations) for WIMP

massesfrom20 GeV

/

c2 to10 TeV

/

c2.Forthesesimulationswe as-sumeastandardsphericalandisothermalgalactichalomodelwith a most probable speed of v0

=

220 km

/

s, an escape velocity of vesc

=

544 km

/

s [29],anda localDMdensityof0

.

3 GeV

/

cm3

fol-lowing Ref. [30]. The same event reduction that was applied to the datawas also appliedto the WIMPMC simulations. Efficien-cies for 60 GeV

/

c2 WIMPs after applying the standard and R

(

T

)

cutsandthe R

(

P E

)

selectionwereevaluated tobe12%, 31%,and 46%,averagedovertheenergyranges2–5,5–10,and10–15 keVee,

respectively, shown in Fig. 7. The definition of efficiency is the numberofretainedWIMPeventsafterapplyingthestandardcut, the R

(

T

)

cut,andthe R

(

P E

)

selection dividedby the numberof WIMPeventsgeneratedinthefiducialvolumeofthedetector.The systematicerrors forourWIMP predictioncome fromthe uncer-taintiesintheLXeopticalparameters,thescintillationdecaytime, theeventselectionefficiency,and

Leff

.Thesystematicerrors com-ing from the LXe optical parameters and the scintillation decay

time were evaluated by comparingWIMP MC simulations

gener-ated withdifferentabsorption andscattering lengthsand scintil-lationdecaytimesof26

.

9+₋0₁._.8₂ns.Thisscintillationdecaytime for nuclearrecoilwas derivedfromanexternal252_{Cf neutron}

calibra-tion [18]. The largest systematic errorfor the 60-GeV

/

c2 _WIMPs

comesfromtheuncertaintyinthescintillationdecaytime;its rel-ativevaluescomparedtothetotaleventrateare₋+₁₀3.3_.4%,+₋4₈._.9₀%,and

+8.4

−2.5% averagedinthe2–5,5–10, and10–15 keVee ranges,

respec-tively.Thesystematicerrors forefficiencies inoureventselection wereevaluatedbycomparingthefractionsoftheremainingevents afterapplyingstandardcutandR

(

P E

)

selectionbetweenthedata andMC simulations.Thedatasetusedforthisevaluationwas ob-tained from 57_{Co inner calibrations with “PEthinning” designed}

tomimic2–15 keVeeevents.Theuncertaintyin

Leff

wasevaluated

bycomparingtheWIMPMCsimulationsgeneratedwithvalues1

σ

aboveandbelowitscentralvalue.Thecentervalueandthe uncer-taintyof

Leff

weretakenfromRef. [31].Thedataenergyspectrum was thenfittedwiththesumoftheBGestimateshowninFig. 6

intheprevious section andthe WIMPcontributioninthe energy rangeof2–15 keVeeusingthefollowing

χ

2 definition:

χ

2

=



i

(

Di

−

B∗_i

−

α

·

W_i∗

)

2 Di

+

σ

∗2

(

Bstat

)

i

+

α

2

·

σ

2

(

Wstat

)

i

+

χ

2_pull

,

(1) B∗_i

=



j pj

(

Bi j

+

kqk

·

σ

(

Bsys

)

i jk

),

(2) W_i∗

=

Wi

+



l rl

·

σ

(

Wsys

)

il

,

(3)

σ

∗2

₍

_B stat

)

i

=



j p2_j

·

σ

2

₍

_B stat

)

i j

,

(4)

χ

2_pull

=



j

(

1

−

pj

)

2

σ

2

₍

_B R I

)

j

+



k q_k2

+



l r_l2

,

(5)

where Di, Bi j,and Wi are thenumber ofeventsinthe data,BG

estimate,andWIMPMCsimulations,respectively.i and j enumer-atestheenergybinandtheBGsourceintheBGMC,respectively. The variables k and l enumerate the different systematic errors in the BGestimate andWIMP MC simulations, respectively. Fur-thermore,

σ

(

Bstat

)

i j and

σ

(

Wstat

)

i arethestatisticaluncertainties

in the BG estimate and the WIMP MC simulations, respectively.

α

scalestheWIMPMCcontribution,while

σ

(

BR I

)

j,

σ

(

Bsys

)

i jk,and

σ

(

Wsys

)

i are uncertainties inthe amount ofRI activity(Table 1)

and the systematic errors in the BG estimate (Table 2) and the WIMPMCsimulations,respectively.Allvalueswerescaledwithout anyenergydependenceby scale factorsof pj,qk,andrl,

respec-tively,witha constraintencapsulatedina pull term(

χ

2

pull). Their

initial values are given with pj

=

1 and qk

=

rl

=

0. The lower

energyforthefittingrangewasdetermined tohavesufficient ef-ficiency(

>

3%)afterapplyingthestandard cut,the R

(

T

)

cut,and theR

(

P E

)

selection.2 keVeecorrespondedto9

.

3 keV nuclearrecoil

energy.Theupperenergywaschosentobe15 keVeesothatmore

than98% oftheeventsexpectedintheWIMPMCsimulationswith massesupto10 TeV

/

c2 _{arecontainedinthatenergyregion.}

Thebestfithada

χ

2_of8.1(n

_.

_d

_.

_f

₌

_{12)withaWIMPfractionof}

α

=

0.Fig.7showstheenergyspectrumofthedataasfilleddots andthe BG estimate asa solid histogramreflecting this best fit. TheshadedbandinFig.7showsthesumofthe1

σ

errorsforthe BGestimate, including

σ

(

Bstat

)

i j,

σ

(

BR I

)

j,and

σ

(

Bsys

)

j.Herethe

sizesof

σ

(

BR I

)

j and

σ

(

Bsys

)

j werederivedusing



χ

2

=

1,which

is smaller than the initial error estimate shown in the bottom panelofFig.6becausethelargestcomponentofthesystematic er-rorfromtheplategapdependencewasstronglyconstrainedbythe shapeoftheenergyspectruminthefittingprocess.Thetotal num-bersofeventsin2–15 keVee was 2270

±

48 whiletheexpectation

fromthebestfitBGMCwas2249

±

47

(

stat

.)

+₋171₂₃₉

(

sys

.)

.Allthe re-mainingeventsareconsistentwithourbackgroundevaluation,and thus 90% confidencelevel(CL) upperlimit onthe WIMP-nucleon crosssection was calculated foreach WIMPmassso that the in-tegralof theprobability densityfunction exp

(−

χ

2

_/

₂

₎

_becomes

Fig. 8. Thespin-independentWIMP-nucleoncrosssectionlimitasafunctionofthe WIMPmassatthe90% CLforthisworkisthesolid(redincoloronline)line.Limits as wellas allowedregions fromotherexperimentalresults arealso shown [4,6, 8–12,32–35].

90% of the total.The 90% CL upperlimit for a 60-GeV

/

c2 WIMP is alsoshownasthe dottedhistogramin Fig.7.This limit corre-spondsto158eventsinthe2–15 keVeeenergyrange.The90% CL

upperlimitsfordifferentWIMP massesare plottedinFig.8.Our lowestlimitis2

.

2

×

10−44_cm2 _{fora60 GeV}

_/

_c2_WIMP.

7. Conclusions

Afiducialvolume(97 kg)DMsearchwasperformedusing705.9 livedaysofdatafromtheXMASS-Idetectorwithacareful evalu-ation oftheBGcontributions.Afterdatareduction,theremaining eventswereconsistentwiththeBGexpectationbasedon indepen-dentassaysofBGRIandsimultaneousfittingofsignalandBG.

Theeventratewas

(

4

.

2

±

0

.

2

)

×

10−3kg−1keV−_ee1day−1 around 5 keVee withthesignal efficiencyof20%. OurBGMC simulations

revealedthattheremainingeventswereprimarilycausedby mis-reconstruction ofeventsthat occurredon thecoppersurface and ingapsandwerewronglyreconstructedinsidethefiducialvolume. A 90% CLupperlimit forthe spin-independentcrosssection was derivedfor20 GeV

/

c2

₋

_{10 TeV}

_/

_c2 _{WIMPsandourlowestlimitwas}

2

.

2

×

10−44cm2 for60 GeV

/

c2 WIMPs. Thisis themoststringent limitamongresultsfromsingle-phaseLXedetectors.

Acknowledgements

We gratefully acknowledge the cooperation of the Kamioka

Mining and Smelting Company. This work was supported by

the Japanese Ministry of Education, Culture, Sports, Science and Technology, the joint research program of the Institute for Cos-mic Ray Research (ICRR), the University of Tokyo, Grant-in-Aid

for Scientific Research, JSPS KAKENHI Grant No. 19GS0204 and

26104004, and partially by the National Research Foundation of Korea Grant (NRF-2011-220-C00006) and Institute for Basic Sci-ence(IBS-R017-G1-2018-a00).

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