A New Possible Way to Explain the DAMA Results

2.8 MB·

by  J. Va'vra

Astronomy&Astrophysicsmanuscriptno.Vavra˙my˙DAMA˙paper (cid:13)c ESO2014
June18,2014
A New Possible Way to Explain the DAMA Results
J.Va’vra
SLAC,StanfordUniversity,CA94309,U.S.A.
e-mail:[e-mail]
ReceivedJanuary10,2014
ABSTRACT
AtpresentthereisanefforttoreconciletheresultsoftheDAMAexperimentwiththosefromotherDarkMatterexperimentssuchas
CoGeNT,CRESST,CDMS,andallLXeexperiments.TheauthorsuggestsanewmodeldescribingtheDarkMattersignalastheresult
4 ofcollisionsofverylight(1-to-fewGeV/c2)WIMPswithhydrogen,andcomparesitwithcurrentlyacceptedmodelsofcollisions
1 with heavy nuclei (Na, Ge or Xe). The hydrogen target would come from H-contamination of NaI(Tl), Ge and CaWO crystals.
4
0 InitialtuningindicatesthatonecanexplainthemodulationamplitudeofDAMAandCoGeNTwiththismodel,assumingaWIMP-
2 protoncrosssectionbetween10−33and10−32cm2.Thispapershouldbeconsideredtobeanewideawhichwillneedsubstantialnew
experimentalinputfromallinvolvedexperiments.
n
u Keywords.DAMAexperiment,DarkMattersearch
J

7
1
1. Introduction

]
A The DAMA experiment observes a small, but clear, oscillatory
signal. The signal is a peculiar modulation of the counting rate
G
of2-6keVsingle-hitevents(i.e.thoseinwhichonlyoneofthe
h. manydetectorsinthesetupfires)satisfyingallthemanyrequire-
p mentsoftheDarkMatterannualmodulationsignature.Theob-
- served yearly modulation is in phase with the Earth’s motion
o
aroundtheSun.DAMAisthefirstexperimenttoobserveaclear
r
t oscillatorysignal[1]and[2],asshownonFig.1.
s
a The CoGeNT experiment (see Fig. 2) also reports evidence
[ ofoscillation,andtheCRESST-IIandCDMSexperimentsalso

report hints of a signal. However, there is no hint of a signal Fig.2. CoGeNT data: counts per 30-day interval from the 0.5-
5
fromanyLXeDarkMatterSearchexperiments,suchasXenon- to-few keVee energy window [3]. The modulation amplitude is
v
8 10,Xenon-100orLUX. ∼0.3counts/day/kg/keV.
9 Figure3,whichwasshownatthe2013Snowmassmeeting,
6 presents one of the possible model-dependent comparisons to
0
the results of dark matter experiments. The important point for
.
1 this paper is that there is great opportunity to explore the cross
0 sectionregionof10−30−10−44cm2ifthemassisindeedlow.
4
1
:
v
i
X
r
a
Fig.3. The model-dependent status of cross section limits for
the detection of the WIMP mass from various experiments
(Snowmass, 2013). The graph also shows the low limit, below
Fig.1. DAMA data: residual rate of the single-hit scintillation
events, measured by DAMA/LIBRA over six annual cycles in whichexperimentswillhavetodealwithneutrinobackground.
Onecanseeclearly,thataWIMPmassbelow∼5GeV/c2would
the(2-6)keVenergyintervalasafunctionoftime[2].Themod-
ulationamplitudeis∼0.01counts/day/kg/keV. notbedetectedbymostofthepresentexperiments.
1
J.Va’vra:ANewPossibleWaytoExplaintheDAMAResults
QF
Fig.5. The semi-empirical calculation5 of the quenching fac-
tor for proton recoils in the NaI(Tl) crystal, for two val-
ues of the Birks constant. DAMA determined a low value of
kB=1.25mg/(cm2MeV)usingalphaparticlesmeasuredintheir
experiment; this in turn gives a higher QF value for very small
protonrecoilenergies.5
Fig.4. As for Fig. 3, but the figure also shows the future reach
of the CDMS experiment at low mass (presented by CDMS at
Snowmass,2013).1
basedononlyoneparameter,kB,theso-calledBirksfactor.The
valueofthekBfactordepends[6]onmanyparameters,suchas
Figure4showstheCDMSfuturelowmasslimitreach1 for
the detector material itself with all its impurities and dopants,
various new detector configurations and using new improved
theconditionsoftheexperimentsuchastemperature,thesignal
electronics.Clearly,CDMSaimstoexplorethelowmassrange,
integration time, etc. Ideally, the QF value should be measured
andsotheideapresentedinthispaperwillbetestedsoon.
in the same experiment, and under exactly the same conditions
as used for data taking. The kB factor could be determined by
fittingexperimentaldataobtainedusingonetypeofparticle,for
2. AnewideatoexplaintheDAMAdata
example α particles from an external source, and then using it
Theauthordiscussesanewidea,whichexplainstheDAMAsig- topredicttheQFvalueforanothertypeofparticle,forexample
nalasbeingduetothescatteringofalightDarkmatterparticle theproton,eveninadifferentenergyregion.Figure5showsV.
(1-to-few GeV/c2) on a light nucleus; specifically on hydrogen Tretyak’sQFcalculation5fortheprotonQFfortwovaluesofthe
presentasasmallOHorH2OcontaminationintheNaI(Tl)crys- Birksconstant,basedontwoextremevaluesobtainedfromdif-
tals. ferent experiments; for kB constant at extreme values between
Table1showsthemaximumcalculatedkinematicallimitin 1.25and6.5mg/(cm2MeV),theprotonQFisbetween0.95and
terms of the nuclear recoil (keVnr) and the electron-equivalent 0.8 at ∼0 keV; for the DAMA case, where kB was determined
recoil (keVee).2 We point out that DAMA quotes the thresh- to be 1.25 mg/(cm2 MeV) using the α particle calibration, the
old in keVee units, so that one has to convert keVnr units to protonQFis∼0.95forverysmallprotonrecoilenergies.Ias-
keVee units. One can easily calculate the keVnr-scale using sumeavalueofQF∼0.95forthecalculationsofTable1.The
two-body kinematics; to convert the keVnr-energy-scale to the conclusions would not change, however, if one would take QF
keVee-scale,oneneedstoknowthequenchingfactor(QF)fora ∼0.8instead.
given nucleus, i.e., EkeVee = QF * EkeVnr. The quenching factor The DAMA experiment detection software threshold was
dependsontherecoilenergy.IncaseofNaI(Tl),forsodiumre- 2keVeeduringmostofdatataking[7],butitwasrecentlylow-
coil, I assume QF ∼ 0.25 with the understanding that the value eredto1keVee[11](whilethehardwarethresholdwasheldat1
couldbelower.3TheprotonquenchingfactorinNaI(Tl)hasnot photoelectron all along). Notice in Table 1 that the maximum
beenmeasuredtoourknowledge.4 Generallyitisexpectedthat electron-equivalent recoil energy for Na-nucleus is below the
theprotonQFisconsiderablyhigherthanforNaorIrecoils,but newDAMAdetectionthresholdunlesstheWIMPmassisabove
notquiteashighas1.0.Intheabsenceofanymeasurement,we ∼4 GeV/c2. On the other hand, it is possible to detect a larger
followthesemi-empiricalcalculationofV.Tretyak[6],whichis WIMP mass than ∼1 GeV/c2 for scattering off the H-nucleus
even with the old DAMA threshold of 2 keVee, assuming that
1 B. Cabrera, private communication; figure presented at the
theprotonQFis∼0.95.
Snowmassmeeting,2013onbehalfoftheCDMSgroup.
2 Itshouldbenotedthattheliteratureindicatesquiteascatterinval- DAMANaI(Tl)crystalsaremadeofUltra-Low-Background
uesoftheGalacticescapevelocity:(a)450km/sec<v <650km/sec (ULB) materials to guarantee low radioactive background.
esc
[8],(b)489km/sec<v <730km/sec[9],and(c)498km/sec<v WhiletheDAMAexperimentdoesquoteverylowradio-purity
esc esc
<608km/sec[10]. levels[7],itdoesnotquotetheH,OHandH Ocontaminationat
2
3 SomeexperimentsmeasuredthequenchingfactorQFforsodiumin all.Generally,theH-contaminationisnotquotedbycrystalpro-
NaI(Tl)closeto0.25-0.3,seeforexample[4]and[6].However,accord- ducers,sincespectroscopicpropertiesofNaI(Tl)crystalsarenot
ingtoprivatecommunicationwithJ.Collar,somemorerecentmeasure- affected by it up to a level of ∼10 ppm. The OH-molecule rep-
mentsindicatevaluescloseto0.1-0.15forarecoilenergyof∼10keVnr resentsalikelysourceofcontaminationoftheprimaryNaIsalt;
[5];recentltthishasbeenmeasuredindependentlyatDukeUniversity,
itsremovalrequiresprolongedpumpingatelevatedtemperature
withasimilarresult(soontobepublished).However,asdiscussedin
[12].Figure6showstypicalOH-contaminationlevelsinNaI(Tl)
thepaper,theQFfactordependsonexactexperimentalconditions,i.e.,
itisnotauniversalconstant[6].
4 ConfirmedbyprivatecommunicationwithJ.Collar,D.McKinsey 5 PrivatecommunicationwithV.I.Tretyak.Thesamecalculationwas
andV.I.Tretyak. usedin[6].
2
J.Va’vra:ANewPossibleWaytoExplaintheDAMAResults
Table 1. Maximum calculated nuclear recoil energy E and
keVnr
maximumelectron-equivalentrecoilenergyE asafunction
keVee
of WIMP mass, for two targets, hydrogen and sodium. It is as-
sumedthattheWIMPvelocityrelativetoEarthisbetween0and
the Galactic escape velocity of ∼650 km/sec, all modulated by
theEarth’svelocityof230±30km/secintheGalacticcoordinate
system.Inthistable,forsodiumrecoilIusedQF=0.25[4],and
forhydrogenQF=0.95.5
WIMPmass[GeV/c2] Nucleus E [keV] E [keV]
keVnr keVee
0.5 H 1.91 1.81
1.0 H 4.30 4.08
1.5 H 6.20 5.89
2.0 H 7.65 7.26
2.5 H 8.78 8.34
3.0 H 9.68 9.20
0.5 Na 0.19 0.05
1.0 Na 0.73 0.18
Fig.6. FTIR spectrum of NaI(Tl) crystals showing the OH-
1.5 Na 1.57 0.39
contaminationinacrystallocatedinaprotectiveenclosure(solid
2.0 Na 2.67 0.67
curve)andtheH Ocontaminationwhenexposedtoair(dashed
2.5 Na 4.00 0.60 2
curve).6
3.0 Na 5.53 1.38
4.0 Na 9.07 2.26
gen.Therefore,eventheultra-pureGehasaH-contaminationat
a level of ∼2x1015 atoms/cm3, or ∼50 ppb [16], and according
crystals6;theFTIRspectrumshowstheOH-contaminationfora
to P. Brink7 this is a reasonable estimate to assume. However,
crystallocatedinaprotectiveenclosure(solidcurve)justafterits
westressthatnorealmeasurementwasmadeontheactualcrys-
production,andtheH Ocontaminationwhenitwasexposedto
2 tals from these two experiments, and so we encourage that this
air(dashedcurve).TheexactleveloftheOHorH Ocontamina-
2 isdone.Forourcalculationweassumealevelof∼50ppb.
tion in NaI(Tl) crystals is generally proprietary information, as
The CRESST-II experiment uses CaWO crystals of total
toldbySaint-GobainCo.However,welearnedfromtheHilger 4
weight ∼ 10 kg. These have been prepared by the Czochralski
Co.thatanOH-contaminationatalevelof1-3ppmisverylikely.
growth method using the solid state reaction from CaCO and
Generally, these companies keep the air humidity at less than 3
WO fromAlfa-Aesarmaterialswithpuritylevelsof99.999%
∼2%whenmachiningacrystalandassemblinganNaI(Tl)detec- 3
and99.998%respectively[17].Thepaperdoesnotmentionthe
tor,althoughagainthisisproprietaryknowledge.But,knowing
H-contaminationlevel,butthepuritylevelofthemajoringredi-
how hard it is to keep humidity low in gases without appropri-
entsusedtoformthecrystalisnotveryhigh,fromourperspec-
ate filtration or without pumping while baking, it would seem
tive. Reference [18] describes another possible method to pre-
to us that water contamination at a level of a few ppm is eas-
pareCaWO crystals,andtheydidmeasureasignificantlevelof
ilypossible.Onceinthedetector,eachDAMANaI(Tl)crystalis 4
OH contamination using the FTIR method. However, we were
encapsulatedinacopperhousingandsealedforallitslife.Inad-
not able to obtain information on the H-contamination for ac-
dition,thedetectorsarecontinuouslymaintainedinhighpurity
tualCRESST-IIcrystals,evenaftercontactingmembersofthat
nitrogenatmosphere.Therefore,ifthereisanyH-contamination,
collaboration. Therefore, for our calculation we assume, in an
itisprobablethatitwouldhaveoccurredduringpreviousmanu-
arbitraryway,anH-contaminationatalevelof100ppb.Again,
facturingsteps.
While the possible presence of H/OH-contamination in the onceabettervalueisknown,ourresultscanbeeasilyscaled.
Ultra-Low-Background (ULB) NaI(Tl) DAMA detectors re-
mains an open question, for our calculation we will assume, in
4. Ratecalculation
anarbitraryway,thattheH-contaminationisatalevelof1ppm.
Onceabetternumberisknown,onecaneasilyscaleourresults. AlowmassWIMPof1-to-fewGeV/c2 representsarealexperi-
mentalchallengeatpresentformostexperiments,asitrequiresa
lowmasshydrogentargetinordertobedetectable.Sofar,exist-
3. OtherDarkMattersearchexperiments ingexperimentsprovidethehydrogentargetonlyasasmall”un-
wanted” contamination, which limits the measured rate. Alkali
If the proposed H-contamination mechanism works for the
halide inorganic crystals, such as NaI(Tl) or CsI(Tl), may have
DAMA experiment, it must also work for CDMSlite [19],
auniqueadvantageoverothermethodsindetectingavery-low-
CoGeNT [3], and CRESST-II [20]. The peak modulation am-
plitude for DAMA is ∼300 events/30 days, for CoGeNT it is massWIMP,iftheyhavesufficientlyhighOH-contamination.
∼10 events/30 days; CDMSlite measures ∼2.9 counts/keV/kg- Wecalculatetherateasfollows:
day(noclearoscillationmeasuredyet).
Rate=σ ·F ·N ·V ·Time·Det (1)
BoththeCDMSliteandCoGeNTexperimentsuseultra-pure WIMP WIMP target target ef
Ge-crystals[16].Hydrogenistheonlygaswhichhasbeensuc-
where Det is the detection efficiency, σ is in [cm2],
cessfully used for high-purity Ge-crystal growth. All commer- ef WIMP
F is flux in [cm−2sec−1], N is number of target parti-
cial detector grade germanium is grown exclusively in hydro- WIMP target
cles in [cm−3], V is target volume in [cm3] and Time is in
target
6 N.Shiran,A.Gektin,InstituteofScintillatingMaterials,Kharkov,
Ukraine,privatecommunication,2014. 7 P.Brink,CDMScollaboration,privatecommunication,2014.
3
J.Va’vra:ANewPossibleWaytoExplaintheDAMAResults
Fig.7. This paper’s prediction for the modulation peak rate
Fig.8.UpperlimitsofWIMP-nucleoncross-sectionsasafunc-
in several experiments as a function of cross-section, assum-
tion of the WIMP mass, plotted for Tevatron [22] and LHC
ing the H-contamination as indicated, WIMP-proton scattering
[23],CMS[24].Thereisalargerangeofpossiblevaluesofcross-
hypothesis, Dark matter density ∼0.3 GeV/cm3 in our nearby sectionlimitsfor∼1GeV/c2WIMP.
Universe [21]. The modulation amplitude peak was calculated
fromadifferentialratebasedontheEarth’svelocityvariationof
230±30 km/sec in the Galactic coordinate system. The vertical
lines indicate a cross-section corresponding to DAMA (dashed
line)andtoCoGeNT(solidline)measuredpeakamplituderates. dark matter particle mass between 1 and a few GeV/c2 should
be done with a proper fit, which includes a realistic simulation
Table 2. Input numbers used in the calculations for Fig. 7 and of the dark matter velocity distribution in the Galaxy, the cross
Table3. section,andtheH-contamination.Anexampleofsuchacalcula-
tionisfoundinRef.[13],andthisdisagreedwithourhypothesis
Experiment weight[kg] H-contamination Detectionefficiency Energyrange[keVee] of hydrogen contamination, as presented in our original paper
DAMA 250 1ppm 0.6 1-6
[14].However,theseauthorsassumedaMaxwelliandistribution
CoGeNT 0.444 50ppb 1.0 0.5-3
CDMSlite 0.6 50ppb 1.0 0.5-3 of dark matter velocities in our Galaxy. We would argue that
CRESST-II 10 100ppb 1.0 0.5-3
thedarkmattervelocitydistributionmayhavetwocomponents
inreality,onecomponentrepresentingtheMaxwelliandistribu-
Table3.Calculatednumberofeventsexpectedover30daysin tion, and the second component representing a direct external
thepeakofthemodulation,forDAMA,CoGeNT,CDMSliteand non-Maxwellian flow distribution, as all galaxies may be inter-
CRESST-IIexperimentsusingtheH-contaminationmodel. connected by streams of dark matter with velocities above the
Galaxyescapevelocity.Thedirectflowcomponentmayenhance
Crosssection[cm2] DAMA CoGeNT CDMSlite CRESST-II thereachtoalowerWIMPmassrangethanthatwhichisshown
10−32 794 3.25 4.69 146.6 inTable1.Thisproblemshouldclearlybestudiedinmoredetail.
10−33 79.4 0.33 0.47 14.7
10−34 7.9 0.03 0.047 1.47 Reference [13] also pointed out a possible conflict with a
model of overheating of the Earth’s atmosphere if low mass
dark matter particles have too large a scattering cross section
[sec].TheWIMP-protonscatteringcrosssectionisnotknownat [15].However,fromRef.[15]weconcludethatwearestillbe-
present.Wewilltreatitasanindependentvariable.Table2lists lowtheirquotedoverheatinglimits,fortheproposeddarkmatter
theinputnumbersusedinthecalculation. massesnear∼1GeV/c2 andacrosssectionbelow∼10−32 cm2.
Figure 7 shows our prediction for the modulation peak rate However, if the local dark matter density increased by a factor
in several experiments as a function of cross section, assum- of∼10,oriftheWIMP-protonscatteringcrosssectionislarger,
ing the H-contamination indicated in the figure, as a function theoverheatingdescribedinRef.[15],mightoccur.
oftheWIMP-protoncrosssection.InordertoobtaintheDAMA The LXe and LAr experiments do not have hydrogen con-
modulation peak of ∼300 events/30 day period a cross section tamination,andthereforeanyDMsignaldetectedbythesemeth-
slightlylowerthan∼10−32 cm2 isrequired.However,toexplain odswoulddirectlycontradicttheproposedmodel.
theCoGeNTcountrate,aslightlyhighervalueofthecrosssec-
tionisrequired.Itisthereforecrucialthatbothexperimentsde-
terminetheH-contaminationintheircrystals.
Table3showsthenumberofeventsexpectedper30daysin 5. ComparisonwithLHCexperiments
themodulationpeakamplitudeforfourexperiments.
In order to make a quantitative comparison to the proposed It is interesting to compare our prediction for the DAMA
model, each of the four experiments should perform an H- WIMP-nucleon cross section range with upper limits obtained
contamination analysis of the crystals used in that experiment; by Tevatron and LHC experiments, where the WIMP is mea-
DAMA should also find out if there is a correlation between suredin”WIMP+WIMP+jets”events[22].Thisisshownin
rate/crystal and the H-contamination in each crystal (if indeed Figure8.Itisclearthattheaccelerator-basedcrosssectionupper
thereisavariationinrate/crystal). limitsarelowerthanvaluesobtainedfromtheH-contamination
ThecalculationinFigure7ismadesimplytogetafeelfor model. However the limits of collider experiments are derived
theproblem,andtoprovidemotivationtomeasurethehydrogen withaneffectiveoperatorapproach,anddirectcomparisonwith
contamination in the existing crystals. The exact tuning of the ourmodelhassomeunknownmodeldependency.
4
J.Va’vra:ANewPossibleWaytoExplaintheDAMAResults
6. Anewproposalforfutureexperiments References
One could attempt to detect diatomic molecular vibration, ex- [1]R.Bernabeietal.,Eur.Phys.J.C23,61(2002).
[2]R.Bernabeietal.,Eur.Phys.J.C73,2648(2013).
cited by gentle WIMP-proton scattering, and hence further re-
[3]C.E.Aalsethetal.,Phys.Rev.D881,012002(2013).
duce the threshold on the WIMP mass [25]. To excite such vi-
[4]G.Gerbieretal.,AstroparticlePhysicsII287(1999).
brations, a very small energy deposit at a level of 1.8-4.3 eV [5]J.Collar,Phys.RevC88,035806(2013),andPhys.Rev.Letters110,211101
is needed. Some fraction of de-excitations goes in the visible (2013).
range, so it should be possible to detect it with the Bialkali [6]V.I.Tretyak,AstroparticlePhysics33,4053(2010).
[7]R.Bernabeietal.,Nucl.Instr.&Meth.A592,297(2008).
photocathode;anIR-responsivephotocathodewouldprovidean
[8]P.J.T.LeonardandS.Tremaine,ApJ,547,228(1990).
even-more-efficientmethod.Todothis,onecoulduse,forexam- [9]C.S.Kochanek,ApJ,353,486(1990).
ple,socalled”wet”fusedsilica,whichhas∼1000ppmofOH- [10]M.C.Smithetal.,arXiv:astro-ph/0611671v2,2012.
contamination by design. Or, one could use simply pure water, [11]R.Bernabeietal.,JINST7,03009(2012).
[12]K.A.Kudinetal.,FunctionalMaterials18,No.2(2011).
and”tune”fortheOH-absorptionlines.Thisavenueispresently
[13]S.ProfumoandF.Queiroz,JCAP1405,038(2014).
not pursued in underground experiments because of high sin-
[14] J.Va’vra, A New Possible Way to Explain DAMA Results,
gle photo-electron noise. It could be considered in accelerator- arXiv:1401.0698v1,2014.
triggeredbeamdumpexperimentssearchingfordarkmatterpro- [15]G.D.Macketal.,Phys.Rev.Lett.112,041302(2014).
duction.Pilotstudiesofthisideaareinprogress. [16]W.L.Hansenetal.,IEEETrans.onNucl.Sci.,Vol.NS-29,No.1,1982.
[17] A. Erb and J-C. Lanfranchi, The Royal Society of Chemistry,
CrystEngComm,15,2301(2013).
[18]Q.Lietal.,HindawiPubl.Co.,JournalofChemistry,ArticleID952954
7. Conclusion (2013).
[19]R.Agneseetal.,Phys.Rev.Lett.112,041302(2014).
[20]G.Angloheretal.,Eur.Phys.J.C72,1971(2012).
ThispapersuggeststhatthemeasuredoscillationintheDAMA
[21]R.CatenaandP.Ullio,JCAP1205,005(2012).
experimentmaybecausedbyscatteringofalightmassWIMP
[22]M.Beltranetal.,JHEP1009,037(2010).
(mass between ∼1 and a few GeV/c2) on a hydrogen nucleus, [23]ATLAScollaboration,
present as a consequence of H-contamination in the NaI(Tl) https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-
crystals. CONF-2011-096.
[24]CMSCollaboration,CMSPASEXO-12-048,2013.
ForourchoiceofparametersfortheH-contaminationmodel,
[25] J.Va’vra, Molecular excitations: a new way to detect Dark matter,
and taking into account the DAMA modulation peak rate of arXiv:1402.0466v1,2014.
∼0.01cpd/kg/keV,theobservedbehaviorcanbeexplainedwith
aWIMP-protonscatteringcrosssectionbetween10−33 cm2 and
10−32cm2(seeFig.7).
As the H-contamination may vary from crystal-to-crystal
in the DAMA experiment. Crystal-dependent rates may be ob-
served.Thisshouldbeinvestigated.
We suggest that the DAMA, CDMS, CoGeNT, and
CRESST-II collaborations perform an FTIR analysis on their
crystals in order to measure the level of H-contamination. This
willproveordisproveourclaimthatasingleWIMP-protonscat-
teringcrosssectioncanexplainallofthedata.
LXe or LAr experiments do not have hydrogen contamina-
tion, and therefore any DM signal detected by these methods
woulddirectlycontradictthemodelproposedinthispaper.
Whileitissomewhatpuzzlingthattheideapresentedinthis
paper requires a very small dark matter mass with a cross sec-
tionmanyordersofmagnitudelargerthanthatforaparticleon
themassscaleoftheWandZbosons,thereisnothingapriori
which, to our knowledge, prevents this from occurring, and so
wesuggestthattheideabetestedverycarefully.
8. Acknowledgements
I also would like to thank CDMS people for discussing issues
about the dark matter detection, especially Prof. B. Cabrera, S.
Yellin,P.Brink,R.Partridge,G.Godfrey,andM.Kelsey.Ialso
thank Farinaldo Da Silva Queiroz and Chris Kelso for discus-
sions regarding reconciliation of ideas of this paper and their
publication[13].CommentsofProf.C.Galbiatiencouragingto
investigate this problem carefully are also appreciated. I would
likethankProf.E.Nappiforshowinginterestintheidea,sharing
itwithProf.C.Broggini,andaskingverygoodquestionsabout
earlyversionofthepaper.IwouldliketothanksProf.E.V.Kolb
forprovidingseveralreferences,whichallowedmetoenterthe
up-to-datestatusofthecolliderWIMPsearches.
5