Probing CP violation in neutrino oscillations with

arXiv:0706.2070v2[hep-ph]3Jul2007ProbingCPviolationinneutrinooscillationswithneutrinotelescopesKfirBlum∗DepartmentofCondensedMatterPhysics,WeizmannInstituteofScience,Rehovot76100,IsraelYosefNir†DepartmentofParticlePhysics,WeizmannInstituteofScience,Rehovot76100,IsraelEliWaxmanDepartmentofCondensedMatterPhysics,WeizmannInstituteofScience,Rehovot76100,IsraelAbstractMeasurementsofflavorratiosofastrophysicalneutrinofluxesaresensitivetothetwoyetun-knownmixingparametersθ13andδthroughthecombinationsinθ13cosδ.Weextendpreviousstudiesbyconsideringthepossibilitythatneutrinofluxesfrommorethanasingletypeofsourceswillbemeasured.Wepointoutthat,ifreactorexperimentsestablishalowerboundonθ13,thenneutrinotelescopesmightestablishanupperboundon|cosδ|thatissmallerthanone,andbythatprovethatCPisviolatedinneutrinooscillations.Suchameasurementrequiresseveralfavorableingredientstooccur:(i)θ13isnotfarbelowthepresentupperbound;(ii)Theuncertaintiesinθ12andθ23arereducedbyafactorofabouttwo;(iii)Neutrinofluxesfrommuon-dampedsourcesareidentified,andtheirflavorratiosmeasuredwithaccuracyoforder10%orbetter.Forthelastconditiontobeachievedwiththeplannedkm3detectors,theneutrinofluxshouldbeclosetotheWaxman-Bahcallbound.Itmotivatesneutrinotelescopesthatareeffectivelyabout10timeslargerthanIceCubeforenergiesofO(100TeV),evenattheexpenseofahigherenergythreshold.†TheAmosde-Shalitchairoftheoreticalphysics∗Electronicaddress:kfir.blum,yosef.nir,[e-mail]goalsoffutureneutrinoexperiments[1]istoobserveCPviolationinneutrinooscillations.ThesignificanceofsuchameasurementgoesbeyondthedeterminationofafundamentalparameterofNature:itcangivefurtherqualitativesupporttoleptogenesis,theideathattheobservedbaryonasymmetryoftheUniversehasitssourceinaleptonasymmetrygeneratedinneutrinointeractions.Insomescenarios,itisevenquantitativelyrelatedtoleptogenesis.Neutrinotelescopes[2],suchastheIceCubeexperiment,aimtoobserveneutrinoscomingfromastrophysicalsources.Theexperimentswillprovideinformationonthedirection,energy,andflavoroftheincomingneutrinos.Inparticular,ratiosbetweenfluxesofdifferentflavorsarrivingtothedetectorcanbemeasured.Ratiosbetweenthesefluxesatthesourcearepredictedbyratherrobusttheoreticalconsiderations.Themodificationsoftheflavorratiosbetweensourceanddetectororiginatefromneutrinooscillations.Thismeansthattherelationsbetweenthefluxesatthesourceandthefluxesatthedetectordependontheneutrinoparametersinacalculableway.Flavormeasurementsinneutrinotelescopescanthusprovideinformationontheneutrinomixingparameters[3,4,5,6,7,8,9].Inparticular,thereissensitivitytotwoyetunknownparameters:themixingangleθ13andtheCPviolatingphaseδ.CPviolationinneutrinooscillationscan,inprinciple,beobservedviainterferenceterms.Forneutrinoscomingfromastrophysicalsources,suchinterferencetermsarewashedout,andthemeasuredfluxesarethereforesensitiveonlytoCPconservingparameters.Specifically,themeasuredflavorratiosaresensitivetothecombinationΔ13≡sinθ13cosδ.(1)Sinceθ13isexperimentallyboundedfromaboveandknowntobesmall,itisconvenienttowritetheflavorratiosinthegeneralforma+bΔ13,whereaandbareknownfunctionsofthetwomeasuredparameters,θ12andθ23,butindependentofθ13andδ.ThebΔ13termprovidesasmallcorrectiontothezerothorderpredictiona.Ifsinθ13=0,orifCPviolationismaximal,i.e.δ=π/2or3π/2,thecorrectiontermisabsent.Ifsinθ13isclosetothepresentexperimentalupperbound,itislikelytobemeasuredinnearfuturereactorexperiments[10].Inthatcase,ifneutrinotelescopesareabletoexclude2acorrectiontermaslargeas±bsinθ13,theywillestablishthatcosδ6=±1and,bythat,willdiscoverthatCPisviolatedinneutrinointeractions.OurgoalinthispaperistoanalyzewhethersuchadiscoveryofCPviolationbyneutrinotelescopesisatallpossible.Moreconcretely,wedothefollowing.Onthequalitativelevel,wefindwhattypesofsourcesandwhattypesofflavorratiosprovidethestrongestsensitivitytotheparametersofinterest.Onthequantitativelevel,weestimatetheaccuracythatisrequiredinthesemeasurementsandinindependentmeasurementsofthemixinganglesinordertoestablishthattheCPviolatingphaseisdifferentfrom0andfromπ.Ourfinalconclusionisthat,withlargeθ13andnear-maximalCPviolation,andundersomefavorablecircumstances,itmaybepossibleforIceCube(or,moreeasily,forfuture,largerdetectors)toestablishCPviolationinneutrinointeractions.II.FLAVORRATIOSANDMIXINGPARAMETERSOurgoalinthissectionistoderiveanalyticalexpressionsforneutrinoflavorfluxesthatcanbemeasuredinneutrinotelescopesand,inparticular,inIceCube.Neutrinotelescopescanidentifytheneutrinoflavor(α=e,μ,τ)viaitscharacteristicinteractiontopology[11,12].IceCubehasanenergythreshold∼100GeVfordetectingmuontracks,and∼1TeVfordetectingelectron-andtau-relatedshowers.Aboveanenergythreshold∼1PeV,itispossibletodistinguishbetweentheelectron-relatedelectromagneticshowersandthetau-relatedhadronicshowers.Finally,aroundE∼6.3PeV,theGlashowresonancemayallowtheidentificationof¯νeevents[7,13].Wedenotethefluxofνα+¯ναmeasuredatthedetectorbyφdα;thefluxofantineutrinos¯ναisdenotedby¯φdα.Weconsiderthefollowingflavorratios:R≡φdμφde+φdτ,(2)S≡φdeφdτ,(3)T≡¯φdeφdμ.(4)BelowE∼PeV,onlyRcanbemeasured.