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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:[email protected] 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 factor for proton recoils in the NaI(Tl) crystal, for two values 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 amplitude 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 contamination, 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