All-flavour search for neutrinos from dark matter annihilations in the Milky Way with IceCube ...

14 Pages·2016·1.33 MB·English

Eur.Phys.J.C (2016) 76:531
DOI10.1140/epjc/s10052-016-4375-3
RegularArticle-ExperimentalPhysics
All-flavour search for neutrinos from dark matter annihilations
in the Milky Way with IceCube/DeepCore
IceCubeCollaboration
M.G.Aartsen2,K.Abraham35,M.Ackermann53,J.Adams16,J.A.Aguilar12,M.Ahlers30,M.Ahrens43,
D.Altmann24,K.Andeen32,T.Anderson49,I.Ansseau12,G.Anton24,M.Archinger31,C.Arguelles14,T.C.Arlen49,
J.Auffenberg1,S.Axani14,X.Bai41,S.W.Barwick27,V.Baum31,R.Bay7,J.J.Beatty18,19,J.BeckerTjus10,
K.-H.Becker52,S.BenZvi50,P.Berghaus34,D.Berley17,E.Bernardini53,A.Bernhard35,D.Z.Besson28,
G.Binder7,8,D.Bindig52,M.Bissok1,E.Blaufuss17,S.Blot53,D.J.Boersma51,C.Bohm43,M.Börner21,F.Bos10,
D.Bose45,S.Böser31,O.Botner51,J.Braun30,L.Brayeur13,H.-P.Bretz53,A.Burgman51,J.Casey5,M.Casier13,
E.Cheung17,D.Chirkin30,A.Christov25,K.Clark46,L.Classen36,S.Coenders35,G.H.Collin14,J.M.Conrad14,
D.F.Cowen48,49,A.H.CruzSilva53,J.Daughhetee5,J.C.Davis18,M.Day30,J.P.A.M.deAndré22,C.DeClercq13,
E.delPinoRosendo31,H.Dembinski37,S.DeRidder26,P.Desiati30,K.D.deVries13,G.deWasseige13,M.deWith9,
T.DeYoung22,J.C.Díaz-Vélez30,V.diLorenzo31,H.Dujmovic45,J.P.Dumm43,M.Dunkman49,B.Eberhardt31,
T.Ehrhardt31,B.Eichmann10,S.Euler51,P.A.Evenson37,S.Fahey30,A.R.Fazely6,J.Feintzeig30,J.Felde17,
K.Filimonov7,C.Finley43,S.Flis43,C.-C.Fösig31,A.Franckowiak53,T.Fuchs21,T.K.Gaisser37,R.Gaior15,
J.Gallagher29,L.Gerhardt7,8,K.Ghorbani30,W.Giang23,L.Gladstone30,M.Glagla1,T.Glüsenkamp53,
A.Goldschmidt8,G.Golup13,J.G.Gonzalez37,D.Góra53,D.Grant23,Z.Griffith30,C.Haack1,A.HajIsmail26,
A.Hallgren51,F.Halzen30,E.Hansen20,B.Hansmann1,T.Hansmann1,K.Hanson30,D.Hebecker9,D.Heereman12,
K.Helbing52,R.Hellauer17,S.Hickford52,J.Hignight22,G.C.Hill2,K.D.Hoffman17,R.Hoffmann52,
K.Holzapfel35,A.Homeier11,K.Hoshina30,b,F.Huang49,M.Huber35,W.Huelsnitz17,K.Hultqvist43,S.In45,
A.Ishihara15,E.Jacobi53,G.S.Japaridze4,M.Jeong45,K.Jero30,B.J.P.Jones14,M.Jurkovic35,A.Kappes36,
T.Karg53,A.Karle30,U.Katz24,M.Kauer30,38,A.Keivani49,J.L.Kelley30,J.Kemp1,A.Kheirandish30,
M.Kim45,T.Kintscher53,J.Kiryluk44,T.Kittler24,S.R.Klein7,8,G.Kohnen33,R.Koirala37,H.Kolanoski9,
R.Konietz1,L.Köpke31,C.Kopper23,S.Kopper52,D.J.Koskinen20,M.Kowalski9,53,K.Krings35,M.Kroll10,
G.Krückl31,C.Krüger30,J.Kunnen13,S.Kunwar53,N.Kurahashi40,T.Kuwabara15,M.Labare26,
J.L.Lanfranchi49,M.J.Larson20,D.Lennarz22,M.Lesiak-Bzdak44,M.Leuermann1,J.Leuner1,L.Lu15,
J.Lünemann13,J.Madsen42,G.Maggi13,K.B.M.Mahn22,S.Mancina30,M.Mandelartz10,R.Maruyama38,
K.Mase15,R.Maunu17,F.McNally30,K.Meagher12,M.Medici20,M.Meier21,A.Meli26,T.Menne21,G.Merino30,
T.Meures12,S.Miarecki7,8,E.Middell53,L.Mohrmann53,T.Montaruli25,M.Moulai14,R.Nahnhauer53,
U.Naumann52,G.Neer22,H.Niederhausen44,S.C.Nowicki23,D.R.Nygren8,A.ObertackePollmann52,A.Olivas17,
A.Omairat52,A.O’Murchadha12,T.Palczewski47,H.Pandya37,D.V.Pankova49,Ö.Penek1,J.A.Pepper47,
C.PérezdelosHeros51,a ,C.Pfendner18,D.Pieloth21,E.Pinat12,J.Posselt52,P.B.Price7,G.T.Przybylski8,
M.Quinnan49,C.Raab12,L.Rädel1,M.Rameez25,K.Rawlins3,R.Reimann1,M.Relich15,E.Resconi35,
W.Rhode21,M.Richman40,B.Riedel23,S.Robertson2,M.Rongen1,C.Rott45,T.Ruhe21,D.Ryckbosch26,
D.Rysewyk22,L.Sabbatini30,S.E.SanchezHerrera23,A.Sandrock21,J.Sandroos31,S.Sarkar20,39,K.Satalecka53,
M.Schimp1,P.Schlunder21,T.Schmidt17,S.Schoenen1,S.Schöneberg10,A.Schönwald53,L.Schumacher1,
D.Seckel37,S.Seunarine42,D.Soldin52,M.Song17,G.M.Spiczak42,C.Spiering53,M.Stahlberg1,M.Stamatikos18,c,
T.Stanev37,A.Stasik53,A.Steuer31,T.Stezelberger8,R.G.Stokstad8,A.Stößl53,R.Ström51,N.L.Strotjohann53,
G.W.Sullivan17,M.Sutherland18,H.Taavola51,I.Taboada5,J.Tatar7,8,F.Tenholt10,S.Ter-Antonyan6,
A.Terliuk53,G.Tešic´49,S.Tilav37,P.A.Toale47,M.N.Tobin30,S.Toscano13,D.Tosi30,M.Tselengidou24,
A.Turcati35,E.Unger51,M.Usner53,S.Vallecorsa25,J.Vandenbroucke30,N.vanEijndhoven13,S.Vanheule26,
M.vanRossem30,J.vanSanten53,J.Veenkamp35,M.Vehring1,M.Voge11,M.Vraeghe26,C.Walck43,A.Wallace2,
M.Wallraff1,N.Wandkowsky30,Ch.Weaver23,C.Wendt30,S.Westerhoff30,B.J.Whelan2,S.Wickmann1,
K.Wiebe31,C.H.Wiebusch1,L.Wille30,D.R.Williams47,L.Wills40,H.Wissing17,M.Wolf43,T.R.Wood23,
E.Woolsey23,K.Woschnagg7,D.L.Xu30,X.W.Xu6,Y.Xu44,J.P.Yanez53,G.Yodh27,S.Yoshida15,M.Zoll43
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531 Page 2 of 14 Eur.Phys.J.C (2016) 76:531
1III.PhysikalischesInstitut,RWTHAachenUniversity,52056Aachen,Germany
2DepartmentofPhysics,UniversityofAdelaide,Adelaide5005,Australia
3DepartmentofPhysicsandAstronomy,UniversityofAlaskaAnchorage,3211ProvidenceDr.,Anchorage,AK 99508,USA
4CTSPS,Clark-AtlantaUniversity,Atlanta,GA 30314,USA
5SchoolofPhysicsandCenterforRelativisticAstrophysics,GeorgiaInstituteofTechnology,Atlanta,GA30332,USA
6DepartmentofPhysics,SouthernUniversity,BatonRouge,LA70813,USA
7DepartmentofPhysics,UniversityofCalifornia,Berkeley,CA94720,USA
8LawrenceBerkeleyNationalLaboratory,Berkeley,CA94720,USA
9InstitutfürPhysik,Humboldt-UniversitätzuBerlin,12489Berlin,Germany
10FakultätfürPhysikandAstronomie,Ruhr-UniversitätBochum,44780Bochum,Germany
11PhysikalischesInstitut,UniversitätBonn,Nussallee12,53115Bonn,Germany
12ScienceFacultyCP230,UniversitéLibredeBruxelles,1050Brussels,Belgium
13DienstELEM,VrijeUniversiteitBrussel,1050Brussels,Belgium
14DepartmentofPhysics,MassachusettsInstituteofTechnology,Cambridge,MA02139,USA
15DepartmentofPhysics,ChibaUniversity,Chiba263-8522,Japan
16DepartmentofPhysicsandAstronomy,UniversityofCanterbury,PrivateBag4800,Christchurch,NewZealand
17DepartmentofPhysics,UniversityofMaryland,CollegePark,MD20742,USA
18DepartmentofPhysics,CenterforCosmologyandAstro-ParticlePhysics,OhioStateUniversity,Columbus,OH43210,USA
19DepartmentofAstronomy,OhioStateUniversity,Columbus,OH43210,USA
20NielsBohrInstitute,UniversityofCopenhagen,2100Copenhagen,Denmark
21DepartmentofPhysics,TUDortmundUniversity,44221Dortmund,Germany
22DepartmentofPhysicsandAstronomy,MichiganStateUniversity,EastLansing,MI48824,USA
23DepartmentofPhysics,UniversityofAlberta,Edmonton,ABT6G2E1,Canada
24ErlangenCentreforAstroparticlePhysics,Friedrich-Alexander-UniversitätErlangen-Nürnberg,91058Erlangen,Germany
25Départementdephysiquenucléaireetcorpusculaire,UniversitédeGenève,1211Geneva,Switzerland
26DepartmentofPhysicsandAstronomy,UniversityofGent,9000Gent,Belgium
27DepartmentofPhysicsandAstronomy,UniversityofCalifornia,Irvine,CA92697,USA
28DepartmentofPhysicsandAstronomy,UniversityofKansas,Lawrence,KS66045,USA
29DepartmentofAstronomy,UniversityofWisconsin,Madison,WI53706,USA
30DepartmentofPhysics,WisconsinIceCubeParticleAstrophysicsCenter,UniversityofWisconsin,Madison,WI53706,USA
31InstituteofPhysics,UniversityofMainz,StaudingerWeg7,55099Mainz,Germany
32DepartmentofPhysics,MarquetteUniversity,Milwaukee,WI53201,USA
33UniversitédeMons,7000Mons,Belgium
34MoscowEngineeringPhysicsInstitute(MEPhI),NationalResearchNuclearUniversity,Moscow,Russia
35Physik-department,TechnischeUniversitätMünchen,85748Garching,Germany
36InstitutfürKernphysik,WestfälischeWilhelms-UniversitätMünster,48149Münster,Germany
37DepartmentofPhysicsandAstronomy,BartolResearchInstitute,UniversityofDelaware,Newark,DE19716,USA
38DepartmentofPhysics,YaleUniversity,NewHaven,CT06520,USA
39DepartmentofPhysics,UniversityofOxford,1KebleRoad,OxfordOX13NP,UK
40DepartmentofPhysics,DrexelUniversity,3141ChestnutStreet,Philadelphia,PA19104,USA
41PhysicsDepartment,SouthDakotaSchoolofMinesandTechnology,RapidCity,SD57701,USA
42DepartmentofPhysics,UniversityofWisconsin,RiverFalls,WI54022,USA
43DepartmentofPhysics,OskarKleinCentre,StockholmUniversity,10691Stockholm,Sweden
44DepartmentofPhysicsandAstronomy,StonyBrookUniversity,StonyBrook,NY11794-3800,USA
45DepartmentofPhysics,SungkyunkwanUniversity,Suwon440-746,Korea
46DepartmentofPhysics,UniversityofToronto,Toronto,ONM5S1A7,Canada
47DepartmentofPhysicsandAstronomy,UniversityofAlabama,Tuscaloosa,AL35487,USA
48DepartmentofAstronomyandAstrophysics,PennsylvaniaStateUniversity,UniversityPark,PA16802,USA
49DepartmentofPhysics,PennsylvaniaStateUniversity,UniversityPark,PA16802,USA
50DepartmentofPhysicsandAstronomy,UniversityofRochester,Rochester,NY14627,USA
51DepartmentofPhysicsandAstronomy,UppsalaUniversity,Box516,75120Uppsala,Sweden
52DepartmentofPhysics,UniversityofWuppertal,42119Wuppertal,Germany
53DESY,15735Zeuthen,Germany
Received:2June2016/Accepted:15September2016
©TheAuthor(s)2016.ThisarticleispublishedwithopenaccessatSpringerlink.com
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Eur.Phys.J.C (2016) 76:531 Page 3 of 14 531
Abstract We present the first IceCube search for a sig- where(cid:2)σ v(cid:3)istheproductoftheself-annihilationcrosssec-
A
nal of dark matter annihilations in the Milky Way using tion,σ ,andtheWIMPvelocity,v,averagedoverthevelocity
A
all-flavourneutrino-inducedparticlecascades.Theanalysis distributionofWIMPSinthehalo,whichweassumetobe
focusesontheDeepCoresub-detectorofIceCube,anduses spherical, mχ is the WIMP mass, dNν/dE is the neutrino
thesurroundingIceCubestringsasavetoregioninorderto energyspectrumperannihilationandJ (ψ)istheintegralof
a
selectstartingeventsintheDeepCorevolume.Weuse329 thesquaredofthedarkmatterdensityalongthelineofsight.
live-daysofdatafromIceCubeoperatinginits86-stringcon- Therefore, searches for the dark matter annihilation signal
figuration during 2011–2012. No neutrino excess is found, in the Galactic halo can probe the WIMP self-annihilation
the final result being compatible with the background-only cross-section, given their spatial distribution. The expected
hypothesis.Fromthisnullresult,wederiveupperlimitson signalisparticularlysensitivetotheadopteddensityprofile
thevelocity-averagedself-annihilationcross-section,(cid:2)σ v(cid:3), of the dark matter halo, which determines the term J (ψ)
A a
fordarkmattercandidatemassesrangingfrom30GeVupto in Eq. (1), ψ being the angle between the direction to the
10TeV,assumingbothacuspyandaflat-coreddarkmatter Galactic Centre and thedirection of observation [5,6].The
haloprofile.Fordarkmattermassesbetween200GeVand densityprofileofdarkmatterhalosdeterminedbynumerical
10TeV,theresultsimproveonallpreviousIceCuberesults simulations of structure formation is still under debate [7–
on(cid:2)σ v(cid:3),reachingalevelof10−23 cm3 s−1,dependingon 12].Toexplicitlyquantifytheeffectofthechoiceofthehalo
A
the annihilation channel assumed, for a cusped NFW pro- profileontheresultsofouranalysis,weadopttwocommonly
file.Theanalysisdemonstratesthatall-flavoursearchesare usedmodels:theNavarro–Frenk–White(NFW)cuspedpro-
competitivewithmuonchannelsearchesdespitetheintrinsi- file[9],andtheBurkertcoredprofile[8,13].Weusetheval-
callyworseangularresolutionofcascadescomparedtomuon uesfortheparametersthatcharacterizeeachprofilefromthe
tracksinIceCube. MilkyWaymodelpresentedin[14].Thedifferencebetween
thetwoprofilesisrelevantonlywithintheSolarcircle,i.e.,
atradiilessthan 10kpc.
1 Introduction InthispaperweusedatafromtheIceCubeneutrinotele-
scopetosearchforhighenergyneutrinosfromtheGalactic
There is strong evidence for extended halos of dark matter Centre and halo that may originate from dark matter anni-
surroundingthevisiblecomponentofgalaxies.Independent hilations. There have been several studies triggered by the
indicationsoftheexistenceofdarkmatterarisefromgravi- observationofaelectronandpositronexcessinthecosmic
tationaleffectsatbothgalacticandgalaxy-clusterscales,as rayspectrum[15–17]whichfavourmodelsinwhichWIMPs
well as from the growth of primordial density fluctuations annihilate preferably to leptons [18–24]. We keep, though,
whichhavelefttheirimprintonthecosmicmicrowaveback- theanalysisagnosticintermsoftheunderlyingspecificpar-
ground [1]. The nature of the dark matter is, however, still ticlephysicsmodelthatcouldgiverisetoWIMPdarkmatter.
unknown.Themostcommonassumptionisthatdarkmatter Inthissenseitisagenericapproach,andourresultscanbe
iscomposedofstablerelicparticles,whosepresent-dayden- interpretedwithinanymodelthatpredictsaWIMP.
sity is determined by freeze-out from thermal equilibrium Weusedatacollectedin329.1live-daysofdetectoroper-
as the universe expands and cools [2–4]. We focus here on ation between May 2011 and March 2012. The analysis
afrequentlyconsideredcandidate–acosmologicallystable focuses on identifying particle cascades produced by neu-
massive particle having only weak interactions with bary- tralorchargedcurrentneutrinointeractionsoccurringinside
onic matter, namely a Weakly Interacting Massive Particle theDeepCoresub-arrayofIceCube,beingthussensitiveto
(WIMP). all flavours. The analysis does not explicitly try to remove
Withinthisparticledarkmatterparadigm,theMilkyWay muon tracks from charged current νμ interactions, but the
isexpectedtobeembeddedinahaloofWIMPs,whichcan eventselectionhasbeenoptimizedtoidentifyandselectthe
annihilateandproduceafluxofneutrinosdetectableatEarth. moresphericallightpatternproducedinthedetectorbypar-
Thedifferentialfluxdependsontheannihilationcrosssection ticleshowers.
oftheWIMPsas
ddφEν = (cid:2)σA2v(cid:3) 4π1m2χ Ja(ψ) ddNEν, (1) 2 TheIceCubeneutrinoobservatory
The IceCube Neutrino Observatory [25] is a neutrino tele-
ae-mail:[email protected] scope located about one kilometer from the geographical
bEarthquakeResearchInstitute,UniversityofTokyo,Bunkyo,Tokyo South Pole and consisting of an in-ice array and a surface
113-0032,Japan air shower array, IceTop [26]. The in-ice array utilizes one
cNASAGoddardSpaceFlightCenter,Greenbelt,MD20771,USA
cubic kilometer of deep ultra-clear glacial ice as its detec-
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ice detector is read out. The average rate of this trigger is
about260s−1.
3 Signalandbackgroundsimulations
In order to keep the analysis general we will assume that
WIMPs annihilate with 100 % branching ratio into a few
benchmark channels (bb¯, W+W−, νν¯, μ+μ− and τ+τ−)
and present results for these cases. Those channels effec-
tively bracket the final particle spectra of realistic models
with several final states. The neutrino spectra were calcu-
latedusingPYTHIA[28]byproducingaresonanceattwice
the mass under consideration and forcing it to decay to the
desiredchannel.Theprogramthentakescareofthefurther
hadronizationand/ordecaysinthestandardway.Weignore
the possible WIMP spin in this approach, which can effect
thefinalneutrinospectrum,mainlywhenconsideringanni-
+ −
hilationsthroughtheW W channel[29].Weassumethat
Fig. 1 Schematic overview of the IceCube string layout seen from
above.Gray-filledmarkersindicateIceCubestringsandblackmarkers the detected neutrinos have undergone full flavour mixing
indicatetheDeepCorestringswithdenserDOMspacing.AllIceCube giventheverylongoscillationbaselinefromthesource,so
stringsmarkedwithablackborderareincludedinthedefinitionofthe
thereareequalnumbersofthethreeflavours.Theexpected
extendedDeepCorevolumeusedintheanalysis
angulardistributionofsignaleventsintheskyisobtainedby
reweightingtheoriginallysimulatedisotropicdistributionby
J (ψ).
a
tormedium.Thisvolumeisinstrumentedwith5160Digital There are two backgrounds to any search for neutrinos
Optical Modules (DOMs) that register the Cherenkov pho- from the Galaxy: atmospheric neutrinos and atmospheric
tons emitted by the particles produced in neutrino interac- muons,bothproducedincosmic-rayinteractionsintheatmo-
tionsintheice.TheDOMsaredistributedon86stringsand sphere. To estimate the effect of these backgrounds on the
aredeployedbetween1.5kmand2.5kmbelowthesurface. analysis,asampleofatmosphericmuonswasgeneratedwith
Out of the 86 strings, 78 are placed in a triangular grid of the CORSIKA package [30] and a sample of atmospheric
125mside,evenlyspacedoverthevolume,andarereferred neutrinoswassimulatedwithGENIE[31]between10GeV
toasIceCubestrings.Theremaining8stringsarereferredto and 200 GeV, and with NUGEN [32] from 200 GeV up to
asDeepCorestrings.Theyareplacedinbetweenthecentral 109GeV,adoptingthespectrumin[33].However,theanaly-
IceCubestringswithatypicalinter-stringseparationof55m. sisdoesnotusebackgroundsimulationstodefinethecuts,but
TheyhaveadenserDOMspacingandphotomultipliertubes instead relies on azimuth-scrambled data. This reduces the
with higher quantum efficiency. These strings, along with systematicuncertaintiesandautomaticallyaccountsforany
some of the surrounding IceCube strings, form the Deep- unsimulateddetectorbehavior.Thebackgroundsimulations
Core low-energy sub-array [27]. In the analysis described were used to verify the overall validity of the analysis and
below,anextendeddefinitionofDeepCorewasused,which theperformanceofthedifferentcutlevels.Sincethemajor-
includesonemorelayerofthesurroundingIceCubestrings, ityoftriggersinIceCubeareduetoatmosphericmuons,the
leavinga3-stringwidevetovolumesurroundingthefiducial distributionsofthevariablesusedintheanalysismustagree
volume used, see Fig. 1. While the original IceCube array betweendataandtheCORSIKAsimulationatearlyselection
hasaneutrinoenergythresholdofabout100GeV,theaddi- levels,whileathigherselectionlevelsthedatashouldshow
tionofthedenserinfilllowerstheenergythresholdtoabout asignificantfractionofatmosphericneutrinos.Atmospheric
10GeV. muonsandparticlesresultingfromneutrinointeractionsinor
TheanalysispresentedinthispaperusesaspecificDeep- nearthedetectorarepropagatedthroughthedetectorvolume
Core trigger, which requires that at least three hits are reg- and their Cherenkov light emission simulated. Cherenkov
isteredwithin2.5µsofeachotherinthenearestornext-to- photonsarethenpropagatedthroughtheiceusingthe PPC
nearestneighboringDOMsintheDeepCoresub-array.When package [34], and the response of the detector calculated.
thisconditionisfulfilled,thetriggeropensa±6µsreadout From this point onwards, simulations and data are treated
windowcenteredaroundthetriggertime,wherethefullin- identicallythroughfurtherfilteringanddatacleaning.
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Eur.Phys.J.C (2016) 76:531 Page 5 of 14 531
4 Dataselection fromthefirstguessreconstructions,areapplied.Thesecuts
bring the experimental data rate down by a factor of about
Thetriggereddataarefirstcleanedofpotentialnoisehitsthat 3000withrespecttotriggerlevel,whilekeepingabout50%
couldeffecttheperformanceofthetrackandcascaderecon- ofthesignal,dependingontheWIMPmassandannihilation
struction algorithms. Hits that lie outside a predetermined channelconsidered.
time window around the trigger time or which do not have At this point three sophisticated likelihood-based recon-
another causally connected hit within a predefined radius, structionsareappliedonalltheremainingevents.Thelikeli-
are removed. The data is then filtered by a fast algorithm hoodreconstructionsaimatdeterminingasetofparameters
thatselectseventsstartingintheDeepCorefiducialvolume, a = (x ,t ,ξ,E ) given a set of measured data points d
0 0 0 i
inordertoremoveeventstriggeredbythrough-goingatmo- (e.g. time and spatial coordinates of every hit in an event).
sphericmuons.TheIceCubestringssurroundingDeepCore Here x isanarbitrarypointalongthetrack,t istheevent
0 0
areusedasavetoforincomingtracks.Thealgorithmselects timeatpositionx ,ξ isthedirectionoftheincomingparti-
0
eventswiththe“amplitude-weighted”centreofgravityofall cleand E isthedepositedenergyoftheevent.Therecon-
0
hitsinsidetheDeepCorevolume,1andnomorethanonehit structionsattempttofindthevalueofa thatmaximizesthe
inthesurroundingIceCubestringscausallyconnectedwith likelihoodfunction,whichisbasedontheProbabilityDen-
thatpoint.Thisfilterreducesthepassingeventratebynearly sityFunction(PDF)ofmeasuringthedatapointd giventhe
i
afactorof10. set of parameters a. For a cascade reconstruction there are
Theeventsampleisfurtherreducedbyrequiringamini- sevendegreesoffreedom,whileaninfinitetrackreconstruc-
mumnumberofeighthitsintheeventdistributedinatleast tionhasonlysixsincethepointx canbechosenarbitrarily
0
four strings. This ensures that the remaining events can be alongthetrack.Thefirstreconstructionisbasedonaninfi-
wellreconstructed.Theeventsarethenprocessedthrougha nitetrackhypothesis,fittingonlydirection,notenergy.The
seriesofreconstructionsaimedatdeterminingtheirtype(cas- secondreconstructionusesacascadehypothesis,anditfits
cadeortrack),arrivaldirectionandenergy.Inafirststage,two forthevertexposition,directionandenergyofthecascade.
first-guessreconstructionsareapplied;fitsforatrackhypoth- Thesetworeconstructionsuseananalyticapproximationfor
esisandforacascadehypothesisareperformedinorderto theexpectedhittimesintheDOMsgivenatrackorcascade
obtainaquickcharacterizationoftheeventsandperforma hypothesis[36],ratherthanafulldescriptionoftheoptical
firsteventselection.Thesefitsarebasedonthepositionand propertiesoftheice.Sincethefocusofthisanalysisistoiden-
timeofthehitsinthedetector,butdonotincludeinformation tifycascades,anadditional,moreadvanced,cascaderecon-
about the optical properties of the ice, in order to speed up structionisalsoperformed,usingthepreviousoneasaseed.
thecomputation.Thetrackhypothesisperformsaχ2fitofa Thissecondcascadereconstructionusesthefulldescription
straightlinetothehitpatternoftheevent,returningavertex oftheopticalpropertiesoftheAntarcticice,aswellasinfor-
andavelocity[35].Thecascadehypothesisisbasedondeter- mationofthepositionofnon-hitDOMsthroughatermadded
miningtheamplitude-weightedcentreofgravityofthehits totheenergylikelihood.Thethreelikelihoodreconstructions
intheeventanditsassociatedtime.Thealgorithmcalculates returnthebestfitvaluesofthevariablesofthevectorathey
thethreeprincipalaxesoftheellipsoidspannedbythespacial fitfor,aswellasalikelihoodvalueoftheirrespectivehypoth-
distributionofhits,andthelongestprincipalaxisisselected esis,whichisusedinafurtherselectionofeventsusinglinear
todeterminethegenericdirectionoftheevent.Sincethespe- cuts.
cificincomingdirectionalongtheselectedaxisisambiguous, ThefinalselectionofeventsusesBoostedDecisionTrees
thehittimesareprojectedontothisaxis,fromlatesttoearli- (BDT)[37]toclassifyeventsassignal-likeorbackground-
est,tocharacterizethetime-developmentofthetracksothat like.TwoBDTsweretrainedusingdataasbackgroundand
itpointstowardswheretheincidentparticleoriginated.The a different benchmark reference signal each. One of the
tensorofinertiareconstructionisgenerallyonlysuitableas BDTs (BDT ) was trained using the neutrino spectrum
LE
¯
a first guess of the direction for track-like events, since for froma100GeVWIMPannihilatingintobb,whiletheother,
cascade-like events the three principal axes of the ellipsoid BDT ,wastrainedontheneutrinospectrumofa300GeV
HE
+ −
will be close to equal in size. This property, however, can WIMP annihilating into W W . These two spectra were
beusedtodiscriminatebetweentracksandcascades.Addi- chosentorepresentasoftandhardneutrinospectrumrespec-
tionally,aseriesofcutsbasedonvariablesderivedfromthe tively,sothesensitivityoftheanalysistootherWIMPmasses
geometricaldistributionofhits,aswellasfrominformation and/orannihilationchannelswithsimilarspectracanbeeval-
uated with the same cuts on the BDT output scores. This
removestheneedtotrainadifferentBDTspecificallyforeach
1 Theam(cid:2)plitude-(cid:2)weightedcentreofgravityofaneventisdefinedas mass and annihilation channel. Since no variables depend-
rCOG= airi/ ai,whereai andri aretheamplitudeandposition
ingonthearrivaldirectionoftheeventsareusedintheBDT
of the ith hit. The sum runs over all the hits in the event (after hit
cleaning).
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¯
Fig. 2 ThescoredistributionfortheBDTtrainedonthebb100GeV eachsignalchanneltheBDTwastrainedforisalsoshown(greylines),
signalchannel(left)andfortheBDTtrainedontheW+W−300GeV normalizedtotheexperimentaldatarate.Thefinalcutsonthescoreare
signalchannel(right).Theplotshowsthepassingeventrate(inHz) markedwithverticallines.Eventswerekeptifanyofthescoreswere
forsimulatedatmosphericmuons(blueline)andatmosphericneutrinos abovethecutvalues.Thelowerpanelineachplotshowstheratioof
(greenlines),aswellasforthesumofthesetwocomponents(totalMC, thedatapassingratetothetotalexpectedbackground
purpleline),comparedwiththedatapassingrate.Thepassingratefor
training, the event sample is kept blind with respect to the valuearereferredtoasthe“high-energy”(HE)sample.The
positionoftheGalacticCentreinthesky. remaining number of events in each sample is 5892 events
Seven variables that showed a good separation power in the LE sample and 2178 events in the HE sample. The
between signal and background, selected among an initial overlap between the two samples (events which have both
largersetofvariablesthatweretried,wereusedtotrainthe BDT scores above the respective cut values) is 664 events.
¯
BDTs.Thevariablesarebasedonthedifferentgeometrical The final BDT score distributions for the 100 GeV bb and
+
patternsthattracksandcascadesleaveinthedetector,aswell the300GeVW W channelsarepresentedinFig.2,withthe
as on their different time development. The whole data set vertical lines marking the optimal cut values used to select
wasclassifiedbythetwoBDTssoeacheventwasassigned thefinaleventsample.
twoBDTscores.Inordertodecideonthebestcutvalueon After the BDT classification, the data has been reduced
eachBDToutput,therangeofBDTscorevalueswasscanned byafactorofabout1(3)×106 fortheLE(HE)sample,but
andthesensitivityoftheanalysiswascalculatedforeachof still contains about 20 % of atmospheric muon contamina-
them. The scores producing the best sensitivity for each of tion. The remaining signal in the two benchmark scenarios
the two signal channels for which the BDTs were trained consideredamountstoabout6%(8%)respectively.Asum-
were selected. Events with a BDT score above the opti- maryoftheeventselectionrates,aswellassignalefficiency,
LE
malvaluearereferredtoasthe“low-energy”(LE)sample, isgiveninTable1.Theeffectiveareaforthetwoeventselec-
andeventswithaBDT scoreabovethecorrespondingcut tions,ameasureofhowefficientthedetectorisforthepresent
HE
Table1 Dataratesatdifferentcutlevels.Forthetwobenchmarksignalchannels,100GeVbb¯and300GeVW+W−,valuesaregivenaspercentage
ofsignalretentionrelativetotheDeepCoreandevent-qualityfilterlevel.Thelivetimeoftheexperimentaldatasetis329.1days
Exp.data(s−1) Atmµ(s−1) Atm.νe(s−1) Atm.νμ(s−1) Totalatm.ν 100GeVbb¯ 300GeVW+W−
(s−1) (%) (%)
Trigger ∼260
DeepCoreand ∼18 ∼17 100 100
event-quality
filter
Pre-BDTlinear 8.07×10−2 8.89×10−2 2.11×10−4 1.12×10−3 1.33×10−3 51.0 46.0
cuts
BDTLE 2.06×10−4 4×10−5 2.58×10−5 7.74×10−5 1.03×10−4 7.78 2.85
BDTHE 7.61×10−5 2×10−5 1.02×10−5 2.56×10−5 3.58×10−5 0.77 5.84
123
Eur.Phys.J.C (2016) 76:531 Page 7 of 14 531
Fig. 3 LeftAll-flavourneutrinoeffectiveareaasafunctionofenergy (basedonthespaceanglebetweenthereconstructedandtruedirection
for the two event selections of the analysis, the low-energy (LE) ofincomingneutrinos)atfinalanalysislevel
andhigh-energy(HE)selections.RightCumulativeangularresolution
Table2 Summaryofsystematicuncertaintiesforboththelow-energy(LE)andhigh-energy(HE)eventselectionspresentedforbothhaloprofiles
usedintheanalysis.Thetotalisthequadraticsumofeachindividualcontribution
Burkertprofile NFWprofile
LEselection(%) HEselection(%) LEselection(%) HEselection(%)
Iceopticalproperties 8 8 12 12
Holeiceopticalproperties 24 15 24 10
DOMefficiency 17 10 35 12
Noisemodel 10 5 8 10
Detectorcalibration <5 <5 <5 <5
Analysis 2 2 2 2
Total 34 21 45 23
analysis, is shown in the left plot of Fig. 3. The right plot IceCubehasbeenderived[38].Theeffectontheuncertainty
in the same figure shows the cumulative angular resolution oftheestimatedabsorptionandscatteringlengthwasinvesti-
(spaceanglebetweenthereconstructedandtruedirectionof gatedbyvaryingthebaselinesettingsby±10%individually.
theincomingneutrino)forthetwobenchmarkchannelsused Their contribution to the uncertainty on the sensitivity lies
intrainingtheBDTs. in the range 8 %–12 %. Furthermore, there are indications
thattheholeicecontainsresidualairbubblesthatresultina
shorterscatteringlengthinthisicecomparedtotheancient
5 Systematicuncertainties glacial bulk ice surrounding it. In the baseline simulation
datasetsthescatteringlengthoftheholeiceissetto50cm.
In order to estimate the effect of experimental systematic Varying this parameter between 30 cm and 100 cm yields
uncertaintiesonthefinalsensitivity,MonteCarlosimulation a 10 %–24 % change on the sensitivity. Recently, a more
studies were done, where the parameters defining a given detailed modeling of the bulk ice has been developed [39].
input were varied within their estimated uncertainty. The Itincludesanisotropicscatteringandaccountsforthetiltof
mainsourceofsystematicuncertaintiesisthelimitedknowl- thedifferenticelayersacrosstheIceCubevolume.Prelimi-
edge of the optical properties of the ice, both the bulk ice narystudiesindicatethattheeffectonthesensitivityofthis
between1450mand2500m,aswellasthe“holeice”,i.e. modelisnegligibleforhigh-energyevents,butitcanbesiz-
theicethatformsasthewaterintheholedrilledforthestring ableforthelowest-energyevents,reducingthesensitivityfor
deploymentrefreezes.Thescatteringandabsorptioncoeffi- lowWIMPmassesupto25%.Theseeffectshavenotbeen
cientsoftheiceasafunctionofdepthhavebeendetermined includedinthisanalysis.
byin-situflashmeasurements,andastandard“icemodel”for
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Fig. 4 ExampleofthespaceanglePDFforoneofthesignalchannels PDF,thescrambleddata, fsd(ψ),andthescrambledsignal, fss(ψ),are
considered(χχ →bb¯)andtwohaloprofiles,theBurkertprofile(left) shown as the gray shaded area and the thin black line, respectively.
and the NFW profile (right). In each plot the signal PDF, fS(ψ), is Theangleψ representstheangulardistancebetweenthedirectionof
shownasathickblackline,andthetwocomponentsofthebackground reconstructedtracksandthelocationoftheGalacticCenter
Fig. 5 Distributionsoftheψ
anglesofthefinalevent
samples.Thebincontentsare
directlyproportionaltothe
numberofobservedevents,to
whichwechoosenottoassign
anystatisticaluncertainty.Left
theLowEnergy(LE)sample,
whichcontains5892observed
events.RighttheHighEnergy
(HE)sample,whichcontains
2178observedevents
The overall efficiency of the process of converting the 6 Analysismethod
Cherenkov light into a detectable electrical signal by the
DOMisanothersourceofuncertainty.Thiseffectwasinves- Weusethedistributionofthespaceangleψ betweenevent
tigatedbychangingtheDOMefficiencyinthesignalsimu- directionsandtheGalacticCentretoconstructalikelihood
lationby±10%,accordingtomeasurementsoftheperfor- function and test the signal hypothesis (excess of events at
manceoftheDOMsinlaboratorytestsbeforedeployment, smallψ values)againstthebackground-onlyhypothesis(an
aswellasinin-situcalibrationmeasurementsafterdeploy- eventdistributionisotropicinthesky).Thesignalandback-
ment.Thisuncertaintytranslatesintoanuncertaintyonthe ground hypotheses are represented by probability density
final sensitivity of 10 %–35 %, depending on event selec- functionsoftheψ distributions,
tion.Theeffectisstrongerforlow-energyeventsthatcanfall
(cid:3) (cid:4)
under the detector threshold if less light is being captured. μ μ
f(ψ |μ)= f (ψ)+ 1− f (ψ |μ), (2)
Additional, but minor, effects arise from the implementa- S B
n n
obs obs
tionofthephotomultiplierdarknoiseinthesimulation,the
timing and geometry calibration of the detector and from
wherethesubscriptsSandBdenotesignalandbackground
theintrinsicrandomnessofseveralstepsoftheanalysis,like
respectively and μ is the number of signal events present
time-scramblingofthedataorthemanypseudo-experiments
amongthetotalnumberofobservedevents,n .Theangle
obs
performedtocalculatethesensitivity. ψ is allowed to be in the full range [0◦, 180◦], therefore
All systematic uncertainties considered are summarized
covering the full sky, as shown in Fig. 4. This allows the
inTable2togetherwiththetotal(quadraticsum)forthelow
analysis to be sensitive to the whole halo instead of just to
and high-energy selections for both halo profiles. In order
theGalacticCentre.However,ifthesignalisallowedtocome
to be conservative, the limits presented in Sect. 6 for each
fromanywhereinthehalo,thebackgrounddistribution,taken
WIMPmass and annihilation channel wererescaled by the
fromdata,isnecessarilycontaminatedbyapotentialsignal:
correspondingtotalsystematicuncertaintyshowninTable2.
therebythedependenceof f (ψ | μ)onμandnotonlyon
B
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Eur.Phys.J.C (2016) 76:531 Page 9 of 14 531
ψ.Inparticularthebackgrounddistributionisconstructedas available statistics at final level in the case of direct anni-
(cid:3) (cid:4)
μ μ hilationof700GeVWIMPstoneutrinosusingtheBurkert
fB(ψ |μ)= fss(ψ)+ 1− fsd(ψ), (3) profile were not sufficient to define an angular distribution
n n
obs obs
which was smooth enough to perform the shape analysis,
where fssand fsdarethePDFofthescrambledarrivaldirec- sowechoosenottoquoteresultsforthismassandchannel
tionsofsignalsimulationanddataeventsrespectively. inTable6.Figures6and7showtheresultsgraphicallyfor
The likelihood that the data sample contains μ signal theNFWandBurkertdarkmatterprofilesrespectively.The
eventsisdefinedas plotsshowthe90%C.L.upperlimits(solidblackline)on
n(cid:5)obs thevelocity-averagedWIMPself-annihilationcrosssection,
L(μ)= f(ψi |μ). (4) (cid:2)σ v(cid:3),togetherwiththecorrespondingsensitivities(dashed
A
i=1 black line) and the 1σ (green) and 2σ (yellow) statistical
where n is the number of observed events and f(ψ | uncertainties.
obs i
μ) is given in Eq. (2). We follow the method described Inordertoputtheresultsofthisanalysisinperspective,
in [40] to calculate a 90 % confidence level upper limit Fig. 8 shows a comparison with results from previous Ice-
on μ, μ , which gives an upper limit on the flux of Cubeanalysesandotherexperiments,fortheττ annihilation
90
neutrinos from the halo as defined in Eq. (1). This limit channel and the NFW profile. Also shown is the allowed
can, in turn, be translated into a limit on (cid:2)σAv(cid:3) for any area in the ((cid:2)σAv(cid:3), mχ) parameter space if the e+ + e−
given WIMP mass, annihilation channel and halo profile. flux excess seen by Fermi-LAT and H.E.S.S. and the
The final limits are shown in the next section, for the positronexcessseenbyPAMELAareinterpretedasoriginat-
event selection that showed the best sensitivity in each ing from dark matter annihilations [41]. There exist, how-
case. ever, conventional explanations based on local astrophysi-
calsources[42,43]that,alongwithcurrentlimitson(cid:2)σ v(cid:3),
A
disfavoursuchexplanation.Thefigureshowsthattheanal-
7 Resultsandconclusion ysis presented in this paper improves on previous IceCube
analyses [44–47] for WIMP masses above about 200 GeV,
At final selection level, a total of 5892 (2178) events were as well as on the ANTARES [48] result for WIMP masses
observed in the full sky for the low-energy (high-energy) below∼1TeV.Thisdemonstratesthatparticlecascadescan
samples respectively. Figure 5 shows the angular distribu- be reconstructed with a good enough angular resolution in
tion of the two event samples at final cut level. The distri- IceCubetomakethischannelcompetitiveinsearchesfordark
butions are compatible with 0 signal events for all WIMP matter signals with neutrinos from the Galactic Centre and
massesandannihilationchannelstested.Tables3,4,5and6 halo.EvenifCherenkovtelescopesandgamma-raysatellites
show the results for the best fit on the number of signal canreachstricterboundson(cid:2)σ v(cid:3)duetotheirbetterangular
A
events,μˆ,togetherwiththe90%upperlimitsonthenum- resolutionand,dependingonthesourceunderconsideration,
ber of signal events, μ , and the corresponding limit on lowbackground,thereisamuch-neededcomplementarityin
90
the thermally-averaged WIMP annihilation cross section, thefieldofdarkmattersearches,whereneutrinotelescopes
(cid:2)σ v(cid:3) .Correspondingquantitieswithatildedenotemedian canplayavaluablerole.
A 90
upperlimits(i.e.,sensitivities).Eachtablecorrespondstoa
given benchmark annihilation channel and it shows differ-
entWIMPmassesforthetwo halomodelsconsidered.The
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Table3 Summarytableoftheresultsfortheχχ → bb¯annihilation μ90 and(cid:2)σAv(cid:3)90 alongwiththeircorrespondingsensitivitiesμ˜90 and
channelforboththeBurkertandNFWhaloprofiles.Thebestfitforthe (cid:2)(cid:2)σAv(cid:3)90.Thevaluesforeachmassarepresentedfortheeventstream
numberofsignaleventsμˆ ispresentedtogetherwiththeupperlimits (LEorHE)withthebestsensitivity
Mass Selection Burkertprofile NFWprofile
(GeV) (LE/HE)
μˆ (#) μ90(#) μ˜90(#) (cid:2)σAv(cid:3)90 (cid:2)(cid:2)σAv(cid:3)90 μˆ (#) μ90(#) μ˜90(#) (cid:2)σAv(cid:3)90 (cid:2)(cid:2)σAv(cid:3)90
(cm3s−1) (cm3s−1) (cm3s−1) (cm3s−1)
30 LE 119 697 540 5.34×10−21 4.14×10−21 125 521 343 2.29×10−21 1.50×10−21
65 LE 118 652 498 2.99×10−21 2.28×10−21 102 446 300 1.05×10−21 7.09×10−22
100 LE 118 630 472 2.67×10−21 2.00×10−21 97.2 418 277 8.61×10−22 5.72×10−22
130 LE 118 614 458 2.59×10−21 1.92×10−21 93.8 401 265 8.14×10−22 5.39×10−22
200 LE 118 593 435 2.64×10−21 1.94×10−21 87.5 373 246 7.94×10−22 5.23×10−22
300 LE 116 574 419 2.85×10−21 2.08×10−21 83.7 357 233 8.41×10−22 5.51×10−22
400 HE 31.3 205 169 2.34×10−21 1.93×10−21 21.7 106 78.7 6.02×10−22 4.46×10−22
500 HE 31.2 204 168 2.16×10−21 1.79×10−21 21.3 104 76.4 5.54×10−22 4.07×10−22
700 HE 31.2 201 165 1.97×10−21 1.60×10−21 20.8 101 74.3 4.90×10−22 3.61×10−22
1000 HE 31.2 200 165 1.80×10−21 1.48×10−21 20.6 99.6 72.9 4.47×10−22 3.28×10−22
2000 HE 30.5 199 164 1.64×10−21 1.35×10−21 20.4 98.0 71.6 4.16×10−22 3.05×10−22
3000 HE 30.7 199 163 1.64×10−21 1.34×10−21 19.5 95.6 70.2 4.08×10−22 3.00×10−22
5000 HE 30.7 198 162 1.73×10−21 1.41×10−21 18.4 92.7 68.8 4.20×10−22 3.12×10−22
7000 HE 30.8 197 161 1.83×10−21 1.51×10−21 17.8 91.1 67.8 4.45×10−22 3.30×10−22
10000 HE 31.1 196 160 2.03×10−21 1.66×10−21 17.3 89.1 66.1 4.85×10−22 3.60×10−22
Table4 Summarytableoftheresultsfortheχχ →τ+τ−annihilation μ90 and(cid:2)σAv(cid:3)90 alongwiththeircorrespondingsensitivitiesμ˜90 and
channelforboththeBurkertandNFWhaloprofiles.Thebestfitforthe (cid:2)(cid:2)σAv(cid:3)90.Thevaluesforeachmassarepresentedfortheeventstream
numberofsignaleventsμˆ ispresentedtogetherwiththeupperlimits (LEorHE)withthebestsensitivity
Mass Selection Burkertprofile NFWprofile
(GeV) (LE/HE)
μˆ (#) μ90(#) μ˜90(#) (cid:2)σAv(cid:3)90 (cid:2)(cid:2)σAv(cid:3)90 μˆ (#) μ90(#) μ˜90(#) (cid:2)σAv(cid:3)90 (cid:2)(cid:2)σAv(cid:3)90
(cm3s−1) (cm3s−1) (cm3s−1) (cm3s−1)
30 LE 118 651 494 2.67×10−22 2.03×10−22 96.1 443 305 9.61×10−23 6.62×10−23
65 LE 118 594 437 2.54×10−22 1.86×10−22 89.5 378 249 7.03×10−23 4.62×10−23
100 LE 116 554 402 2.80×10−22 2.03×10−22 78.3 334 219 7.77×10−23 5.08×10−23
130 HE 31.7 206 170 2.08×10−22 1.70×10−22 22.5 111 82.3 5.36×10−23 3.98×10−23
200 HE 31.0 206 170 1.65×10−22 1.36×10−22 21.2 105 77.7 4.40×10−23 3.25×10−23
300 HE 31.3 202 164 1.73×10−22 1.41×10−22 19.8 97.8 72.1 4.46×10−23 3.29×10−23
400 HE 31.6 200 163 1.69×10−22 1.37×10−22 19.5 95.3 69.9 3.83×10−23 2.81×10−23
500 HE 31.9 199 163 1.56×10−22 1.27×10−22 19.3 94.5 69.5 3.44×10−23 2.53×10−23
700 HE 29.8 199 164 1.41×10−22 1.17×10−22 20.3 97.0 70.8 3.43×10−23 2.50×10−23
1000 HE 29.7 198 164 1.39×10−22 1.15×10−22 20.3 95.8 69.5 3.55×10−23 2.58×10−23
2000 HE 31.9 200 163 1.50×10−22 1.22×10−22 17.0 90.0 67.4 3.59×10−23 2.69×10−23
3000 HE 31.2 197 161 1.70×10−22 1.39×10−22 16.4 87.7 65.7 4.10×10−23 3.07×10−23
5000 HE 32.6 195 158 2.19×10−22 1.76×10−22 16.2 84.3 62.4 5.15×10−23 3.81×10−23
7000 HE 32.2 193 155 2.74×10−22 2.21×10−22 14.9 80.7 60.1 6.16×10−23 4.58×10−23
10000 HE 31.7 191 153 3.76×10−22 3.02×10−22 14.5 80.1 60.0 8.57×10−23 6.43×10−23
123