Kaluza-Klein Dark Matter and the Positron Excess(3)

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.3:ThepositronfractionfromannihilationofKKDMforseveralchoicesofpropagationparameters.ThesolidlinerepresentsthemodelwiththesamepropagationparametersasinFig.2.Thedashedlineisforamodelwithanenergylossratesmallerbyafactoroftwo.Themodelsrepresentedbydot-dashedanddottedlinesusethefullenergylossratebutdi usionconstantsthatare80%and50%stly,thespectrumwithbothhalfthedi usionconstantandhalftheenergylossratefallsalmostexactlyontopofthesolidline.Forallcases,mB(1)=300GeVandL=4kpcwereused.

stantwithastrongerenergydependence:K(Ee+)∝E0e+.6.

ThiswasalsousedinthedefaultsoftheDark-Susypackage[21].Alternatively,esalargerdi usionconstantwithaweakerenergydependence,K(Ee+)=4.2×1028(Ee+/1GeV)0.33cm2/s,andasmallerenergylossrateb(Ee+)=5×10 17(Ee+/1GeV)2GeV/s[9].Thenete ectofthesechoicesisaconsiderablyharderspec-trum,whichhelpstoexplainwhytheycould ndreason-able tstotheHEATdatausingsupersymmetricdarkmatterthatannihilateslargelytob¯b.Finally,Ref.[22]providesasetofGreen’sfunctionsforthepropagationofpositronswhile ttingseveralsourcesofastrophysicaldata.We ndthatthistechniquegivesaverysimilarspectrum.

FromFigs.2and3weseethatKKDMclearly tsthedataconsiderablybetterthanthebackground.Infact,forallofthevariationsoftheparametersthatwehaveconsidered,weconsistentlyfoundagood ttothedata,uptonormalization.InTableI,weshowtheχ2perdegreeoffreedomofthe ttothedataforseveralB(1)massesandpropagationmodels.ItisremarkablethatKKDMisableto tthespectralshapeoftheHEATobservationstobetterthanχ2=1.1perdegreeoffreedominallofthesecases.

TheannihilationcrosssectionofKKDMintofermions

inthelowvelocitylimitis σv =95g4

1/324πm2B(1)

[15].χ2/d.o.f.BFρ=0.3BFρ=0.8

m=300,K0=3.3,b0=1

10.1/12

66.7

9.4

m=500,K0=3.3,b0=1

9.4/12253.835.712.9/12

23.8

3.3

m=300,K0=2.6,b0=1

10.2/12

16.7

2.3

m=300,K0=1.7,b0=0.5m=400,K0=3.3,b0=0.5

9.8/12

56.3

7.9

m=400,K0=1.7,b0=1

10.1/12

33.4

4.7