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The long-lived stau as a thermal relic [Elektronische Ressource] / Josef Pradler

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Technische Universit¨at Mu¨nchen, Physik Department, T30dMax Planck Institut fu¨r Physik (Werner Heisenberg Institut)DissertationThe long-lived stau as a thermal relicJosef PradlerVollsta¨ndiger Abdruck der von der Fakulta¨t fu¨r Physik der Technischen Universita¨tMu¨nchen zur Erlangung des akademischen Grades einesDoktors der Naturwissenschaften (Dr. rer. nat.)genehmigten Dissertation.Vorsitzender: Univ.-Prof. Dr. L. OberauerPru¨fer der Dissertation: 1. Univ.-Prof. Dr. A. Ibarra2. Univ.-Prof. Dr. W.F.L. HollikDie Dissertation wurde am 23.06.2009 bei der Technischen Universita¨t Mu¨nchen einge-reicht und durch die Fakulta¨t fu¨r Physik am 20.07.2009 angenommen.iiSummaryThe results presented in this thesis have in part already been published in Refs. [1, 2,3, 4, 5] listed overleaf (page v). We consider physics beyond the Standard Model whichimplies the existence a of long-lived electromagnetically charged massive particle species±(CHAMP) which we denote byX . We discuss in detail the unique sensitivity the earlyUniverse exhibits on the mere presence and on the decay of such a particle. A CHAMPcan be realized in supersymmetric (SUSY) extensions of the Standard Model. We carryeout a detailed study of gravitino (G) dark matter scenarios in which the lighter scalartau (stau, τe ) is the lightest Standard Model superpartner so that τe = X. We also1 1provide a thorough investigation of the thermal freeze-out process of τe .

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TechnischeUniversit¨atMu¨nchen,PhysikDepartment,T30d
MaxPlanckInstitutfu¨rPhysik(WernerHeisenbergInstitut)

Dissertation

Thelong-livedstauasathermalrelic

JosefPradler

Vollsta¨ndigerAbdruckdervonderFakulta¨tfu¨rPhysikderTechnischenUniversita¨t
Mu¨nchenzurErlangungdesakademischenGradeseines

DoktorsderNaturwissenschaften(Dr.rer.nat.)

genehmigtenDissertation.

Vorsitzender:Univ.-Prof.Dr.L.Oberauer
Pru¨ferderDissertation:1.Univ.-Prof.Dr.A.Ibarra
2.Univ.-Prof.Dr.W.F.L.Hollik

DieDissertationwurdeam23.06.2009beiderTechnischenUniversita¨tMu¨ncheneinge-
reichtunddurchdieFakulta¨tfu¨rPhysikam20.07.2009angenommen.

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mmauSyr

TheresultspresentedinthisthesishaveinpartalreadybeenpublishedinRefs.[1,2,
3,4,5]listedoverleaf(pagev).WeconsiderphysicsbeyondtheStandardModelwhich
impliestheexistenceaoflong-livedelectromagneticallychargedmassiveparticlespecies
(CHAMP)whichwedenotebyX±.Wediscussindetailtheuniquesensitivitytheearly
Universeexhibitsonthemerepresenceandonthedecayofsuchaparticle.ACHAMP
canberealizedinsupersymmetric(SUSY)extensionsoftheStandardModel.Wecarry
outadetailedstudyofgravitino(Ge)darkmatterscenariosinwhichthelighterscalar
tau(stau,e1)isthelightestStandardModelsuperpartnersothate1=X.Wealso
provideathoroughinvestigationofthethermalfreeze-outprocessofe1.
Thethesisisdividedintothreeparts:
PartI:Inthispartweconsideragenericbutweak-scaleCHAMP.InChapter1we
setthestageforthecominginvestigationsbyshortlyreviewingtheframeworkofBig
BangNucleosynthesis(BBN),byworkingoutthetypicalCHAMPfreeze-outabundance,
andbyreviewingthestringentconstraintsarisingfromsuchadecayingcomponent
during/afterBBN.WealsotakeacriticallookattheBBNconstraintsarisingfrom
thehadronicdecaymodesofanarbitraryexotic.Inparticular,wedeveloponarened
treatmentoftheCoulombstoppingmechanismofchargedhadrons.
InChapter2wediscussthephysicswhichemergeswhenthelightelementsfusedin
BBNarecapturedbyXatthetimeofprimordialnucleosynthesis.Sincetheassociated,
moststrikingeectswereonlydiscoveredrecently,weprovideadetailedexpositionof
thetopic.Inparticular,weexplicitlyshowhowtoobtaintheratesforboundstate
formationwhichcarryanitechargeradiuscorrectionofthenucleus.Intheremainder
ofthischapter,whichisbasedon[4],wefocusonthecatalyticproductionof6Liand
9Be.There,wealsodiscusstheissueofapotentiallate-timecatalysisduetoproton-
CHAMPboundstates.UponsolutionofthefullsetofBoltzmannequationsweobtain
stringentconstraintsontheprimordialpresenceoflong-livedXfromoverproduction
of6Li.Moreover,settinganupperlimitontheabundanceofprimordial9Beallowsus

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toconstrainthisscenarioalsofromcatalytic9Beproduction.
PartII:ThesecondpartisdevotedtoscenariosinwhichGeisthelightestsupersym-
metricparticle(LSP)ande1isthenext-to-lightestSUSYparticle(NLSP).InChapter3
wefocusonthegravitinoLSPasadarkmattercandidate.Werecollecttheresultson
thermalgravitinoproduction,considerexplicitlythepost-inationaryreheatingprocess,
andobtainanupdateontheupperboundonthereheatingtemperatureoftheUniverse
fromthermalproduction.
InChapter4wethenfocusongravitinodarkmatterscenariosinwhiche1isthe
NLSP.Thischapterresemblesmanyoftheresultsoftheresearchpapers[1,2,3,4].We
constrainthegravitino-stauscenariobyincorporatingtheBBNboundsfrome1-decays
previouslyobtainedintheliterature.Inaddition,theconcreterealizationofthelong-
livedCHAMPscenarioallowsustoemployourresultsonthecatalyticproductionof
9Beand6Li.IntheframeworkoftheconstrainedminimalsupersymmetricStandard
Model(CMSSM)ae1NLSPcanbenaturallyaccommodated.There,weshowthatthe
novelcatalyticeectsseverelyconstrainthereheatingtemperatureoftheUniverseand
potentiallyimplyveryheavysuperparticlemassspectrawhichwillbehardtoprobeat
theupcomingLargeHadronCollider(LHC)experiments.Wealsoconsiderexplicitly
thepossibilityofanon-standardcosmologicalevolutionandcheckfortheviabilityof
thermalleptogenesis.
PartIII:Chapter5constitutesthenalpartofthisthesisandisbasedon[5].There,
wetakeanin-depthlookintothechemicaldecouplingprocessofthelong-livede1from
theprimordialplasma.Thequantityofinterestisthethermalfreeze-outabundanceof
thestau.WeidentifyitsdependenceonthecrucialSUSYparametersandalsoshow
thatitsensitivelydependsonthedetailsoftheHiggssector.Stauannihilationintonal
stateHiggsesaswellasresonantannihilationviatheheavyCPevenHiggsbosoncan
substantiallydepletethedecouplingyield.Remarkably,wendthesefeaturesarealready
realizedintheCMSSM.Inthoseregionsoftheparameterspaceeventhemostrestrictive
boundsfromthethermalcatalysisofBBNreactionscanpotentiallyberespected.We
discusstheimplicationsforthegravitino-stauscenario.

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Theresultsobtainedinthisthesishaveinpartalreadybeenpublishedinthefollowing
references:

[1]ConstraintsontheReheatingTemperaturein
GravitinoDarkMatterScenarios
J.PradlerandF.D.Steen
Phys.Lett.B648,224(2007)[arXiv:hep-ph/0612291]

[2]ImplicationsofCatalyzedBBNintheCMSSMwith
GravitinoDarkMatter
J.PradlerandF.D.Steen
Phys.Lett.B666,181(2008)[arXiv:0710.2213]

[3]CBBNintheCMSSM
J.PradlerandF.D.Steen
Eur.Phys.J.C56,287(2008)[arXiv:0710.4548]

[4]ConstraintsonSupersymmetricModelsfromCatalytic
PrimordialNucleosynthesisofBeryllium
M.Pospelov,J.Pradler,andF.D.Steen
JCAP0811,020(2008)[arXiv:0807.4287]

[5]ThermalRelicAbundancesofLong-LivedStaus
J.PradlerandF.D.Steen
Nucl.Phys.B809,318(2009)[arXiv:0808.2462]

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Acknowledgements

IwouldrstliketoexpressmygratitudetowardsmyresearchadvisorFrankDaniel
SteenattheMaxPlanckInstituteforPhysics(MPI)forhiscontinuoussupport,col-
laboration,andforthemanyinterestingdiscussionswehad.Ifurtherthankhimforthe
coordinationoftheInternationalMaxPlanckResearchSchoolfromwhereIalsohave
receivedmyfunding.IamthankfultotheMPIforprovidinganoptimalplacetowork,
inparticular,tothesecretaryRositaJurgeleitforherfriendlyhelpandtoThomasHahn
forhiscomputersupport.
IwouldliketothankAlejandroIbarraforbeingmyocialadvisorattheTechnical
UniversityMunichandthusforprovidingtheacademicframeworktomyPhDstudies.
Forhissupport,advice,andforholdingtogethertheenjoyableatmosphereintheMPI
“AstroparticleGroup”IamgratefultoGeorgRaelt.
ManyinsightsoftherstpartIowetoMaximPospelovwhomIalsowouldliketothank
forhisinvitationtotheUniversityofVictoria.IamgratefultoGarySteigmanforhis
friendlyexplanationsduringhisvisitinMunich.SimonEidelman,TilmanPlehnand
StefanHofmannIwantthankfortheirgeneraladvice.
ManythankstothefriendswhichIhadthechancetomeetattheMPI,inparticular,
toSteveBlanchet,KoushikDutta,FlorianHahn-Woernle,MaxHuber,andFelixRust.
FortheirfriendshipIamalsomostgratefultoUlrichMattandErikHo¨rtnagl.
Iamdeeplyindebtedtomyfamily,foremosttomyparents,fortheirunconditional
loveandsupportandtoIrinaBavykinaforallherunderstanding,encouragement,and
patienceoverthelastthreeyears.

TothememoryofFlorianKunz.

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Contents

Summary

Acknowledgements

IBBNwithalong-livedCHAMP

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1

1BBNandparticledecays3
1.1PrimordialnucleosynthesisafterWMAP...................3
1.2BBNasaprobeforNewPhysics.......................4
1.3TypicalCHAMPabundances.........................7
1.4ParticledecaysduringBBN..........................11
1.5AcriticallookathadronicconstraintsforT.100keV...........14
1.5.1Energytransferinbinarycollisions..................15
1.5.2Hadron-electronscattering.......................17
1.5.3Cutoconsiderationsforchargedparticles..............19
1.5.4DiscussiononCoulombstopping...................22
1.ALorentztransformations............................25

2BoundstatesandcatalysisofBBN27
2.1Basicboundstateproperties.........................27
2.2Wavefunctionsoftherelativemotion....................29
2.2.1Discretespectrum...........................30
2.2.2Continuousspectrum..........................34

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2.3Formationofboundstates...........................37
2.3.1Photo-dissociationandrecombinationcrosssection.........39
2.4Nuclearreactionswithboundstatesandtheircatalysis...........41
2.4.1Catalysisof6Liproduction......................43
2.4.2Catalysisof9Beproduction......................46
2.5Chargeexchangereactionsandlatetimecatalysis.............49
2.5.1Relaxationafterchargeexchange...................55
2.6ConstraintsontheXlifetimeandabundance...............57

IIThegravitino-stauscenario

16

3Gravitinosasaprobefortheearliestepochs63
3.1Thegravitino-stauscenario..........................63
3.2Supergravityandbasicpropertiesofthegravitino..............64
3.3Thermalgravitinoproductionandreheating.................65
3.3.1Reheatingphase............................69
3.4ConstraintsonT...............................71
R

4ThestauastheNLSP75
4.1Genericconstraintsonthegravitino-stauscenario..............75
4.2Thegravitino-stauscenariointheCMSSM.................82
4.2.1Lowerlimitonm..........................83
2/14.2.2UpperboundonT..........................86
R4.2.3ExemplaryparameterscansintheCMSSM.............87
4.2.4Late-timeentropyproduction.....................93
4.2.5Viabilityofthermalleptogenesis...................97

IIIThelong-livedstauasathermalrelic

5Thermalrelicstauabundances

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103

Contentsxi

5.1Staumixingandmasseigenstates.......................105

5.2Calculationofthethermalrelicstauabundance...............106

5.3Dependenceofstauannihilationonthestaumixingangle.........110

5.4Eectsoflargestau-Higgscouplings.....................115

5.5Resonantstauannihilation..........................121

5.6Ontheviabilityofae1-e1asymmetry....................123
5.7ExceptionallysmallabundanceswithintheCMSSM............124
5.8Prospectsforcolliderphenomenology.....................129

5.9Implicationsforgravitinodarkmatterscenarios...............131

Conclusions

References

135

141

ListofFigures

1.1ElectromagneticandhadronicBBNconstraints...............
1.2Stoppingpowerofachargedhadron.....................

42.1Radialwavefunctionsfor(HeX)......................
82.21Sradialwavefunctionsfor(BeX).....................
2.3Continuumwavefunctions...........................
62.4CBBNevolutionofLi.............................
92.5CBBNevolutionofBe............................
2.6Protonpotentialforchargeexchange.....................
2.7(pX)abundanceafterchargeexchange...................
2.8Beobservationsinhalostars.........................
2.9ContourplotofCBBNyields.........................

3.1Gravitinoyieldfromthermalproduction...................
3.2Reheatingphase................................
3.3UpperboundonT..............................
R

4.1Genericconstraintsonthegravitino-stauscenario..............
64.2UpperboundonLi..............................
4.3NLSPyieldcontours..............................
4.4CMSSMplanesfortan=10.........................
4.5CMSSMplanesfortan=30.........................
4.6Latetimeentropyproduction.........................

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2132

134353448405458595

760727

774898092959

7.4

8.4

1.52.53.54.5

.55

6.5

7.5

8.5

ListofFiguresxiii

EntropyproductionbeforeandafterNLSPdecoupling...........98

Entropyproductionandtheviabilityofleptogenesis............100

SchematicoverviewofthecalculationofYe.................109
Dependenciesofmassesandannihilationcrosssectionsone.......112
GeneraldependenceofYeone........................114
EnhancedannihilationintolightHiggses...................118

EnhancedannihilationintoheavyHiggses..................119

Resonantstauannihilation..........................122

EnhancedannihilationintheCMSSMfortan