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arXiv:hep-ph/0406115v110Jun2004LEPTOGENESIS,NEUTRINOMIXINGDATAANDTHEABSOLUTENEUTRINOMASSSCALEaP.DiBariIFAE,UniversitatAut`onomadeBarcelona,08193Bellaterra(Barcelona),SpainRecentdevelopmentsinthermalleptogenesisarereviewed.Neutrinomixingdatafavorasimplepicturewherethematter-antimatterasymmetryisgeneratedbythedecaysoftheheavyRHneutrinosmildlyclosetothermalequilibriumand,remarkably,inthefullnonrelativisticregime.Thisresultsintopredictionsofthefinalbaryonasymmetrynotdependingontheinitialconditionsandwithminimizedtheoreticaluncertainties.AfterashortoutlineofageometricalderivationoftheCPasymmetrybound,wederiveanalyticboundsonthelightestRHneutrinomassandontheabsoluteneutrinomassscale.Neutrinomasseslargerthan0.1eVarenotcompatiblewiththeminimalleptogenesisscenario.Wediscusshowtheresultsgetjustslightlymodifiedwithintheminimalsupersymmetricstandardmodel.Inparticularaconservativelowerboundonthereheatingtemperature,TR&109GeV,isobtainedintherelevanteffectiveneutrinomassrangeem1&3×10−3eV.Wealsocommentontheexistenceofa‘too-short-blanketproblem’inconnectionwiththepossibilityofevadingtheneutrinomassupperbound.aCompendiumof1and2mostlybasedon3withsomenewresultsin3.4,3.8and3.9.1IntroductionCosmicraysandCMBRobservationsindicatethatourobservableUniverseisbaryonasym-metric4.MoreovertheobservationoftheacousticpeaksinthepowerspectrumofCMBR5,combinedwithlargescalestructuresobservations6,provideapreciseandrobustmea-surementofsuchanasymmetrythatcanbeexpressedintermsofthebaryontophotonnumberratioattherecombinationtime,ηCMBB=(6.3±0.3)×10−10,(1)inverygoodagreementwiththelatestdeterminationfrom(NACREupdated)StandardBBNandprimordialDeuteriummeasurementsthatgive7ηSBBNB=(6.1±0.5)×10−10.(2)AtthesametimethereisagrowingevidencethataninflationarystageoccurredduringtheearlyUniverse.Inthiscasethiswouldhavedilutedanypre-existinginitialasymmetrytoalevelmanyordersofmagnitudebelowthemeasuredvalue,thusrequiringanexplanationoftheobservedbaryonasymmetryintermsofadynamicalgeneration,theaimofamodelofbaryogenesisthatnecessitatestheaccomplishmentofthethreefamousSakharov’scon-ditions:CandCPviolation,Bviolationanddeparturefromthermalequilibrium.WithintheStandardModelallthreeconditionsarefulfilled,yettheobservedvalueistoolargetobeexplainedandthereforeasuccessfulmodelofbaryogenesisrequiressomenewphysicsingredient.AhostofmodelshavebeenproposedsincethefirstSakharovidea8.Someexamplesoftypologiesofbaryogenesismodelsare:Planckscalebaryogenesis,baryogene-sisfromphasetransitions,Affleck-Dinemodels,baryogenesisfromblackholesevaporation,modelsofspontaneousbaryogenesis9.Eventhoughleptogenesis10andGUTbaryogenesis11,12exhibit,fromaparticlephysicspointofview,substantialdifferences,theycanbejointlyregardedastwodifferentexamplesbelongingtotheoldestclassofmodelsofbaryogenesisfromheavyparticledecays.Suchaclassificationprivilegesthethermodynamicalaspectenlighteninggeneralpropertiesthatdonotdependonthespecificparticlephysicsframework.Wewillthusdiscussthekinetictheoryofheavyparticledecaysinthefirstpart,whileinthesecondpartwewillseehowleptogenesisisaspecificremarkableexampleinwhichthenewphysicsingredientisprovidedbytheseesawmechanismandsuchthattheobservedbaryonasymmetryisnicelyrelatedtoneutrinomixingdata.2Baryogenesisfromheavyparticledecays2.1Out-of-equilibriumdecaysLetusconsideraself-conjugateheavy(MX≫MEW)particleXwhosedecaysareCPasymmetric,insuchawaythatthedecayingrateintoparticles,Γ,isingeneraldifferentfromthedecayingrateintoanti-particles,¯Γ,andsuchthatthesingledecayprocessintoparticles(anti-particles)violateB−LbyaquantityΔB−L(−ΔB−L).TheCPasymmetryparameteristhenconvenientlydefinedasε=Γ−¯ΓΓ+¯Γ.(3)Forajointdiscussionofbaryogenesis(ΔB−L0)andleptogenesis(ΔB−L0)models,itisusefultointroducethequantityeε=ΔB−Lε.ThetotaldecayrateΓD=Γ+¯Γistheproductofthetotaldecaywidth,ΓrestD,timestheaverageddilationfactorh1/γiΓD=ΓrestD1γ.(4)Sphaleronprocesses,whileinter-convertingBandLseparately,leaveB−Lunchanged13andforthisreasonthekineticequationsgetmuchsimpleriftheB−LevolutionistrackedinsteadoftheseparateBorLevolution.Moreoveritisconvenienttouse,asanindependentvariable,thequantityz=MX/TandtointroducethedecayfactorD=ΓD/(Hz).AnotherusefulchoiceistotrackthenumberofXparticles,NX,andtheamountoftheasymmetry,NB−L,inaportionofcomovingvolumeR3normalizedinsuchawaytocontain,averagelyinultra-relativisticthermalequilibrium,justoneXparticle(i.e.NeqX(z≪1)=1).ThesimplestcaseiswhentheXlife-time,τ=1/ΓrestD,ismuchlongerthantheageoftheUniverse,tU=(2H)−1,atz=1,whentheXparticlesbecomenonrelativistic.InthiswaydecayswilloccurwhenthetemperatureismuchbelowtheXmassandtheX-productionfrominversedecays,orotherpossibleprocesses,isBoltzmannsuppressed.InthissituationdecaysaretheonlyrelevantprocessesandthekineticequationsfortheX-abundanceandtheB−Lasymmetryareparticularlysimpletobewritten,dNXdz=−D(z)NX(z)(5)dNB−Ldz=−˜εdNXdz,(6)andsolved,NB−L(z)=NiB−L+˜εNiX−NX(z)(7)NX(z)=NiXe−Rzzidz′D(z′).(8)ThesolutionscanbefullydescribedjustintermsofthedecayparameterK=ΓrestDH|z=1,(9)intermsofwhichD=Kzh1/γi.Thedilationfactor,averagedontheBoltzmannstatistics,issi
本文标题:Leptogenesis, neutrino mixing data and the absolut
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