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CMSSM Spectroscopy inlightofPAMELA and ATIC Ilia Gogoladze∗,† Rizwan Khalid,‡ Qaisar Shafi,§ and Hasan Yu¨ksel¶ Bartol Research Institute, Department of Physics and Astronomy University of Delaware, Newark, Delaware 19716 (Dated:January20,2008) Darkmatterneutralinosintheconstrainedminimal supersymmetricmodel (CMSSM)mayaccount forthe recentcosmicrayelectronandpositronobservations reportedbythePAMELAandATICexperimentseither through self annihilation or via decay. However, to achieve this, both scenarios require new physics beyond the‘standard’CMSSM,andaunifiedexplanationofthetwoexperimentssuggestsaneutralinomassoforder 700 GeV - 2 TeV. A relatively light neutralino with mass around 100 GeV (300 GeV) can accomodate the PAMELAbutnottheATICobservationsbasedonamodelofannihilating(decaying)neutralinos.Westudythe implicationsofthesescenariosforHiggsandsparticlespectroscopyintheCMSSMandhighlightsomebench- 9 markpoints. Anestimateofneutrinofluxexpectedfromtheannihilatinganddecayingneutralinoscenariosis 0 provided. 0 2 PACSnumbers:95.35.+d,98.62.Gq,98.70.Vc,95.85.Ry n a J I. INTRODUCTION energyanti-protonandpositronfluxes, andtheir mostrecent 0 publicationclaimsa significantpositron‘excess’[4] withno 2 Itisgenerallyacceptedthatnearly23%oftheuniverse’sen- correspondinganti-proton excess [5]. This result appears to confirmpreviousresultsfromHEAT[6]andAMS[7]within ergydensityresidesintheformofnon-luminous‘dark’mat- ] theerrorbars.Ithasbeenpointedoutthatpulsarsand/orother h ter [1]. This is a new form of matter which is non-baryonic p andmanifestsitselfprimarilythroughitsgravitationalinterac- nearby astrophysical sources may account for the PAMELA - tions. ThehighlysuccessfulStandardModel(SM)ofstrong, results[8,9]. Morerecently,theATICexperiment [10](see p alsoPPB-BETS[11])hasreportedanappreciablefluxofelec- weakandelectromagneticinteractionsdoesnotpossessavi- e tronsandpositronsatenergiesaround100–800GeV,which h abledarkmattercandidate.Thus,newphysicsbeyondtheSM [ isrequiredtoincorporatedarkmatter,andmanypotentialdark appears to be considerably higher than the expected back- mattercandidateshavebeenproposedintheliterature[2]. groundattheseenergies. 3 A unified explanation of the PAMELA and ATIC experi- v Supersymmetry, more precisely MSSM, (minimal super- mentsinvolvingneutralinoasthedarkmattercandidatecould 3 symmetric SM), with R-parity conservation, is arguably the bebasedononeofthefollowingtwomechanisms: 2 mostcompellingextensionoftheSM.TheMSSMpredictsthe 9 existence of a stable new elementaryparticle called the neu- 0 The dark matter is a stable neutralino with mass tralino(lightestsupersymmetricparticle). Withmassoforder • . around 700 GeV which primarily annihilates into lep- 1 100 GeV – TeV, the thermal relic abundance of the lightest tons through new interactions which lie outside the 0 neutralinohastherightorderofmagnitudetoaccountforthe 9 MSSM framework[12]. Dependingonthe framework observeddarkmatterdensity. 0 chosen, this scenario also invokes some ‘boost’ factor Manyrecentinvestigationsof the MSSM havefocusedon : physicssuchasSommerfeldenhancement[13]. v atheoreticallywellmotivatedspecialcasecalledtheCMSSM i [3] (constrained MSSM, based on supergravity)which is far X The dark matter is not entirely stable [14, 15] but ex- r more predictive than the generic MSSM version. The latter • tremelylong-lived,withalifetime 1026sec. Forneu- a canhavemorethanahundredfreeparameters,incontrastto tralinodarkmatter, onecouldintro∼ducesuitably‘tiny’ the CMSSM with just 5 or so parameters. In these investi- R (or ‘matter’) – parity violating couplingswhich sat- gationsthe stable neutralinois usuallyfoundto be relatively isfy the lifetime constraint and allow the neutralino to light(100–fewhundredGeV),anditsindirectdiscoveryrelies decay primarily into leptons. The tiny ( 10−13) R- ondetectingcosmicraysignals(includingpositrons,antipro- ∼ parity violating couplings can be understood through tons, gamma rays, etc.) from neutralino decay or pair anni- non-renormalizable couplings with additional discrete hilationinthegalactichalo,galacticcenter,andthehaloesof symmetries [16]. A simple example of this is pro- nearbygalaxies. videdbytheR-parityviolatingsuperpotentialcoupling The PAMELA experimentis currentlytaking data of high LLEc,whichleadstoathree-bodydecaymodeforthe neutralino [14]. With a neutralino mass of around 2 TeV,thiscansimultaneouslyexplainthePAMELAand ATICdata. ∗Onleaveofabsencefrom:AndronikashviliInstituteofPhysics,GAS, Tbilisi,Georgia. IfoneignoressaytheATICresult,itispossibletoexplain †Electronicaddress:[email protected] thePAMELAobservationswithadecayingneutralinoofmass ‡Electronicaddress:[email protected] §Electronicaddress:shafi@bartol.udel.edu 300 GeV, which would make supersymmetry, and in par- ∼ ¶Electronicaddress:[email protected] ticular the sparticles, far more accessible at the LHC. Even 2 lighter( 100GeV)neutralinomassisfeasibleintheannihi- flux units using the primary electron spectrum. As shown ∼ lationscenario. in the figure, the corresponding positron flux based on the MotivatedbythePAMELAandATICobservationswehave PAMELAdatasuggestsastrongdeviationfromthesecondary performedan ISAJET [17] based analysis of CMSSM spec- positronbackground. While themeasurementsbyPAMELA trocopyin which particularattentionis paid to those regions below 10 GeV might depend on solar modulation effects, ∼ oftheCMSSMparameterspacewhichcontainheavy( 300 the excess in the positronflux measurementswith respect to ∼ GeV –2 TeV)neutralinos,with arelic abundanceconsistent themodelexpectationsisevidentathigherenergies. withtheWMAP5darkmatterbounds[1],andwhichprovide The ATIC measurementof the total electron/positronflux aunifiedexplanationofthePAMELAandATICobservations. alsoshowssomeexcessbeyond 100GeV,mostprominently ∼ Theplanofthepaperisasfollows. Wesummarizetheob- at 700 GeV (once the baseline for the primary electron ∼ servations by PAMELA/ATIC experimentsin Section II and spectrumisnormalizedtotheATICdataatlowenergieswhere review their implications in the context of dark matter de- thepositroncontributionissmall). Eventhoughthereported caysorannihilationsinSectionIII.InSectionIVanestimate excessintheATICdataisnotlargecomparedtotheiruncer- ofneutrinofluxexpectedfromtheannihilatinganddecaying tainties [10] and possible systematic effects, and earlier ex- neutralinoscenariosisprovided.SectionVdiscusseshowthe perimentsinasimilarenergyrangeshowaratherlargescatter CMSSM could be supplemented by new physics while pre- (seee.g. compilationin[11]),ATICobservationsnonetheless servingtheneutralinocolddarkmatterframework.Weoutline provide avenues for exploringnew physics, especially when inSectionVItheprocedurethatweusetoscantheCMSSM takentogetherwithPAMELA. parameterspaceandthevariousexperimentalboundsthatwe OnecaninterpretthecombinedobservationsofPAMELA take into account. In Section VII we present plots display- andATICasahintofanunknownsourcecapableofproduc- ingtherelevantCMSSMparameterspaceandhighlightinTa- ingcomparablenumbersofelectronsandpositronsintheen- blesIandIIa fewbenchmarkpointsthatareconsistentwith ergyrangeof10–700GeV.Forinstance,ifthefluxofexcess thePAMELAandATICmeasurements. Ourconclusionsare e±pairsfollows,approximately,apowerlawoftheform summarizedinSectionVIII. −2.2 E J(E) 0.4 GeV−1 m−2 s−1 sr−1, (1) ≃ (cid:18)GeV(cid:19) II. OBSERVATIONS with a cut-offaround 700GeV (solid line in Fig. 1), then ≃ both ATIC(dashed line) and PAMELA (dot-dashedline) re- The spectra of cosmic ray electrons and positrons should havecontributionsfromknownsourcesincludinge− acceler- quirementscanbereasonablysatisfied. ated in supernova remnants and e± from collisions between A very promising possibility that can account for the ex- cosmicraysandinterstellarprotons[18]. Besideswellknown cessisastrophysicalinorigin,i.e.,pulsarwindnebulaewhich guaranteedbackgrounds,anyevidenceforanadditionalcom- could accelerate e± pairs produced around a neutron star, ponentmaycarryindicationsof anew phenomon. Recently, and which would naturally yield equal numbersof positrons the PAMELA [4] and ATIC [10] experimentshave observed cosmicraypositronsand/orelectronswithintheenergyrange 3 fromseveralGeVuptoafewTeV,andprovidednewhintsfor 10 thelongsuspectedexcessintheirfluxes[6,7]withrespectto the model expectations [19]. The revitalized interest in this ] 1 longstandingpuzzlehasrecentlygeneratedmuchinterestin -sr finding both astrophysicaland perhapsmore exotic explana- 2-1s 102 -m tions. 2 V TheATICexperimenthasmeasuredthecombinedelectron e G aenradlpToesVitraosnsflhuoxwfnroinmF∼ig3.01G. eTVhereparcimhianrgyeenleercgtrieosnusppetoctsruevm- E) [ 101 J( is based on calculations of Ref. [19] (light shaded) is also 3E shown.Asthenormalizationoftheprimaryelectronspectrum isalreadyquiteuncertain,werenormalizethisdownbyafac- 0 tor 0.8in orderto matchthe low energypartof the ATIC 10 0 1 2 3 4 ∼ 10 10 10 10 10 data. Unlikeelectrons,whiletherearenoprimarysourcesof E [GeV] positronsinthismodel(seealso[20]),theexpectedsecondary positronspectrummainlyduetocosmicrayinteractions(dark FIG. 1: Cosmic ray electron (light shaded) and positron (dark shaded)is also presented. Thereis also a muchsmaller sec- shaded) spectra from the model of Ref. [19]. Data has been taken ondaryelectroncomponent(notshowninthefigure). from Ref. [10] (squares), and Ref. [4] (circles). An additional The PAMELA data is originally reported as the positron contribution of e± pairs with spectra J(E) ≃ 0.4(E/GeV)−2.2 fractionof totalelectron/positronflux up to 100GeV [4]. GeV−1m−2s−1sr−1 withacut-off around ≃ 700 GeV (solidline) Inordertoshowbothelectronandpositrond∼ataonthesame canprovide a better fittoboth ATIC(dashed lined) and PAMELA figure, we have converted the reported ratios into absolute (dotdashedline)measurements. 3 3 3 10 10 1] 1] -sr -sr -1s 102 -1s 102 2 2 -m -m 2V 2V e e G G E) [ 101 E) [ 101 J( J( 3 3 E E 0 0 10 10 0 1 2 3 4 0 1 2 3 4 10 10 10 10 10 10 10 10 10 10 E [GeV] E [GeV] 3 10 1] 1] -1-ssr 102 -1-ssr 102 2 2 -m -m 2V 2V e e G G E) [ 101 E) [ 101 J( J( 3 3 E E 0 10 0 10 0 1 2 3 4 0 1 2 3 4 10 10 10 10 10 10 10 10 10 10 E [GeV] E [GeV] FIG.2: Modelsofcosmicrayelectron/positronbackgroundspectraandobservationsasinFig.1. Heretheadditionale±contribution(solid line) is assumed to be originated from dark matter decay (top panels) or annihilation (bottom panels) and aimed at explaining either only PAMELA(leftpanels;asalowerboundondarkmattermass)oralsoATIC(rightpanels;asanupperboundondarkmattermass). Seetext fordetails. andelectrons. Indeed,thetentativedetectionofTeVgamma ricandthedensityprofilecanbeexpressedasfunctionofthe rays from Geminga [21], a nearby pulsar, immediately sug- distancefromthecenterofthehalo, geststhe possibility ofparticle accelarationup to multi–TeV ρ energies [9] (provided that the origin of the gamma rays is ρ(r)= 0 , . (2) (r/r )γ[1+(r/r )α](β−γ)/α s s inverse Compton scattering). Unlike electrons, which can alsobeaccelaratedinsupernovaremnants,positronshaveno wheretheparameters(α,β,γ,rs) = (1,3,1,20kpc)forthe other known primary sources, and thus the resulting excess NFWprofile[22],whichalsosuggeststhatthedensityofdark in positron flux could be very prominent and similar to the matteratthesolarcircleisρ(Rsc 8.5 kpc) = ρsc 0.3 PAMELAobservations[8,9]. GeV/cm3. ≃ ≃ As our main motivationis to accountfor the observations ofATICandPAMELA,weshallfocusongenericleptophilic scenariosin whichthe dominantannihilation/decayproducts III. POSITRONS/ELECTRONSFROMDARKMATTER are assumed to be positrons and electrons. In such models, onceelectrons/positronsarecreated,theirdensitynatagiven Another exciting explanation is that some exotic mecha- place,timeandenergy,isgovernedbythediffusionequation, nismsuchasdarkmatterdecayorannihilation,whicharethe ∂n ∂ main subjects of this study, might be responsible for the ex- = [ (E) n]+ [ℓ(E)n]+Q(r,E), (3) cessesseen in observations. We willassumethroughoutthat ∂t ∇· D ∇ ∂E thedarkmatteristhelightestCMSSMneutralino.Forastudy where Q(r,E) is the source term describing the particle in- on the signals from dark matter annihilation/decayproducts, jectionrateasdiscussedbelow,ℓ(E)= ℓ (E/GeV)−2 isthe 0 anunderstandingofthedistributionofdarkmatterwithinthe energyloss rate and (E) = (E/GeV)δ is the diffusion 0 D D galaxy is essential. Simulations of cold dark matter suggest coefficient,bothassumedtobeindependentofspace. thatdarkmatterassemblesinhalos.Thedarkmatterdistribu- The spectrum of a particle per dark matter annihilation, tionwithinthehaloisusuallytakentobesphericallysymmet- χχ e+e−, can be written as φa(E) = δ(E m ) in χ → − 4 terms of the Dirac δ function, where m is the mass of the theoreticalexpectationstotheobservationsmightbevisually χ darkmatterparticle. Thecorrespondingsourcetermisthen improved.However,anexactreproductionoftheobservations cannotbe essential since (1) the observationsare highly un- Qa(r,E)= ρ(r) 2 1 ρ2scf σv φa(E), (4) certain, and more importantly (2) the backgroundfluxes are (cid:20) ρ (cid:21) (cid:20)2m2 Bh i(cid:21) not well known and already strongly dependent on models. sc χ Sinceanattempttoover–constrainthetheorieswhileassum- wherethefactorof1/2arisesbyassumingthatthedarkmat- ing a perfectknowledgeof the backgroundelectron/positron ter candidate is its own antiparticle. Here the term fB σv fluxes may not yield additional useful results, we choose to h i is the product of the annihilation cross section and the rela- probe only the most generic features of the observations by tive velocitytogetherwith the requried‘boostfactorfB’ that PAMELA andATICandpresentourresultsfora NFW dark may come from either new particle physics or astrophysical matter profile together with the MED diffusion model [23] enhancements. with appropriate parameters (D = 0.0112 pc2/yr,δ = 0 If the dark matter decays into three light particles such as 0.7,ℓ =10−16 GeV/s). χ e+e−ν, the spectrum of each daughter particle, to a Nex0tweoutlinehowthePAMELAandATICobservations rou→gh approximation, is given by φd(E) δ(E m /3) χ could be accounted for by a neutralino dark matter scenario ≃ − withthecorrespondingsourceterm through annihilation or decay, and what would be the ex- ρ(r) ρ pected ranges of parameters such as dark matter mass, life- Qd(r,E)= sc φd(E), (5) time or annihilation cross section under these assumptions. ρ (cid:20)m τ(cid:21) sc χ We identifytwo scenarioswhich can reasonablyaccountfor where τ is the lifetime correspondingto this decay channel, the positron excess observed by PAMELA with a relatively which may arise from new physics. Note that the prefactor light ( 100 300 GeV) dark matter candidate. In addi- ∼ − ρ is introducedto makethe term in the secondparanthesis tion we consider two scenarios with an appropriately heavy sc dimensionlessandwillcanceloutinourfinalresults. ( 700GeV 2TeV)darkmattercandidatewhichprovidea ∼ − Withthesedefinitionsofthesourceterms,wefollowanap- unifiedexplanationofboththePAMELAandATICobserva- proachsimilartoRef.[23,24]inevaluatingthelocalparticle tions. flux. Assuming steady-state conditions, typical in assessing In Fig. 2, the additionale± contribution(solid line) is as- the particle flux fromdark matter annihilation/decay,the so- sumed to originate from dark matter decay or annihilation. lutionofthediffusionequationcanbecastas The dashed line shows the expectationfor total electron and positron flux when both e− and e+ fluxes are added to the ∞ ′ ′ ′ primary electron background (light shaded). This can be n(E)=κ dE φ(E )ζ(E,E ). (6) Z compared to the ATIC data which corresponds to the to- E tal lepton spectrum. We also show the total positron spec- Thecoefficientκencodesparticlephysicsinputsuchthatfor trum(dot-dashedline)byaddingonlytheadditionalpositron annihilationsκa = 1(ρ2 /m2)f σv ,whilefordecaysκd = 2 sc χ Bh i flux fromdark matterannihilationor decayto the secondary ρ /(m τ). Thespectrumofeachgivendaughterparticleper sc χ positron spectrum (dark shaded), which is then compared to annhilationordecayisφ. Thefunctionζencodesdependence thePAMELAdata. Thetheoreticalfitsareslightlysmoothed ofthesolutiononthechosendarkmatterhaloprofileaswell outtosimulatefiniteresolutionofexperiments.Thefourpan- as particle propagationand diffusion and has a form similar toI˜inRef.[23]forannihilationsuptomultiplicativefactors. elsdisplayedare: ThefluxofparticlesissimplyJ(E) = (c/4π)n(E),wherec Top-Left: A decayingdarkmatterscenariowith a life- isthespeedoflight. • time τ 2 1027 s andm 0.3TeV which is the The meaning of Eqn. 6 is as follows. For a particle to be ∼ × χ ∼ minimal mass required to account for PAMELA (dot- observedlocallyatagivenenergyE,ithastobeproducedat dashed line) without causing significant tension with ′ a higher energy E at a more distant location in the galaxy. ATIC(dashed-line). Thentheparticlewillloseenergyanddiffuseuntilitreaches the solar system, abiding by the constraints of the diffusion Top-Right:Adecayingdarkmatterscenariowithalife- equation.Ashighenergyparticleslooseenergyfast,theirob- • time τ 3 1026 s and m 2 TeV which is the χ servedflux shouldbe dominatedby nearbyprocesseswithin maximu∼mma×ssthatcanaccoun∼tforATICobservation a few kiloparsecs. Higher production rate for rather cuspy with rather sharp cut-off around 0.7 TeV (dashed halo profiles, especially for annihilations around the central line) andalsoaccountforPAMEL∼A (dot-dashedline). partsofthegalaxyareonlyimportantatlowerenergies.Since Thus,massesintherangeof 0.3–2TeVwith alife- wefocusonleptophilicscenarios,plausiblesevereconstraints time of 1027 s can be rega∼rded as acceptable for a duetofinalstatesotherthane±pairs,suchasantiprotons,are decaying∼neutralinodarkmatterscenario. alreadyavoided.Thustheexactparametrizationoftheunder- lyingdarkmatterhaloprofileislessrelevantaslongasthelo- Bottom-Left:Anannihilatingdarkmatterscenariowith calnormalizationofdarkmatterdensity,ρ 0.3GeV/cm3 • f σv 1.5 10−25 cm3/s and m 0.1 TeV, sc B χ ≃ h i ∼ × ∼ isconsistent. whichcorrespondstotheminimalmassrequiredtoex- Besideselectrons/positrons,ifotherchargedleptonicinter- plain PAMELA (dot-dashedline) withoutsignificantly mediatestatesexist,suchastauthatdecaytoe±,thefitofthe exceedingtheATICmeasurement(dashed-line). 5 Bottom-Right: An annihilating dark matter scenario areprovidedbytherequirementtoaccountforthePAMELA • with f σv 6 10−24 cm3/s and m 0.7 TeV andATICobservations.Thefluxesarealsoaveragedoverthe B χ h i ∼ × ∼ that can simultaneously fit the PAMELA excess (dot- wholeskywhichdampensanyrelativeenhancementofanni- dashedline)andATICexcessandalsotheobservation hilationcomparedto decayscenarios, especiallytowardsthe ofrathersharpcut-offaround 0.7TeV(dashedline). centeroftheGalaxy. ∼ Foranannihilatingscenario,thepreferredmassranges These can be compared to the atmospheric neutrino are 0.1–0.7TeVwithf σv 10−24cm3/s. spectrum (solid line) which is based on measurements by B ∼ h i∼ Refs.[30,31,32,33,34]andalsoagreeswiththetheoretical The predictions for dark matter annihilation and decay modellingofRef.[35]. Thebumpsat 100GeVwhichare ∼ barely differ only at low energies as can be seen in Fig. 2, devisedtoaccountforPAMELAonlyfallshortbyseveralor- wherethefluxfromtheformerislarger.Thisisduetothefact dersofmagnitudebelowtheatmosphericneutrinoflux.How- that the annihilation rate is proportionalto the square of the everatenergies 700GeV,thecorrespondingneutrinofluxes ∼ darkmatterdensityandanyenhancementtowardstheGalac- arewithinreachoftheatmosphericneutrinobackground,thus ticCenterwillcauseanenhancedcontributionsatlowerener- offerhopetotestthisscenariointhenearfuture. gies. Aswehavefocusedhereonleptophilicscenarios,wedonot discussmodelsinwhichgammarayfluxesareamongthepri- mary decay or annihilationproducts(see e.g. Refs. [36, 37] IV. NEUTRINOSFROMDARKMATTER where the dominantdark matter annihilation/decayproducts are gamma rays). However, gamma rays might accom- pany the production of e± pairs such as through internal An interesting application of these results is the plausible bremsstrahlung[38]. AlsoinverseComptonandsynchrotron presenceofotherleptonicfinalstatessuchasneutrinos.Dark emissionmightbeproducedfromtheelectronsandpositrons. matter annihilating dominantly into neutrinos has been con- Insuchcases,especiallyforannihilations,darkmatterprofiles sidered in Ref. [25, 26] and more recently in the context of thatareshalloweraroundthecenteroftheGalaxycompared more recent observations [27, 28]. For instance, neutralino decay may yield neutrinosbesides pairs of e±. Similarly, it totheNFWparametrizationmightbepreferred[39]. isconceivablethatinannihilation,neutrinosande± pairsare producedincomparablenumbers. To further illustrate the implication of the four scenarios, V. FROMOBSERVATIONSTOCMSSM we calculate the total neutrino flux (utilizing prescriptions outlined in Refs. [26, 29]) using the above parameters and Inordertounderstandtheunexpectedlyhighelectronicflux presenttheresultsinFig.3. Thetotalneutrinofluxforthese observedby PAMELA and ATIC the CMSSM must be sup- bumpsis 6 10−9 cm−2s−1sr−1 whenaveragedoverthe plementedbynewphysics.Ifonewishestopreservethebasic ∼ × wholesky(bothsmoothedwitha10%Gaussianinthefigure). neutralinocolddarkmatterframework,whichweproposeto Thefluxesfromthedecay(thicklines)andannihilation(thin dointhispaper,atleasttwooptionsareavailable. lines) scenariosare comparableastheir main normalizations Perhapsthesimplestmodificationonecouldcontemplateis to include R-parity violating superpotentialcoupling(s) with suitably tiny dimensionless coefficient(s), such that the neu- 10-2 tralinoprimarilydecaysintoleptons,withlifetime 1026sec. ] A simple example is provided by the coupling LL∼Ec [14], 1 1-sr10-3 whichleadsto3-bodyleptonicdecaysoftheneutralino. This -s modification has an important advantage in that it preserves 2 -m thebasicstructureoftheCMSSM,especiallybyleavingintact V c10-4 the standard calculations for estimating the relic neutralino e abundance. The implications for CMSSM spectroscopy for G E [ 10-5 dthisiscucsasseedwinhiScehchtiaosnaVrIaIt.herheavyneutralino(∼ 2 TeV) are d Φ/ -6 Darkmatterneutralinosannihilatinginthehalosofgalax- d10 iesprovideanexcitingnewsourceforcosmicraysincluding 2 E positrons.ToexplainthePAMELAandATICobservationsin -7 terms of neutralino annihilations, the CMSSM must be sup- 10 101 102 103 104 plementedby new physicswhichshouldaccomplishthe fol- E [ GeV ] lowingthree things: allow neutralinoannihilationsprimarily intoleptonicchannels,produceaboostfactoroforder103 or FIG.3:Theatmosphericneutrinospectrumaveragedoverwholesky sothroughSommerfeldenhancement[13],andlastbutbyno (solidline)iscomparedtothetotalneutrinofluxassociatedwiththe meansleast, ensurethattherelicabundanceofneutralinosis parameters used in top-left ( top-right, bottom-left, bottom-right) consistent with WMAP bounds. Several interesting propos- panelofFig.2whichisdenotedwithathin-dot-dashed(thin-dashed, alsforannihilatingWIMPSthatexplainPAMELAandATIC thick-dot-dashed,thick-dashed)line.Seetextfordetails. havebeenputforward[12]. However,itisnotobviousifthey 6 FIG.4: Plotsin(m1/2,m0)and(m1/2,tanβ)planesforµ > 0(leftpanel)andµ < 0(rightpanel). Graypointssatisfyconstraintsfrom colliders(BR(B →µ+µ−),BR(B→X γ),andthecharginoandHiggsmassbounds).LightbluepointssatisfytheWMAPupperbound s s ondarkmatterrelicabundance. Green(mχ˜01 ≤ 0.3TeV),red(0.65TeV ≤ mχ˜01 ≤ 0.75TeV),black(1.9TeV ≤ mχ˜01 ≤ 2.1TeV),and darkblue(mχ˜01 ≤ 2.5TeV)pointssatisfyboththeupperandlowerboundsondarkmatterrelicabundance. Green,redandblackpointsare subsetsofdarkbluepoints. DenseregionsinallfigurescorrespondtoparametervaluesthatareespeciallyrelevantforPAMELAandATIC, andforwhichadditionaldatahasbeenaccumulated. canbeeasilyadaptedtotheCMSSMscenarioweareconsid- VI. PHENOMENOLOGICALCONSTRAINTSAND eringinwhichtheneutralinomakesuptheobservedcolddark SCANNINGPROCEDURE matterintheuniverse. Thus,eventhoughanexplicitparticle physicsconstructionforneutralinoannihilationsatisfyingthe We employISAJET7.78package[17]toperformrandom aboveconditionsisnotyetavailable,wewillinthefollowing scans over the parameter space. In this package, the weak discussion present spectroscopy results which cover a wide scalevaluesofgaugeandthirdgenerationYukawacouplings rangeofneutralinomassescurrentlyfavoredbyPAMELAand are evolved to M via the MSSM renormalizationgroup GUT ATIC,includingthe700GeVorsovaluemotivatedfromneu- equations (RGEs) in the DR regularization scheme, where tralinoannihilation. M is defined to be the scale at which g = g . We GUT 1 2 do not enforce an exact unification of the strong coupling g = g = g atM , since a fewpercentdeviationfrom 3 1 2 GUT unificationcanbeassignedtounknownGUT-scalethreshold 7 FIG.5:Plotsin(m0,A0)and(m1/2,A0)planesforµ>0(leftpanel)andµ<0(rightpanel).ColorcodingsameasinFig.4. corrections [40]. At M , the CMSSM boundary condi- Therequirementofradiativeelectroweaksymmetrybreak- GUT tions are imposed and all the SSB parameters, along with ing (REWSB) [42] puts an important theoretical constraint the gauge and Yukawa couplings, are evolved back to the ontheparameterspace. Anotherimportantconstraintcomes weak scale M . In the evaluation of Yukawa couplings the fromlimitsonthecosmologicalabundanceofstablecharged Z SUSY threshold corrections [41] are taken into account at particles [43]. This excludes regions in the parameter space the common scale MSUSY = √mt˜Lmt˜R. The entire pa- wherechargedSUSY particles, suchas τ˜1 ort˜1, becomethe rameter set is iteratively run between M and M using lightestsupersymmetricparticle(LSP).Weacceptonlythose Z GUT the full 2-loop RGEs until a stable solution is obtained. To solutionsforwhichtheneutralinoistheLSP. betteraccountforleading-logcorrections,one-loopstep-beta Wehaveperformedrandomscansforthefollowingparam- functions are adopted for gauge and Yukawa couplings, and eterrange: the SSB parametersm are extractedfromRGEsat multiple i scales m = m (m ). The RGE-improved 1-loop effective i i i 0 m 20TeV, potential is minimized at an optimized scale MSUSY, which ≤ 0 ≤ effectively accounts for the leading 2-loop corrections. Full 0 m1/2 10TeV, ≤ ≤ 1-loop radiative correctionsare incorporatedfor all sparticle 3 A /m 3, 0 0 − ≤ ≤ masses. 5 tanβ 58, (7) ≤ ≤ 8 FIG.6: Plotsin(mA, mχ˜01)and(mχ˜±1,mχ˜01)planesforµ > 0(leftpanel)andµ < 0(rightpanel). Graypointssatisfyconstraintsfrom colliders(BR(B →µ+µ−),BR(B→X γ),andthecharginoandHiggsmassbounds).LightbluepointssatisfytheWMAPupperbound s s ondarkmatterrelicabundance. Darkbluepointssatisfyboththeupperandlowerboundsondarkmatterrelicabundance. Orangeandbrown pointssatisfytheconstraint from∆a (forµ > 0, asexpected). Orange pointssatisfyonly thelower bound on darkmatterrelicdensity, µ whilebrown ones satisfyboth theupper and lower bounds. Verticallines correspond tomχ˜01 = 0.3,0.65,0.75,1.9 and2.1 TeV. ATIC imposes0.65 TeV ≤ mχ˜01 ≤ 0.75TeV(1.9TeV ≤ mχ˜01 ≤ 2.1TeV)basedonannihilating(decaying) neutralinos. PAMELArequires mχ˜01 ≥0.1TeV(mχ˜01 ≥0.3TeV)basedonannihilating(decaying)neutralinos. withµ>0andµ<0,andm =172.6GeV[44]. successively on the data that we acquired from ISAJET. As t Aftercollectingthedata,weusetheIsaToolspackage[45] afirststepweapplytheconstraintsfromBR(B µ+µ−), s → toimplementthefollowingphenomenologicalconstraints: BR(B X γ), chargino mass, and Higgs mass. We then s → mχ˜±1 (charginomass)≥103.5GeV [43], adpaprklymthateteWr fMolAloPweudppbeyrtbhoeucnodnostnratihnet orenlitchedemnusiotny aonfocmolad- m (lightestHiggsmass) 114.4GeV [46], h BR(Bs →µ+µ−)<5.8×≥10−8 [47], lroeguisomn.aFgnineatilcly,mwoemaepnptlayµth=elo(wge−rb2o)uµn/d2oant tthheed3aσrkalmloawtteedr 2.85 10−4 BR(B X γ) 4.24 10−4(2σ) [48], Ω ×h2 =0≤.111+0.01→1 (2σs) ≤ × [1], relicabundance. Thedataisthenplottedshowingthesucces- CDM −0.015 siveapplicationofeachoftheseconstraints. 3.4 10−10 ∆a 55.6 10−10 (3σ) [49]. µ × ≤ ≤ × We have applied the constraints from experimental data 9 FIG.7:Plotsin(mg˜,mχ˜01)and(mt˜,mχ˜01)planesforµ>0(leftpanel)andµ<0(rightpanel).ColorcodingsameasinFig.6.Verticallines correspondtomχ˜01 =0.3,0.65,0.75,1.9and2.1TeV.ATICimposes0.65TeV≤mχ˜01 ≤0.75TeV(1.9TeV≤mχ˜01 ≤2.1TeV)based onannihilating(decaying)neutralinos.PAMELArequiresmχ˜01 ≥0.1TeV(mχ˜01 ≥0.3TeV)basedonannihilating(decaying)neutralinos. VII. IMPLICATIONSFORCMSSM • mχ˜01 > 0.1 TeV: This region of neutralino masses canex∼plainthePAMELAobservationifweassumethat neutralinosannihilate,ratherthandecay,preferentially PAMELAandATIC,asdiscussedpreviously,havesetcon- intoelectronsandpositrons. straints on the mass and other properties of the dark matter cparenfdeirdraetdemwahsischv,ailnueosuarreCaMsSfoSlMlowcas:se,istheneutralino. The • p0.la6i5nTtheeVre<∼sulmtsχ˜f01rom<∼b0o.7th5PTAeMVE: LTAhisanrdegAioTnICcabnaseexd- onannihilatingneutralinos. • mtoχ˜e01xp>∼lai0n.3thTeePVA:MTEhLisAreregsiuolntsisbainsetedreosntidnegciafywinegwneisuh- Wenowpresenttheresultsoftherandomscanfocusingat- tralinos. tention on the above mentioned neutralino mass ranges. In Fig.4weplottheresultsinthe(m ,m )and(m ,tanβ) 1/2 0 1/2 • r1a.n9gTeeoVfn<∼eutmraχl˜i01no<∼ma2s.s1eTxepVla:inTshthiserreelsautlitvseflyronmarbrootwh polfatnheessefoproµints>sa0tis(fleyftthpeatnheelo)raentidcaµlre<qu0ire(rmigehnttpoafnReEl)W. ASBll PAMELAandATICbasedondecayingneutralinos. and correspond to a neutralino with mass less than 2.5 TeV. 10 FIG.8:Plotsin(mh,mχ˜01)and(mτ˜,mχ˜01)planesforµ>0(leftpanel)andµ<0(rightpanel).ColorcodingsameasinFig.6.Verticallines correspondtomχ˜01 =0.3,0.65,0.75,1.9and2.1TeV.ATICimposes0.65TeV≤mχ˜01 ≤0.75TeV(1.9TeV≤mχ˜01 ≤2.1TeV)based onthemodelofannihilating(decaying)neutralinos. PAMELArequiresmχ˜01 ≥0.1TeV(mχ˜01 ≥0.3TeV)basedonannihilating(decaying) neutralinos. Inaddition,thesepointssatisfythevariousexperimentalcon- • Greenpointscorrespondtomχ˜01 ≤0.3TeV. straintslistedearlier. Graypointssatisfytheconstraintsfrom BR(Bs µ+µ−), BR(B Xsγ), and the Higgs and • Black points correspond to 1.9 TeV ≤ mχ˜01 ≤ → → 2.1TeV. chargino masses. After application of the WMAP 5 upper bound on neutralino dark matter (light blue points), the al- lowed region is drastically shrunk, with the remaining gray • Red points correspond to 0.65 TeV ≤ mχ˜01 ≤ 0.75TeV. pointsassociatedwithanunacceptablyhighdarkmatterrelic density. Theothercolors(green,red,darkblueandblack)in NotethatifwewanttoexplainjustthePAMELAdatathrough Fig.4correspondtodifferentrangesofneutralinomasssuch neutralinoannihilationwitha suitable‘boost’factor,thereis thattheneutralinosatisfiesboththeWMAP5upperandlower almost no constraint on the CMSSM parameter space as it bounds on dark matter relic abundance. The specific mass requires in this case mχ˜01 > 0.1 TeV, which is satisfied by rangeshavebeenpickedoutasinterestingintryingtoexplain almostallCMSSMallowed∼points. thedatafromPAMELAandATIC.Theseare; The(m ,m )planeforµ>0isdistinctlydifferentfrom 1/2 0 thatofµ < 0. Withµ < 0,theratiobetweenm1/2 andmχ˜01