Search for dark matter in the form of hidden photons and axion-like particles in the XMASS detector

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Search

for

dark

matter

in

the

form

of

hidden

photons

and

axion-like

particles

in

the

XMASS

detector

XMASS

Collaboration



K. Abe

a

,

d

,

K. Hiraide

a

,

d

,

K. Ichimura

a

,

d

,

Y. Kishimoto

a

,

d

,

K. Kobayashi

a

,

d

,

M. Kobayashi

a

,

S. Moriyama

a

,

d

,

M. Nakahata

a

,

d

,

H. Ogawa

a

,

d

,

1

,

K. Sato

a

,

H. Sekiya

a

,

d

,

T. Suzuki

a

,

O. Takachio

a

,

A. Takeda

a

,

d

,

S. Tasaka

a

,

M. Yamashita

a

,

d

,

B.S. Yang

a

,

d

,

2

,

N.Y. Kim

b

,

Y.D. Kim

b

,

Y. Itow

c

,

e

_,

_{K. Kanzawa}

c

_,

_{K. Masuda}

c

_,

_{K. Martens}

d

_,

_{Y. Suzuki}

d

_,

_{B.D. Xu}

d

_,

K. Miuchi

f

,

N. Oka

f

,

Y. Takeuchi

f

,

d

,

Y.H. Kim

g

,

b

,

K.B. Lee

g

,

M.K. Lee

g

,

Y. Fukuda

h

,

M. Miyasaka

i

,

K. Nishijima

i

,

K. Fushimi

j

,

G. Kanzaki

j

,

S. Nakamura

k

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

d_{KavliInstituteforthePhysicsandMathematicsoftheUniverse(WPI),theUniversityofTokyo,Kashiwa,Chiba,277-8582,Japan}

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

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

j_{DepartmentofPhysics,TokushimaUniversity,2-1MinamiJosanjimachoTokushimacity,Tokushima,770-8506,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: Received24July2018

Receivedinrevisedform28September 2018

Accepted24October2018 Availableonline30October2018 Editor:M.Doser Keywords: Darkmatter Hiddenphoton Axion-likeparticle Lowbackground Liquidxenon

Hiddenphotonsandaxion-likeparticlesarecandidatesforcolddarkmatteriftheywereproduced non-thermallyintheearlyuniverse.Weconductedasearchforbothofthesebosonsusing800live-daysof datafromtheXMASSdetectorwith327kgofliquidxenoninthefiducialvolume.Nosignificantsignal was observed,and thuswesetconstraintsonthe

α

/

α

parameterrelatedtokineticmixingofhidden photonsandthecouplingconstant

g

Aeofaxion-likeparticlesinthemassrangefrom40to120keV/c2, resultingin

α

/

α

<6×10−26 _{and g}

Ae<4×10−13.Theselimitsarethemoststringentoverthismass rangederivedfrombothdirectandindirectsearchestodate.

©2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

TheexistenceofDarkMatter (DM)isinferred frommany cos-mologicalandastrophysicalobservations [1].Allindicationsforits existence so far were based on its gravitational interaction only,

 _{E-mailaddress:xmass.publications11@km.icrr.u-tokyo.ac.jp.}

1 _{NowatDepartmentofPhysics,CollegeofScienceandTechnology,Nihon} Uni-versity,Kanda,Chiyoda-ku,Tokyo101-8308,Japan.

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

and the nature of DM beyond that is still shrouded in mystery. One of the theoretical realizations of DM is Weakly Interacting MassiveParticles(WIMPs),which areexpectedtohavemassesof roughly10GeV/c2 toafew TeV/c2.Althoughmanydirectand in-direct experiments are searching for WIMPs, no concrete signal hasyetbeenfound.HiddenPhotons(HPs)andAxion-likeParticles (ALPs), which are respectively vector and pseudo-scalar realiza-tions of bosonic super-WIMPs [2], are alternative candidates for DMwithexpectedmasses

<

1MeV/c2_{.AHPis thegauge boson} of a hiddenU(1) sector that kinetically mixes withthe standard

https://doi.org/10.1016/j.physletb.2018.10.050

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

modelphoton [3].ALPsarise aspseudo-Nambu-Goldstone bosons thatappeargenericallyinallstringcompactifications [4].Although ascenarioinwhichtheywerethermallyproducedintheearly uni-verse was ruled out [5] or disfavored [2], HPs andALPs can be coldDMcandidatesthatgiverisetotheobservedDMabundanceif theywere producednon-thermallyvia themis-alignment mecha-nism [4].HPsandALPsareexperimentallyinterestingbecauseboth ofthem areabsorbedby materials withan interaction analogous toaphotoelectriceffect [2],transferringtheirtotalenergyto elec-trons.AssumingtheyarecoldDM,i.e. theyarenon-relativistic,the energytheydepositisequivalenttotheirrestmass.

The calculationin Ref. [2] islimitedto bosons withkeV-scale mass up to roughly 100 keV/c2_{. In this mass region, indirect} searches give stringentlimitsof

<

10−26 _{on the}

_α



_/

_α

_parameter ofHP,whichrepresentsthestrengthofthekinetic mixing,inthe massrangefrom1eV/c2 to50keV/c2 andabove 140 keV/c2 [6]. Around the mass of 90 keV/c2, however, the indirect limit is relatively weak as

α



/

α

<

O

(

10−24

)

. XMASS already carried out searches around this mass region for HPs and ALPs using data taken in 2010–2012, and had given limits in the mass range of 40–120keV/c2_{[5].Inthispaper,wereportanimprovedresult} us-ing 800live-days of datafrom November2013 to July2016 and a fiducial volume containing 327 kg of liquid xenon. The sensi-tivity of the search is improved by an overall reduction of the background (BG), advances in our understanding of the BG, and asignificantincreaseinavailableexposure.

2. XMASSdetector

The XMASS detector [7] is located at the Kamioka Observa-tory,which is an undergroundlaboratory in Japan, ata depth of 2,700-mwaterequivalent.ThedetectorconsistsofanInner Detec-tor(ID)andanOuterDetector(OD).

TheIDisaliquidxenonscintillatorcontainedinavacuum in-sulatedcoppervessel.The832kgofliquidxenoninthesensitive regionaresurroundedby642inward-facingphotomultipliertubes (PMTs). The PMTs are arranged in a copper holder the shape of which is an approximate sphere with a radius of

∼

40 cm. The photocathodes ofthe PMTs cover 62% of that inner surface. Alu-minumusedasasealmaterialinthePMTcontainssome radioac-tiveisotopes(RIs)whichwerethemainBGsourcesinourprevious analysis [5,7].In 2013we installedcopper coversover these alu-minumsealstoreducethisBG [8].Onlynewdatatakenafterthis installationisusedinthisanalysis.

TheODenclosestheID,whichisatitscenter.TheODisa wa-terCherenkovcounter ofcylindricalshape,10mindiameterand 10.5 minheight,andisread outby 7220-inchPMTs. TheOD is usedasan activevetoforcosmic-raymuonsandserves asa pas-siveradiationshieldagainstenvironmentalneutronsand

γ

-rays.

The signals from the ID-PMTs are recorded by CAEN V1751

waveform digitizers with a sampling rate of 1 GHz. Data acqui-sitionistriggeredifatleast4PMTsdetectsignalswithin200nsof eachotherover0.2photoelectron(PE)threshold.Thegainsofthe IDPMTs weremonitoredwithablueLEDembedded intheinner surfaceofthedetector,dimmedtoprovidesingle PEsignallevels. Thedetectorresponsetoscintillationlightwastracedbyinserting a57Cosource [9] intothe IDevery twoweeks.The lightyield of thedetectorfor122keV

γ

-rayandboththeabsorptionlengthand thescatteringlengthoftheliquidxenonwereextractedfromthis regularcalibration.Thetimeevolutionofthesevalueswasusedas inputparametersfortheGeant4-basedXMASSMonteCarlo simu-lation(MC) [7].

Fig. 1. Distributionofreconstructedverticesasafunctionofradiuscubed.Events passingthestandardcutswithNPEcorbetween588–1764PEswereplotted.The

ra-diusisnormalizedtotheradiusofthewindowsurfaceofthemostdistantPMTs (42.6 cm).Black dotsshow thedata. Thestackedhistogramsshow theBG MCs ofRIsin/onthedetector components(green),RIsinthe liquidxenon(red),and neutron-activatedxenonisotopes(lightblue).Theverticaldashedlinemarksthe cutvalue.

3. Analysis

3.1. Eventselectionandvertexreconstruction

EventswithoutassociatedODactivity(8ormoreODPMTs de-tectsignalsovera0.4PEthreshold)wereusedfortheanalysis.We appliedour‘standardcuts’,whicharesummarizedin [8],toreject eventsoriginatingfromPMTafter-pulsesandelectronic noise.We alsorequiredthetiming differencetothe subsequenteventtobe

>

1 ms, to reject 214Bi

β

-ray eventsfrom the 214Bi–214Po decay sequenceinthe222Rndecaychain.

The eventvertex was then reconstructed based on the maxi-mum likelihoodevaluationof theobservedPE distribution inthe ID PMTs [7]. The expected number of PE on each PMT was ob-tained from MC simulations for various vertex positions



r and xenonabsorptionlengthslabs,andusedtocalculatealikelihoodfor

each eventposition. As theregular 57Co calibrationprovided the time evolution of labs, the MC expectations updated accordingly.

Theposition



r whichmaximizesthelikelihoodwasacceptedasthe event vertex. We requiredthe radius of thereconstructed vertex Rrec(

≡ |

r

|

withthecenteroftheIDastheoriginofourcoordinate

system) tobe

<

30 cm.Thisfiducialvolumecut stronglyreduces BGeventsoriginatingfrom

γ

-raysor

β

-raysfromRIin/onthe de-tector’s inner surfacesandbulk materials;itsimpact isshownin Fig.1.

ThePE acceptancedependsonthevertexpositionandalsoon opticalparameterssuchaslabsandlightyieldintheliquidxenon.

We thususea correctednumberofPEs(NPEcor) asa measureof

the energydeposittoavoidsuch dependencies. NPEcor isdefined

as:

NPEcor

≡

NPE

×

μ

(



r

= 

0

,

labs

)

μ

(



r

,

labs

)

×

ν

,

(1)

where

μ

(



r

,

labs)isthedetectionefficiencyforthescintillationlight generatedat



r whentheabsorptionlengthislabs,and

μ

(



r

= 

0

,

labs)

istheefficiencyatthedetectorcenter.Theseefficienciesare calcu-latedfromtheMCexpectationsusedinthevertexreconstruction. The

ν

isthe time dependentcorrection factorforthePE yieldat the detector center obtained from the regular 57_{Co calibrations.}

Changesof

ν

canbeexplainedbychangesintheabsorptionlength ofliquidxenonasdiscussedin [10].Thechangeof

ν

overthedata takingperiodarecontrolledwithin

±

7%fromitsaveragedvalue. 3.2.SignalMC

TheabsorptionofHPsandALPsisanalogoustothe photoelec-triceffect.The cross-sectionoftheabsorption

σ

abs forHPcan be

writtenintermsofthecross-sectionofthephotoelectriceffect

σ

pe

whenreplacingthephotonenergy

ω

bytheHPmassmH P,as:

σ

abs

υ

σ

pe

(

ω

=

mH P

)

c

=

α



α

,

(2)

where

υ

isthevelocityoftheHP,

α

isthefinestructureconstant, and

α

isitsanaloguefortheHP.Assumingadarkmatterdensity of0.3GeV/cm3,theeventrateisexpressedas [2]:

RH P

[

1

/

kg/day

] =

4

×

1023 A

α



α

σ

pe

[

barn

]

mH P

[

keV

]

,

(3)

where A

=

131

.

3 isanatomicmassofxenonofnatural composi-tion.

Asfortheabsorption ofALPs,whichisalsoreferred toasthe axio-electriceffect, its cross-section and expected eventrate are calculatedas [2]:

σ

abs

υ

σ

pe

(

ω

=

mAL P

)

c

=

3m2 AL P 4π αfa2

,

(4) and RAL P

[

1

/

kg/day

] =

1

.

2

×

1019 A g 2 Ae

σ

pe

[

barn

] ·

mAL P

[

keV

],

(5)

wheremAL P and gAe are themassandtheaxio-electriccoupling

constantoftheALPs,respectively.The faisadimensionalcoupling

constantforALPsdefinedas fa

≡

2me/gAe,whereme isthemass

oftheelectron.Inthisanalysis,theexpectedratedoesnotdepend onDMvelocitydistributionasindicatedinEqs. (3) and (5).Inthe followinganalysisweconcentrateonHPs.TheresultforALPscan beobtainedby replacingtheeventratefromEq. (3) bythat from Eq. (5).

Wesimulatedthephotoelectriceffectofphotonswithenergies equal to mH P and used this simulation assignal MC. This

sim-ulationis identical to the absorption ofthe HPs, because all the energyof the incident particle, including its rest mass, is trans-ferred to electrons. Photons were generated uniformlyinside the

ID. We made the momentum directions of the photons simply

isotropic,sincetheydonotaffectonresultofphotoelectriceffect. ThesignalMCwas madeformH P from40to120keV/c2 insteps

of2.5keV/c2.Thesame selectioncriteriaasdescribed inSec.3.1

were applied. The ratioof the numberof events passing the se-lectiontotheonesgeneratedinthe30-cm-radiusfiducialvolume is0.95–0.98forany oftheHPmasses. Examples oftheexpected signalspectrumareshowninFig.2.

3.3.BackgroundMC

MCsampleswerepreparedforeveryBGsourceseparately.The BGsources were divided into three groups: RIs dissolved in the liquidxenon,xenonisotopesactivated byneutrons, andRIs in/on thedetectorcomponents.

For the RIs in the liquid xenon, the amount of 214_{Pb in} the detector, which is a daughter of 222Rn, was estimated from

214_Bi–214_{Po coincidences in the} 222_{Rn decay chain to be}

8.53

±

0.16 mBqonaveragethroughoutthedatatakingperiod [11].

Fig. 2. NPEcor distributions of the HP signal expected from MC with α/α

=4×10−26_{. Thecorrespondingγ-rayenergyisalsoshownonthe upper} hori-zontalaxis.Thered,green,blue,andorangelinesshowsignalsformH P of50,70,

90,and110keV/c2_{,respectively.}

The average amount of 85_{Kr in the detector was estimated to} be 0.25

±

0.04 mBq using the coincidence of its

β

emission with Qβ

=

173 keV followed by a 514-keV

γ

-ray emission [8]. The

amountofthe2

ν

ββ

decayof136Xe( Qββ

=

2

.

46 MeV)isestimated

from its natural abundance (8.9%) assuming T1/2

=

2

.

21

×

1021 years [12].Acontaminationofargonwasfoundfromacomponent analysisofthedetector’sxenongas.The

β

decayof39_Arcanbea BGsource.Alsoacontamination of14Cwas indicatedbyits char-acteristicspectral shape intheobserved energyspectrumthough itschemicalformisnotknown.Thecontributionsof39_Arand14_C wereevaluatedfromtheobservedspectrum [11].

The xenon isotopes and their daughters, mainly 131m_{Xe and} 125_{I,arethoughttobeproducedingasphasebythermalneutrons} whenthegasisoutsideoftheODwatershield,andthenreturned to the liquid xenon in the detector. The amounts of 131mXe and 125_{Iwere calculated fromthe measured thermalneutron flux in} theKamiokaObservatory

(

0

.

8

−

1

.

4

)

×

10−5 cm−2s−1 [13,14].

The amounts of RIs in/on the detector components were

ob-tained from screening with germanium detectors and from the

shapeoftheobservedenergyspectrumbetween30and3000keV withoutthefiducialvolumecut,assummarizedin [8].

The uncertainties of the BGamounts were considered as sys-tematic uncertainties in our signal peak search process, as de-scribedinSec.3.5.

3.4. MCtreatmentanditsuncertainty

Several corrections, which were mainly based on calibration data,were applied tothe MC assummarizedin Table1. For ref-erencepurpose we labelour fivecorrectionsC1 through C5. The correction C1 followsthe standard MC treatment inXMASS [11]. Inaddition,thecorrectionsC2–C5wereintroducedtoincludeour knowledgeofthevariousBGcomponentsintheenergyrangeused inthis analysis.The uncertaintyin each ofthesecorrectionswas usedasasystematicuncertaintyinthefittingprocessdescribedin Sec.3.5.

The correction C1 is for the non-linear scintillation efficiency of xenon, which is important for the signal search as a change of non-linearitymovesthe signal peak position anddeforms the BG spectrum shapes. The non-linearity was taken into account in our MC based on the model described in [15]. As with the XMASSstandardtreatment [11],itwas thencalibratedusing sev-eral

γ

-raysources;55_Fe(5.9keV),241_Am(59.5keV

_γ

_{-ray,17.8 keV}

Table 1

CorrectionstotheMCandtheirerrors.Forthenon-linearitycorrectionC1,theresultsofourfivecalibrationpointswereconnectedusingfmodelasdescribedinthetext.As

fortheenergyandpositionresolutioncorrectionsC2andC3,theresultsat59.3 and122.1 keVwereinterpolatedwithafunctionofenergyA⊕B/√E wheretheoperator ⊕representsquadraticsum,andtheparametersA andB weredeterminedbyrequiringthefunctiontoconnecttheresultsatthetwocalibrationpoints.

ID kind of correction (energy ofγ-rays or events used to derive the correction) correction factor and its error (≡Cm± δCmused in Eq. (8))

C1 non-linearity of Xe scintillation_ (5.9 keV) (17.8 keV) (30 keV) (59.3 keV) (59.5 keV) Data MC relative to 122.1 keV  80+5 −5% 79+ 3 −4% 91+ 3 −3% 91+ 3 −3% 94+ 3 −3% C2 NPE_corresolution (59.3 keV) (122.1 keV)

(δE/E)2

data− (δE/E)2MC



3.8±2.0% 1.1±0.4%

C3 _Rrecresolution (59.3 keV) (122.1 keV)

(δRrec)2data− (δRrec)2MC



2.6±1.1 mm 1.3±0.3 mm C4 event increase due to dead PMTs (441<NPEcor<515)

(Data/MC−1) (7±14)%

C5 event increase due to dead PMTs (515≤NPEcor<588)

(Data/MC−1) (19±16)%

Fig. 3. MCcorrectionforthe NPEnon-linearity.Thevalueat 122.1keVγ-rayis normalizedto1.Theblackdotsshowtheresultsfromdifferentcalibrationsources. Examplesforthe fmodelfunctionsareshownasthesolid(linearinterpolation),the

dotted(splineinterpolation),andthedashed(6-thdegreepolynomialfitting)lines.

Np’s X-ray, and

∼

30 keV escape peak of Xe’s X-ray), and 57_Co (122.1keV

γ

-rayand59.3keVX-rayfromthetungstenhousingof thesource). The resultswere expressed relativeto the 122.1keV 57_Co

_γ

_{-rays.Thesecalibrationpointswerelinearlyinterpolatedto} model the energy dependence of the non-linearity as shown in Fig. 3,and the observed energyin the MC was scaled according tothemodelfunction.The measurementerrorofeachcalibration pointwasconsideredasasystematicuncertainty.Theuncertainty ofthe energydependencemodel was alsotakeninto account.In thisanalysis, in addition to the linearinterpolation, we modeled theenergydependencewithseveralinterpolationmethods(spline, andpolynomialinterpolation),andalsofittedthecalibrationpoints withpolynomialfunctionsofvariousorder,aswellasusing combi-nationsoflinearinterpolationandfitting.Examplesofsuchmodel functions( fmodel)areshowninFig.3.AsdescribedinSec.3.5,the

significanceofsignalswas evaluatedincludingsuch model uncer-tainties.

The resolutions for energy (NPEcor) and position (Rrec) were

evaluatedfromthe59.3keVand122.1keVpeaksinthe57_Co cal-ibration runs.The energyresolutioninthe datawas evaluatedto be8

.

3

±

0

.

8%at59.3keVand3

.

9

±

0

.

2%at122.1keV,whichwere worsethanintheMC.Thequadraticsubtractionoftheresolution

in the MC from the one in the data was 3.8% at 59.3 keV and

1.1%at122.1keV.TheenergyspectrumoftheMCwasadditionally smearedtocompensateforthisdifference(correctionC2).The

po-sitionresolutioninthedatawasevaluatedtobe6

.

6

±

0

.

5 mmfor 59.3keVX-raysand4

.

5

±

0

.

1 mmfor122.1keV

γ

-raysatthe fidu-cialvolumeradius(=30cm).TheresolutionintheMCwasslightly better,thequadraticsubtractionofwhichfromtheoneinthedata was2.6mm(1.3mm)for59.3keVX-rays(122.1keV

γ

-rays).The efficiencyforthefiducialvolumecutdependsontheposition res-olution. TheefficiencyintheMC was thuscorrectedaccordingto thisdifference (correctionC3),butcomparedto theother correc-tionsitsimpactontheanalysisisnotsignificant.

Depending on the period of data taking, eight to ten PMTs among all 642PMTs were not operational because of their high noise ratesorelectrical problems.OurMC simulationshowsthat eventsgeneratedonthedetectorsurfacenearthesedeadPMTsare often mis-reconstructed within the fiducial volume. Such events comefromRIsinthePMTsor210_{Pbanditsdecayproductsinthe} copper cover forthe aluminumseal, andcontribute in particular tothe lowenergyregion [8].ByartificiallymaskingnormalPMTs in the data,we found that the reconstructedvertices (



r) of such eventsconcentratearoundtheaxesconnectingthedetectorcenter withthedeadPMTs,andthatreconstructionmovesthemtowards the centerofthedetector.Theprobabilities ofmis-reconstruction in thedataandtheMC were estimatedusingthisfeature [8] for twoenergyregionsseparately.Accordingtothedifferencebetween theprobabilities,theeventrateintheMCwasincreasedby7%for the441

<

NPEcor

<

515 regionand19%forthe515

<

NPEcor

<

588

region(correctionC4andC5). 3.5. Signalpeaksearch

We canextract a potential signalfromthe databy comparing the observed energy spectrum withthe combined predictions of signalandBGMCincludingtheirrespectiveuncertainties.

Theenergyspectrumafterapplyingalltheselectionsisshown in Fig. 4. The peak around NPEcor

=

2400 came from residual 131m_{Xe after calibration with} 252_{Cf, which was useful as a} ref-erence for the global energy scale of the MC. The energy range between NPEcor

=

590

−

1760 (corresponding to

γ

-ray energies

of 40–120 keV) was used for the signal search. In this region the spectrum is almost flat with an event rate of

∼

5

×

10−4 day−1kg−1keV−1.

TosearchfortheHPsignal,thehistogramoftheobserved en-ergy spectrum was fitted with the sumof a putative signal and theBGMCspectra.Therangeofthehistogramusedforfittingwas 440–2650 NPEcor (correspondingto

∼

30–180keV

γ

-rayenergy),

anddividedequallyinto 150NPEcor bins.The chi-squarewas

Fig. 4. BestfitNPEcor distributions.Theupperscaleistranslatedintothe

corre-spondingγ-rayenergies.Theblackdotsrepresentthedata.Thestackedhistograms showtheBGMCforRIsin/onthedetectorcomponents(green),RIsintheliquid xenon(red),andxenonisotopesactivatedbyneutrons(lightblue).Thedarkhatched blueareashowstheestimatedcontributionfromdeadPMTs.Themagentapartof thehistogramshowsthebestfitHPsignalforaHPmassofmH P=85 keV/c2.

χ

2_{f it}



mH P

,

α



/

α



≡

Nbin



i



Ri obs

−

RiBGtot

−

RiH P

(

mH P

,

α



/

α

)



2



δ

Ri_obs



2

+



δ

R_BGtoti



2

+



δ

Ri_{H P}



2

+

χ

2 sys

,

(6)

whereRi_obs

,

Ri_BGtot,andRi_{H P} aretheeventrateinthei-thbinfor data,BGMC,andHPMC,respectively,andthe

δ

Ri_obs,

δ

Ri_BGtot,and

δ

Ri_{H P} aretheirrespectivestatisticalerrors.RBGtot isthesumofthe

differentBGMCeventrates,i.e.: RBGtot

=



j:RI types

pjRj-th BG

,

(7)

wherethesummationistakenforalltheRIsofthethreeBG cate-goriesdescribedinSec.3.3.TheRj-th BGistheexpectedeventrate

fromthe j-thRIand pj isits scaleparameterwhoseinitial value

isunity.The

χ

2

sys isapenaltytermtohandlesystematic

uncertain-ties.Itisdefinedas:

χ

_sys2

=

j =14_C,39_Ar



j:RI types



1

−

pj

δ

pj



2

+

5



m=1



Cm

δ

Cm



2

,

(8)

wherethe

δ

pj are the 1

σ

uncertainties of the BGestimates

de-scribedinSec.3.3.Thefirstsummationontherightsideconstrains theparameters pj around

±

1

σ

fromunityduringthefit.Because

theamountsof14_Cand39_{Arinxenonare obtaineddirectlyfrom} thefit tothe data,theseRIs are not includedin thissummation whilethey areincluded inthesummation inEq. (7). The second summationisapenaltytermrelatedtothefivespecialMC correc-tions C1–C5 described inSec. 3.4.The m-th correction factor Cm

listedinTable1ismodifiedby

Cminthefit,anditsuncertainty

δ

Cm constrainsthismodification.Rj-th BGandRH P arefunctionsof

the

Cm,themodelfunctiontype fmodeldescribedinSec.3.4,and

aglobalenergyscale



E:

Rj-th BG

=

Rj-th BG

(



E

,

C1

, ...,

C5

;

fmodel

) ,

(9) RH P

=

RH P

(

mH P

,

gAe

;



E

,

C1

, ...,

C5

;

fmodel

) .

(10)

The

χ

2

f it was minimized separately for every 2.5 keV/c

2 _{step in} HPmassbetween40and120keV/c2 _{andforeachstepof}

_α



_/

_α

_in

Fig. 5. ConstraintsongAeoftheALPs(top)andα/αoftheHP(bottom).Thered

lineshowsthe90%CLconstraintpresentedinthispaper.Theblacklineshowsour previousresult [5].Theblue,magenta,green,andorangelinesarelimitsreportedby theXENON100 [18],theMajoranaDemonstrator [19],theLUX [20],andthe PandaX-II [21].Thedotted,dashed,anddash-dottedlinesinlightbluecolorareconstraints fromindirectsearches derivedfromredgiantstars(RG),diffuseγ-rayflux,and horizontalbranchstars(HB),respectively [6].

the

α



/

α

>

0 region, by fittingthe pj,

Cm,



E, and fmodel.The

optimizationoftheseparametersexceptfor fmodelwasdoneusing

ROOTTMinuit [16].Asfor fmodel,each fmodelwastestedseparately,

and the one givingthe smallest

χ

2

f it was chosen for each mass

and each

α



/

α

. This methodcorresponds to handling the model functionshapeasoneofthefittingparameters [17].Thesensitivity obtained with this method is conservative compared to sticking withone model.We thus obtainedthe

χ

2

f it profile asafunction

of

α



/

α

foreach mass.The minimumof the profile is the most probable

α



/

α

parameterforthatmass.

4. Result

The best fit result for HP with mH P

=

85 keV/c2 is shown

in Fig. 4,where the minimum

χ

2

f it/NDF= 131/122with

α



/

α

=

1

.

1

×

10−26_{.Nosignificant signalwas foundatanyHPmass.The} difference betweenthe minimum

χ

2

f it andthe

χ

2

f it with no

sig-nal was atmost 1.62. We thus setthe 90% confidence level(CL) constrainton

α



/

α

fromtherelation:



a90 0 exp

−

χ

2 f it

/

2

da



_∞ 0 exp

−

χ

2 f it

/

2

da

=

0

.

9

,

(11)

wherea anda90denote

α



/

α

andits constraint,respectively.The constraintforeachmassisshowninFig.5.Comparedtoour pre-vious work, the constraints improved by a factor of 10–50. The constraintsfromotherdirectandindirectsearchesarealsoshown inthefigure.Ourresultgivesthemoststringentlimitinthemass range from 40 to 120 keV/c2. The indirect limits forHP around 90keV/c2 are

α



/

α

<

O

(

10−24

)

,relativelyweak comparedto the higherandlower mass regions (

α



/

α

<

O

(

10−27

₎

_form

or

≤

40 keV/c2_{). Ourlimit,}

_α



_/

_α

_≤

₂

_×

₁₀−27_–6

_×

₁₀−26_{, bridges} thatregionofrelativeweaknessfortheindirectlimits.

Thesameresultconvertedtoa constrainton gAe forALPs

us-ingEqs. (3) and (5) isalsoshowninthefigure.LUXandPandaX-II present limits for ALPs below 20 keV/c2. Our result covers the

highermass region.While XENON100and theMajorana

Demon-stratorreportlimitsoverawidermassregion,ourconstraintgAe

<

afew10−13isthebestlimitformAL P

>

40 keV/c2. 5. Conclusion

The searchesfor HPsandALPs, whichare candidates forcold DM,wereconductedusing800live-daysXMASSdatawith327kg xenonin a 30-cm-radiusfiducialvolume. We searchedfor signal peaksfromHPsorALPsinteractionsanalogoustothephotoelectric effectintheenergyspectrumaroundtensofkeV,wheretheevent rateinXMASSis

∼

5

×

10−4 day−1kg−1keV−1.Withtheabsence of any significant signal, we set the most stringent upper limits forthe parameterfor kinetic mixing

α



/

α

ofthe HPandforthe couplingconstant gAe ofthe ALPs inthe massrange from40to

120keV/c2_. 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, Grant-in-Aid for Scientific Research, JSPS KAKENHI

Grant No. 19GS0204 and 26104004, the joint research program

ofthe Institutefor CosmicRayResearch (ICRR),the University of

Tokyo, andpartially by the National Research Foundation of Ko-rea Grant (NRF-2011-220-C00006) andInstitute for BasicScience (IBS-R017-G1-2018-a00).

References

[1]C.Patrignani,etal.,ParticleDataGroup,Chin.Phys.C40(2016)100001. [2]M.Pospelov,A.Ritz,M.Voloshin,Phys.Rev.D78(2008)115012. [3]B.Holdom,Phys.Lett.B166(1986)196.

[4]P.Arias,D.Cadamuro,M.Goodsell,J.Jaeckel,J.Redondo,A.Ringwald,J. Cos-mol.Astropart.Phys.(2012)013.

[5]K.Abe,etal.,XMASSCollaboration,Phys.Rev.Lett.113(2014)121301. [6]H.An,M.Pospelov,J.Pradler,A.Ritz,Phys.Lett.B747(2015)331. [7]K.Abe,etal.,XMASSCollaboration,Nucl.Instrum.MethodsA716(2013)78. [8]K.Abe,etal.,XMASSCollaboration,arXiv:1804.02180 [astro-ph.CO],2018. [9]N.Y.Kim,etal.,XMASSCollaboration,SymposiumonRadiationMeasurements

andApplications,Nucl.Instrum.MethodsA784(2015)499,2014(SORMAXV). [10]K.Abe,etal.,XMASSCollaboration,Phys.Rev.D97(2018)102006.

[11]K.Abe,etal.,XMASSCollaboration,Prog.Theor.Exp.Phys.(2018)053D03. [12]A. Gando, et al., KamLAND-Zen Collaboration, Phys. Rev. Lett. 117 (2016)

082503.

[13]W.Ootani,Master’sthesis,theUniversityofTokyo,1994(writteninJapanese). [14]A. Minamino, Master’s thesis, the University of Tokyo, 2004 (written in

Japanese).

[15]T.Doke,etal.,in:ProceedingsoftheInternationalWorkshoponTechniqueand ApplicationofXenonDetectors(Xenon01),2001,p. 17.

[16] R.Brun,F.Rademakers,in:ProceedingsAIHENP’96,in:Nucl.Instrum.Methods A,vol. 389,Sep.1997,p. 81,Workshop,seealsohttp://root.cern.ch/,1996. [17]P.DDauncey,M.Kenzie,N.Wardle,G.JDavies,J.Instrum.10(2015)P04015. [18]E.Aprile,etal.,XENONCollaboration,Phys.Rev.D96(2017)122002. [19]N.Abgrall,etal.,MajoranaCollaboration,Phys.Rev.Lett.118(2017)161801. [20]D.S.Akerib,etal.,LUXCollaboration,Phys.Rev.Lett.118(2017)261301. [21]C.Fu,etal.,PandaX-IICollaboration,Phys.Rev.Lett.119(2017)181806.