Kaluza-Klein Dark Matter and the Positron Excess(2)

The excess of cosmic positrons observed by the HEAT experiment may be the result of Kaluza-Klein dark matter annihilating in the galactic halo. Kaluza-Klein dark matter annihilates dominantly into charged leptons that yield a large number and hard spectrum

FIG.1:Thepositronspectrumfromgenericparticledarkmatterannihilations,priortopropagation,forselectedan-nihilationmodeswithmDM=300GeV.Solid,dot-dash,dottedanddashedlinescorrespondtothepositronspectrumperannihilationintoµ+µ ,τ+τ ,b¯bandgaugebosons,re-spectively.Chargedlepton nalstatesclearlyproduceacon-siderablyharderspectrumofpositronsthaninothermodes.Thespectrumforannihilationintoe+e (notshown)istriv-iallyadeltafunctionatanenergyequaltothedarkmatterparticlemass.

FIG.2:ThepositronfractionfromannihilationofKKDMisshownasafunctionofpositronenergy.Thesolidanddashedlinesrepresent300and600GeVB(1)s,respec-tively.Theannihilationratewastreatedasafreeparam-eter,usedfornormalization.Thedottedlinerepresentsthebackgroundpredictedwithnocontributionfromdarkmatterannihilation.Theerrorbarsshownarefromthe1994-95and2000HEAT ights.Thepropagationparame-tersK(Ee+)=3.3×1028(Ee+/1GeV)0.47cm2/s,b(Ee+)=10 16(Ee+/1GeV)2GeV/sandL=4kpcwereused.

calculatedusing

PYTHIA[20]asitisimplementedintheDarkSusypackage[21].

Followingtheirproduction,positronstravelthroughthegalactichalounderthein uenceofinterstellarmag-netic eldsandloseenergyviainverseComptonandsynchrotronprocesses.Thee ectsofpropagationonthepositronspectrumcanbecalculatedusingastan-darddi usionmodel[7,22].Suchatechniqueislimited,however,bytheuncertaintiesintherelevantparameters,suchasthedi usionconstantandenergylossrate.

Cosmicraymeasurements(primarilytheborontocarbonratio)indicateadi usionconstantbest ttoK(Ee+)=3.3×1028(Ee+/1GeV)0.47cm2/s[23]with20to25%uncertaintiesatthe1σcon dencelevel.Forthepositronenergylossrate,onlyaroughestimateispos-sible,andthevalueofthisparametercouldvarywithlocation.Weuseavaluefortheenergylossrateofb(Ee+)=10 16(Ee+/1GeV)2GeV/s.Weconsidera2L=8kpcthickslabforthedi usionzone,whichisthewidthbest ttoobservations[23,24].Whilewehaveusedamodi edisothermalspherepro le,we ndthatotherpro lessuchasNFWproduceverysimilarresults.Thee ectofvaryingLisalsosmall.Thisisbecausepositrons,unlikegamma-raysandanti-protons,travelonlyafewkpcbeforelosingtheirenergy.Forfurtherdis-cussionoftwo-zonedi usionmodels,seeRefs.[7,24,25].Tominimizethee ectsofsolarmodulation,the

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spectrumofcosmicpositronsisgenerallyshownasa“positronfraction”,ortheratioofpositronstopositronspluselectronsatagivenenergy.Weconvertourpositron uxtoapositronfractionbyusingthespectrumofsec-ondarypositrons,secondaryelectronsandprimaryelec-tronsfoundinRef.[4].This ux(withoutadarkmattercontribution)constitutesthebackgroundtoapotentialsignal.

ThepositronfractionpredictedfromKKDMannihila-tionisshownasafunctionofpositronenergyinFig.2.Thelevel-oneKKspectrumwasassumedtobealmostdegeneratealthoughwefoundonlyveryslightvariationforaspectrumincludingthee ectsofradiativecorrec-tions[13].Comparingourresultstothemeasurementsofthe1994-95and2000HEAT ights,itisclearthatabove7-8GeVthebackground-onlycurvefailstomatchthedatawhileKKDMannihilationcanprovideareasonablygood ttothedata.

Withsubstantialuncertaintiesinthepropagationpa-rameters,itisimportanttoconsiderthee ectofvaryingthesequantitiesonthepositronspectrum.InFig.3,weshowthepositronfractionformB(1)=300GeVwithvariouschoicesofthedi usionconstantandenergylossrate.

Tocompareourpropagationmodelandparameterswiththoseusedinotherstudies,weremarkontwoothercollaborations’treatmentofthisproblem.First,Edsj¨oandBaltz[7]usedaconsiderablylowerdi usioncon-