Table Of ContentGeVWIMPsscatteringoffofOHimpuritiescannotexplaintheDAMAsignal
Stefano Profumo∗ and Farinaldo S. Queiroz†
DepartmentofPhysicsandSantaCruzInstituteforParticlePhysicsUniversityofCalifornia,SantaCruz,CA95064,USA
(Dated:May6,2014)
InthepresenceofOHimpuritiesintheDAMAcrystals,GeV-scaleWIMPselasticallyscatteringoffofhydro-
gennucleiwithaspinindependentcrosssectionof∼10−33cm2mightexplaintheannualmodulationobserved
bytheDAMAexperiment,whilebeingconsistentwithotherdirectdarkmattersearches,asscatteringwould
occuratenergiesbelowtheenergythresholdofotherdetectors. Inthisworkweexaminethispossibilityand
showthat,independentofthelevelofOHimpuritiesintheDAMAcrystals,forseveralreasonsthisscenario
doesnotprovideaviableexplanationtotheDAMAsignal.
I. INTRODUCTION 1−8GeV)window,andthusextendingthemassrangeorigi-
4 nallyunderconsiderationinRef.[1]. Wealsostudytheeffect
1 The particle nature of the dark matter (DM) remains one ofavariationintheassumptionsabouttheWIMPvelocitydis-
0 of the most troubling mysteries of our universe. Weakly in- tributionintheGalaxy. WeconcludethatingeneralOHim-
2 teracting massive particles, or WIMPs, are for many reasons puritiesdonotprovideaviablescenariotoexplaintheDAMA
y leading particle dark matter candidates, and, as such, they signal,duetoavarietyofconstraints,includingresidualscat-
a are being very actively searched in a broad variety of exper- tering off of Na nuclei, results from high-altitude detectors,
M iments. In the recent past, a variety of puzzling signals have and unacceptably large contributions to the heat flow of the
beengatheredfromseveraldirectdetectionexperiments,ten- Earth.
5
tatively pointing, if interpreted as originating from WIMP-
nuclei scattering, towards a mass window in the 5-10 GeV
]
h range. Such WIMPs, light compared to standard theory- II. PRELIMINARIES
p
drivenexpectations,mightforexampleprovideaninterpreta-
-
p tiontotheexcesseventsreportedbyCDMS-SI[2],CoGeNT Direct detection of dark matter refers to measurements of
e [3–5],CRESST[6]andDAMA[7]. the energy recoil of a WIMP-Nucleus scattering event. Be-
h Whetherornotalltheputativesignalslistedabovecanbe causeoftheEarthorbitalmotionanannualmodulationinthe
[ madeconsistentwitheachotherismatterofsomecontention WIMPsscatteringsrateinundergrounddetectorsgenerically
2 [5, 8]. More importantly, null results from the XENON [9] exists. Intheelasticdarkmattersetupwecandefinethedif-
v andLUX[10]collaborationsareentirelyincompatible,atlast ferentialscatteringrateperunitdetectormassas:
3 atfacevalue,withalightWIMPinterpretation,withthepossi-
5 bleexceptionofhighlytunediso-spinviolationscenarios[11], dR = 2ρχ (cid:90) d3vvf(v,t) dσ (q2,v), (1)
2 dE m dq2
or if the scintillation properties of LXe are fiercely changed nr χ
4
fromtheassumptionsusedbytheLUXexperiment[10]. Ad-
1. ditionally,themostrecentCDMSlite[12]andSUPERCDMS whereqisthemomentumtransfer,ρχ (cid:39)0.3GeV/cm3isthe
0 localdarkmatterdensity, f(v,t)isthelocaldarkmatterve-
[13]thatusethesametargetnucleusstronglystronglydisfa-
4 locity distribution, which we assume to be time-independent
vortheselightdarkmatter(7−10GeV)positivesignals.
1 andofthefunctionalform
Recently, it was pointed out in Ref. [1] that a O(1) GeV
:
Xiv WsigInMalPcomnisgihsttepnrtowviitdheoathpeorsdsiirbelcetdexetpelcatnioatnioenxpteoritmheenDtsA.MThAe fSHM(u)=(cid:40)Nv031π3/2e−u2/v02 ifu<vesc (2)
key point made in Ref. [1] is that a contamination of OH- 0 otherwise,
r
a molecules is likely to be present in the NaI(Tl) crystals used
by the DAMA collaboration. The precise level of such con- and, finally, where ddqσ2(q2,v) is the differential WIMP-
tamination is unknown, but, if at all at a reasonable level, it Nucleusscatteringcrosssectiongivenby,
would be supposedly sufficient to allow a O(1) GeV WIMP
dσ σ
to strike a Hydrogen nucleus only, which in turn would pro- (q2,v)= SI F2(q), (3)
dq2 4µ2v2
ducephotonsthencapturedbythePMTsintheDAMAdetec-
tor. Ref.[1]hypothesizesandutilizesa1ppmcontamination
with F2(q) the Helm form factor which accounts for the fi-
level;Inwhatfollowswewillassumethissamevalue.
nite size of the nucleus, µ the WIMP-nucleus reduced mass,
In this study we explore whether OH impurities indeed
andσ thespinindependentWIMP-nucleonscatteringcross
lead to a self-consistent explanation of the DAMA signal, SI
section. Thelattercanbecastas,
focussing on the broad very light WIMP (for definiteness,
4
σ = µ2[Zf +(A−Z)f ]2, (4)
SI π p n
∗[email protected] f ,f being the effective couplings to proton and neutrons,
p n
†[email protected] respectively, A the atomic mass number and Z the atomic
2
number. TheseeffectivecouplingsandtheHelmformfactor follows:
aredeterminedfollowingawellknownprocedure, described dR (cid:90) ∞ dR
e.g. in [15]. Sincewe are interested in theverylight WIMP dE (Eee,t)= dEnrφ(Enr,Eee)dE (Enr,t), (5)
andenergyregion,theformfactordependenceismodest[15], ee 0 nr
therefore different form factors induce very mild changes in where φ(E ,E ) is the differential response function and
nr ee
ourconclusions. φ(E ,E )∆E is the probability that a nuclear recoil of
nr ee ee
In this study we adopt a Standard Halo Model for the ve- energy Enr will produce a scintillation signal measured be-
locitydistribution,giveninEq.(2).Wealsodiscussdepartures tweenEeeandEee+∆Eee,foundtobe
fromthismodel,especiallywhenitcomestochangingtheone 1
crucialinputquantityforlow-massWIMPs,i.e. thedarkmat- φ(Enr,Eee)= (cid:112) e−(Eee−QEnr)2/2σ2(QEnr),
2πσ2(QE )
terGalacticescapevelocityV . nr
esc (6)
with
(cid:112)
σ(QE )=α QE +βQE , (7)
nr nr nr
III. OVERVIEWOFTHEDAMA/LIBRAEXPERIMENT √
whereα = (0.448±0.035) keVeeandβ = (9.1±5.1)×
10−3.
The DAMA/LIBRA experiment, located in the under-
As discussed in the previous section, due to the changing
groundINFNGranSassoNationalLaboratoryinItaly,makes
WIMP velocity distribution at Earth as the Earth orbits the
useofalargemassdetectorofabout250kghighlyradiopure
Sun, there is a small (∼ 1-10%) variation (or modulation) in
NaI(Tl). The experiment is designed to detect nuclear recoil
therecoilratethroughouttheyear[7].
events through scintillation light, and is optimized to search
Thetimedependenceintherecoilratecanbedescribedas
fortimevariationsintheeventrate,ratherthantoidentifydark
matterscatteringonanevent-by-eventbasis. Thestrategyof dR
(E ,t)=S (E )+S (E )cosω(t−t )+... (8)
lookingforanannualmodulationcanbeusedtodistinguisha dE ee 0 ee m ee 0
ee
dark matter signal from most possible backgrounds sources,
whereS istheaveragerate,S isthemodulationamplitude,
although one may worry about possible sources of back- 0 m
and higher-order terms are neglected due to the small mod-
ground which could potentially also exhibit seasonal varia-
ulation amplitude, in the absence of streams [16]. We have
tion.
packedthe36binsreportedbyDAMAinto8bins,inorderto
The DAMA/LIBRA collaboration claims, however, that
improvethesensitivityofstatisticaltests,accordingtoTableI
there exists no background satisfying at once all of the fol-
below.
lowingcriteria:
Usingthisdataset,wehaveperformedachi-squaredanal-
(i)havingaco-sinusoidalmodulationrate; ysis,withtheχ2definedasfollows:
(ii)existingonlyinadefinitelowenergyrange;
(iii)havingexactlyaoneyearperiod; χ2(m ,σ)=(cid:88)(cid:0)Smex,pi −Smth,i(mχ,σ)(cid:1)2 , (9)
(iv)possessingtheproperphase; χ σ2
i i
(v)producingsingle-hitevents;
whereSth (m ,σ)isthetheoreticallyexpectedamplitudefor
(vi)havingthepropermodulationamplitude. m,i χ
a WIMP model of a given mass (m ) and spin independent
χ
The DAMA/LIBRA collaboration has so far released re- scatteringcrosssection(σ),whereasSexpistheexperimental
sultscorrespondingtoatotalexposureof1.17tonyrover13 m,i
valueofthemodulationamplitudeforagivenbini,andσ is
i
annualcyclessupportingthedetectionofasignalpossiblydue
theuncertaintyasindicatedinTableI.
todarkmatteratthe∼9σlevel[7].
Regardingdetectordetails, itisimportanttopointoutthat
thecollaborationusesgammaraysources,whichinduceelec- Energy AverageS
m
tronrecoil, tocalibratetheirdetectors. Thereforeforagiven [keVee] [cpd/kg/keVee]
electronrecoilwithenergyEeetheDAMAexperimentiscal- 2.0-2.5 0.0161±0.0040
ibratedtotheresultingamountoflightproduced. Whenanu-
2.5-3.0 0.0260±0.0044
clearrecoilhappensandsomeamountofenergyisproduced,
3.0-3.5 0.0220±0.0044
DAMAthusquotestheelectronequivalentenergythatwould
3.5-4.0 0.0084±0.0041
haveyieldedthesameamountoflight.Basedonthisinforma-
tion,wecandefineaquenchingfactor(Q)whichtranslatesthe 4.0-5.0 0.0080±0.0024
ratio of the amount of scintillation light created by a nuclear 5.0-6.0 0.0065±0.0022
recoiltothatproducedbyaelectronrecoilofthesameenergy. 6.0-7.0 0.0002±0.0021
Thequenchingfactorvaluevariesaccordingtothetarget,and 7.0-20.0 0.0005±0.0006
in our work, we will use the values reported by the collab-
oration, Q = 0.3 and Q = 0.09. Moreover, we have TABLEI.Averagemodulationamplitudesforthe8binsusedinthis
Na I
accountedfortheenergyresolutionofthedetectorbywriting analysis. Theoriginal36binsofwidth0.5KeVeewerepackedinto
the differential rate in terms of the electron recoil energy as 8asshowninthetable.
3
105 105 105
104 Including H scattering only 104 104
111000231 Vesc = 3 D0A0 MkmA /9s9% C.L 111000231 Includ iDDngAA MMH AAsc 99a09t%%te rCCin..LLg only 111000231 IVnecslcu =d 7 iDn0gA0 MHkm Asc /9as9t%te rCin.Lg only
σ (pb)SI111000−−021 σ (pb)SI111000−−021 Vesc= 544 km/s σ (pb)SI111000−−021
LUX
10−3 10−3 10−3 CDMSlite
10−4 CDMSlite 10−4 10−4
10−5 10−5 LUX 10−5
10−6 10−6 CDMSlite 10−6
10−7 10−7 10−7
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Mwimp (GeV) Mwimp (GeV) Mwimp (GeV)
FIG.1. ThebestfitregionsundertheassumptionofexclusiveWIMP-Hydrogenscattering(noNascattering)usinganescapevelocity,from
lefttoright,of300,544and700km/s.Weusea1ppmcontaminationofHydrogeninNaI(Tl)crystals.The90%C.Lregionisexcludedforall
casesbymanyordersofmagnitudebyCDMSlite;asmallmasswindow2.5−3.5GeVisstillconsistentwithcurrentlimitsforlargeenough
escapevelocities,butisinconsistentwithotherbounds(seethetext).
IV. RESULTS valuesfortheWIMPescapevelocityinanattempttosuppress
Na scatterings (left panel, V = 300 km/s), the predicted
esc
signalprovidesaverypoorfittothemodulationobservedby
Ref.[1]assumesthatdarkmatterparticlesmightonlyscat-
DAMA/LIBRA.
ter off of Hydrogen, but not off of Na. This, if at all possi-
ble, would definitely make for highly peculiar particle prop-
erties. We examine this possibility and compare the best fit WethusconcludethataverylightWIMPasacandidateto
regions with available constraints, in fig. 1. There, we as- explaintheDAMAmodulationisexcludedatalmost∼4σ.In
sume a quenching factor of one and a standard Mawellian thisconfiguration,infact,theWIMPsinthetailofthevelocity
velocity distribution, with three different escape velocities: distributionareresponsibleforscatteringoffofNa, andpro-
v = 300, 544 and 700 km/s. The reason for testing dif- duceanextremelylargenumberofevents,thereforeentailing
esc
ferentescapevelocitiesistochecktheeffectofchangingthe apoorfittothemodulationsignal. Weverifiedthatevenas-
standardassumptionsregardingthestandardhalomodel. No- sumingaverysmallescapevelocitydoesnotimprovethesit-
ticethatintheleftmostpanelinfig. 1,onlyCDMSlitebound uation: whilethebestfitregionisshiftedtolowermasses,the
appliesduetotheverylowescapevelocity. fittothemodulationsignalisoverallworsethanwithhigher
escapevelocities.
Fig. 1 illustrates that even if one neglected Na recoils and
consideredHydrogenscatteringonly,theDAMAsignalcould
be fit satisfactorily only down to a mass of 2.5 GeV, at the Itiscrucialtonotethatthereexistotherlinesofargument
99% C.L.. The 90% C.L region is excluded for all cases by why a 1 GeV WIMP with a large scattering cross section is
manyordersofmagnitudebyCDMSlite;thesmallmasswin- strongly disfavored as an explanation to the DAMA/LIBRA
dow2.5−3.5GeVisstillconsistentwithcurrentlimitsonly modulation signal: high-altitude detectors and Earth heat-
forlargeenoughescapevelocity. Noticethatsmallerquench- ing. A light and strongly interacting particle would violate
ing factors (which are much more likely) would shift the fa- boundsfromhigh-altitudedetectors[17]whichunlikeunder-
voredregiontoevenhighermasses,andstrengthenthebounds grounddetectorsarenotshielded. Withsuchlargecrosssec-
comingfromotherexperiments. Highermassesarevastlyex- tions,largeportionsofthefavoredparameterspaceinthelight
cludedbyordersofmagnitude,asalsoshowninfig.1. Even WIMPscenarioisindisagreementwithobservation.
only at a mass of 3 GeV the large cross sections required
wouldbeintensionwiththeCDMSliteresults(assumingthat Even stronger bounds come from precision measurements
the WIMP would scatter off of Ge). In the very small mass of the Earth heat flow. When the dark matter scattering rate
region (2.5 to 3.5 GeV) such large cross sections are incon- issufficientlylarge,theenergydepositionbydarkmatterself-
sistent with high-altitude detector results and with heat flow annihilation products captured by the Earth gravitational po-
measurements,aswediscussbelow. tential would grossly exceed the measured heat of Earth. A
We now consider the more realistic case where scattering largelymodel-independentconstraintonthedarkmatterscat-
happensoffofnucleiinbothHandNa.Infig.2weshowbest- tering cross section with nucleons can be placed [18], under
fitcontoursofconstantχ2values(44and32.9),aswellasthe theassumptionthatannihilationoccurs. Wedisplayforrefer-
bestfitpoint(redX).Thefavoredmassregionisnotexcluded encetheresultingconstraintsfromEarthheatingastheshaded
by other direct detection experiments, but the best-fit input regioninFig.3: theexcludedregioncompletelyrulesoutthe
parametersprovideaverypoorfittotheDAMA/LIBRAdata. best-fit DAMA region even when only Hydrogen scattering
Forexample,eventhebest-fitpoint(indicatedwitharedcross aretakenintoaccount(weusehereaquenchingfactorofone
σ = 104 pbandM = 1.7GeV)isexcludedatthe3.9σ level and escape velocity of 544 km/s, but our results are largely
forV =544and700km/s. Evenifoneusedextremelylow independentofthesetwoassumptions).
esc
4
105 105 105
Including H+Na scatterings Including H+Na scatterings
Includχin2g = H4+4N/8a dS.coa.ftterings χχ22==4342/.98/ d8 .od..of.f χχ22==4342/.98/ d8 .do..of.f
Vesc=300 km/s Vesc = 544 Km/s Vesc = 700 Km/s
σ(pb)SI 104 σ (pb)SI104 σ (pb)SI104
best fit point is excluded at 3.9σ 2
best fit point is excluded at 4.9σ
2best fit point is excluded at 3.9σ
2
103 103 103
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
Mwimp (GeV) Mwimp (GeV) Mwimp (GeV)
FIG.2. ThebestfitregionsincludingbothHandNascatteringusingV = 300,544and700km/s(fromlefttoright). Thefavoredmass
esc
regionisnotexcludedbyotherdirectdetectionexperiments,butthebest-fitinputparametersprovideaverypoorfittotheDAMA/LIBRAdata.
Forexample,eventhebest-fitpoint(indicatedwitharedcrossσ =104pbandM =1.7GeV)isexcludedatthe3.9σlevelforV =544
esc
and700km/s(thefitforV =544km/sisevenworse).AllcontoursaregoodnessoffitcontoursusingthebinningschemedescribedinRef.
esc
[14].
106 favoredscenarioforthefollowingreasons:
105 (i) under the unmotivated assumption that the WIMP only
Including H+Na Scatterings
104 χ2=44/8 d.o.f scatteroffofHydrogenbutnotNa,weshowedthatthefavored
χ2=32.9/8 d.o.f mass range would place the proton-WIMP cross section in a
103 Vesc = 544 Km/s
b) regiongrosslyruledoutbycurrentexperiments;
σ (pSI102 (ii)ifscatteringoffofNaexistsconcurrentlywithH,there-
101 sultingsignaldoesnotprovideagoodfittotheDAMAsignal,
100 andisruledouttoalmostthe4σlevel;
10−1 Earth heating (ii)ifscatteringoffofGeexistsconcurrentlywithH,then
10−2 CDMSlitelimitseliminatethefavoredWIMPcandidatemass;
100 101 102 103 (iv) indirect constraints such as limits from high-altitude
Mwimp (GeV)
detectorsandfromtheEarthheatflowaregenericallyincom-
patiblewiththeproposedmassandcrosssection.
FIG.3. ExclusionregionbasedonthecaptureofDarkMatterpar-
ticlesintheEarthandsubsequentannihilation,producinganexcess
overthemeasuredheatflowofEarth[18].Weshowwithgreencon- ACKNOWLEDGMENTS
toursthebest-fitDAMAregionforanescapevelocityof544km/s.
The authors thank Ritoban Basu, Will Shepherd, Patrick
Draper for relevant discussions and Chris Kelso for read-
V. CONCLUSIONS ing the manuscript and discussing the results. SP is partly
supported by Department of Energy Award SC0010107, and
In this analysis we demonstrated that a light, O(1) GeV FSQ by Department of Energy Award SC0010107 and Na-
WIMP scattering off of Hydrogen nuclei from residual OH tionalCouncilforScientificandTechnologicalDevelopment
contaminationintheDAMANaI(Tl)crystalsisahighlydis- (CNPq).
[1] J. Va’vra, “A New Possible Way to Explain DAMA Results,” [7] R.Bernabei,P.Belli,A.DiMarco,F.Cappella,A.d’Angelo,
arXiv:1401.0698[astro-ph.GA]. A. Incicchitti, V. Caracciolo and R. Cerulli et al.,
[2] R. Agnese et al. [CDMS Collaboration], [arXiv:1304.4279 arXiv:1301.6243[astro-ph.GA].
[hep-ex]]. [8] P.J.Fox,G.Jung,P.SorensenandN.Weiner,arXiv:1401.0216
[3] C.E.Aalsethetal.[CoGeNTCollaboration],Phys.Rev.Lett. [hep-ph].
106,131301(2011).[arXiv:1002.4703[astro-ph.CO]]. [9] E. Aprile et al. [XENON100 Collaboration], Phys. Rev. Lett.
[4] C. E. Aalseth, P. S. Barbeau, J. Colaresi, J. I. Collar, J. Diaz 109,181301(2012)[arXiv:1207.5988[astro-ph.CO]].
Leon, J. E. Fast, N. Fields, T. W. Hossbach et al., Phys. Rev. [10] LUXCollaboration,[arXiv:1310.8214].
Lett.107,141301(2011).[arXiv:1106.0650[astro-ph.CO]]. [11] J.L.Feng,J.Kumar,D.MarfatiaandD.Sanford,Phys.Lett.B
[5] C.E.Aalsethetal.,arXiv:1401.3295[astro-ph.CO]. 703,124(2011)[arXiv:1102.4331[hep-ph]].
[6] G. Angloher, M. Bauer, I. Bavykina, A. Bento, C. Bucci, [12] CDMSliteCollaboration,[arXiv:1309.3259].
C. Ciemniak, G. Deuter, F. von Feilitzsch et al., [13] SUPERCDMSCollaboration,[arXiv:1402.7137].
[arXiv:1109.0702[astro-ph.CO]].
5
[14] Chris Kelso, Pearl Sandick, Christopher Savage, JCAP 1309 [16] C.Savage,K.FreeseandP.Gondolo,Phys.Rev.D74,043531
(2013)022,[arXiv:1306.1858]. (2006)[astro-ph/0607121].
[15] Katherine Freese, Mariangela Lisanti, Christopher Savage, [17] J.Rich,R.RocchiaandM.Spiro,Phys.Lett.B194,173(1987).
Rev.Mod.Phys.85(2013)1561-1581,[arXiv:1209.3339]. [18] G. D. Mack, J. F. Beacom and G. Bertone, Phys. Rev. D 76,
043523(2007)[arXiv:0705.4298[astro-ph]].
