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Describingthefundamentaltheoryofparticlephysicsanditsapplications,this bookprovidesadetailedaccountoftheStandardModel,focusingontechniques thatcanproduceinformationaboutrealobservedphenomena.
ThebookbeginswithapedagogicaccountoftheStandardModel,introducing essentialtechniquessuchaseffectivefieldtheoryandpath-integralmethods.Itthen focusesontheuseoftheStandardModelinthecalculationofphysicalproperties ofparticles.Rigorousmethodsareemphasized,butotherusefulmodelsarealso described.
Thissecondeditionhasbeenupdatedtoincluderecenttheoreticalandexperimentaladvances,suchasthediscoveryoftheHiggsboson.Anewchapteris devotedtothetheoreticalandexperimentalunderstandingofneutrinos,andmajor advancesin CP violationandelectroweakphysicshavebeengivenamoderntreatment.Thisbookisvaluabletograduatestudentsandresearchersinparticlephysics, nuclearphysicsandrelatedfields.
This title, first published in 2014, has been reissued as an Open Access publication on Cambridge Core.
JohnF.Donoghue isDistinguishedProfessorintheDepartmentofPhysics, UniversityofMassachusetts.Hisresearchspansparticlephysics,quantumfield theoryandgeneralrelativity.HeisaFellowoftheAmericanPhysicalSociety.
EugeneGolowich isEmeritusProfessorintheDepartmentofPhysics, UniversityofMassachusetts.Hisresearchhasfocusedonparticletheoryandphenomenology.HeisaFellowoftheAmericanPhysicalSocietyandisarecipientof theCollegeOutstandingTeacherawardfromtheUniversityofMassachusetts.
BarryR.Holstein isEmeritusProfessorintheDepartmentofPhysics, UniversityofMassachusetts.Hisresearchisintheoverlapareaofparticleand nucleartheory.AFellowoftheAmericanPhysicalSociety,heisalsotheeditor of AnnualReviewsofNuclearandParticleScience andisalongtimeconsulting editorofthe AmericanJournalofPhysics.
CAMBRIDGEMONOGRAPHSONPARTICLEPHYSICS,NUCLEAR PHYSICSANDCOSMOLOGY
GeneralEditors:T.Ericson,P.V.Landshoff
Availabletitlesinthisseries:
3.E.LeaderandE.Predazzi: AnIntroductiontoGaugeTheoriesandModernParticlePhysics, Volume1:ElectroweakInteractions,the‘NewParticles’andthePartonModel
4.E.LeaderandE.Predazzi: AnIntroductiontoGaugeTheoriesandModernParticlePhysics, Volume2:CP-Violation,QCDandHardProcesses
6.H.GrosseandA.Martin: ParticlePhysicsandtheSchrödingerEquation
7.B.Andersson: TheLundModel
8.R.K.Ellis,W.J.StirlingandB.R.Webber: QCDandColliderPhysics
10.A.V.ManoharandM.B.Wise: HeavyQuarkPhysics
11.R.Frühwirth,M.Regler,R.K.Bock,H.GroteandD.Notz: DataAnalysisTechniquesfor High-EnergyPhysics,Secondedition
12.D.Green: ThePhysicsofParticleDetectors
13.V.N.GribovandJ.Nyiri: QuantumElectrodynamics
14.K.Winter(ed.): NeutrinoPhysics,Secondedition
15.E.Leader: SpininParticlePhysics
16.J.D.Walecka: ElectronScatteringforNuclearandNucleonStructure
17.S.Narison: QCDasaTheoryofHadrons
18.J.F.LetessierandJ.Rafelski: HadronsandQuark-GluonPlasma
19.ADonnachie,H.G.Dosch,P.V.LandshoffandO.Nachtmann: PomeronPhysicsandQCD
20.A.Hofmann: ThePhysicsofSynchrotronRadiation
21.J.B.KogutandM.A.Stephanov: ThePhasesofQuantumChromodynamics
22.D.Green: High PT PhysicsatHadronColliders
23.K.Yagi,T.HatsudaandY.Miake: Quark-GluonPlasma
24.D.M.BrinkandR.A.Broglia: NuclearSuperfluidity
25.F.E.Close,A.DonnachieandG.Shaw: ElectromagneticInteractionsandHadronicStructure
26.C.GrupenandB.A.Schwartz: ParticleDetectors,Secondedition
27.V.Gribov: StrongInteractionsofHadronsatHighEnergies
28.I.I.BigiandA.I.Sanda: CPViolation,Secondedition
29.P.JaranowskiandA.Królak: AnalysisofGravitational-WaveData
30.B.L.Ioffe,V.S.FadinandL.N.Lipatov: QuantumChromodynamics:Perturbativeand NonperturbativeAspects
31.J.M.Cornwall,J.PapavassiliouandD.Binosi: ThePinchTechniqueanditsApplicationsto Non-AbelianGaugeTheories
32.J.Collins: FoundationsofPerturbativeQCD
33.Y.V.KovchegovandE.Levin: QuantumChromodynamicsatHighEnergy
34.J.RakandM.J.Tannenbaum: High-pT PhysicsintheHeavyIonEra
35.J.F.Donoghue,E.GolowichandB.R.Holstein: DynamicsoftheStandardModel, Secondedition
DYNAMICSOFTHESTANDARD MODEL secondedition
JOHNF.DONOGHUE UniversityofMassachusetts
EUGENEGOLOWICH UniversityofMassachusetts
BARRYR.HOLSTEIN UniversityofMassachusetts
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DOI: 10.1017/9781009291033
© John F. Donoghue, Eugene Golowich and Barry R. Holstein 2022
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ToLincolnWolfenstein
TheStandardModelisthebasisofourunderstandingofthefundamentalinteractions.Atthepresenttime,itremainsinexcellentagreementwithexperiment.It isclearthatanyfurtherprogressinthefieldwillneedtobuildonasolidunderstandingoftheStandardModel.Sincethefirsteditionwaswrittenin1992there havebeenmajordiscoveriesinneutrinophysics,in CP violation,thediscoveries ofthetopquarkandtheHiggsboson,andadramaticincreaseinprecisioninboth electroweakphysicsandin QCD.Wefeelthatthepresentisagoodmomentto updateourbook,astheStandardModelseemslargelycomplete.
Theopportunitytoreviseourbookatthistimehasalsoenabledustosurveythe progresssincethefirsteditionwenttoprint.Besidestheexperimentaldiscoveries thathavetakenplaceduringthesetwodecades,wehavebeenimpressedbythe increaseintheoreticalsophistication.Manyofthetopicswhichwerenovelatthe timeofthefirsteditionhavenowbeenextensivelydeveloped.Perturbativetreatmentshaveprogressedtohigherordersandnewtechniqueshavebeendeveloped. Tocoverallofthesecompletelywouldrequiretheexpansionofmanychapters intobook-lengthtreatments.Indeed,inmanycases,entirenewbooksdedicatedto specializedtopicshavebeenpublished.1 Ourrevisionismeantasacoherentpedagogicintroductiontothesetopics,providingthereaderwiththebasicbackground topursuemoredetailedstudieswhenappropriate.
TherehasalsobeengreatprogressonthepossibleNewPhysicswhichcould emergebeyondtheStandardModel–darkmatteranddarkenergy,grandunification,supersymmetry,extradimensions,etc.Weareatamomentwherethisphysics couldemergeinthenextroundofexperimentsattheLargeHadronCollider(LHC) aswellasinprecisionmeasurementsattheintensityfrontier.Welookforwardwith greatanticipationtothenewdiscoveriesofthenextdecade.
1 Forexample,see[BaP99,Be00,BiS00,EISW03,FuS04,Gr04,IoFL10,La10,Ma04,MaW07,Co11]
Wethankourcolleaguesandstudentsforfeedbackaboutthefirsteditionofthis book.Alistoferrataforthesecondeditionwillbemaintainedatthehomepage ofJohnDonoghueattheUniversityofMassachusetts,Amherst.Weencourage readerswhofindanymistakesinthiseditiontosubmitthemtoProfessorDonoghue atdonoghue@physics.umass.edu.
Fromtheprefacetothefirstedition TheStandardModellagrangian LSM embodiesourknowledgeofthestrongand electroweakinteractions.Itcontainsasfundamentaldegreesoffreedomthespin one-halfquarksandleptons,thespinonegaugebosons,andthespinzeroHiggs fields.Symmetryplaysthecentralroleindeterminingitsdynamicalstructure.The lagrangianexhibitsinvarianceunder SU(3) gaugetransformationsforthestrong interactionsandunder SU(2) × U(1) gaugetransformationsfortheelectroweak interactions.Despitethepresenceof(alltoo)manyinputparameters,itisamathematicalconstructionofconsiderablepredictivepower.
Therearebooksavailablewhichdescribeindetailtheconstructionof LSM and itsquantization,andwhichdealwithaspectsofsymmetrybreaking.Wefeltthe needforabookdescribingthenextsteps,how LSM isconnectedtotheobservable physicsoftherealworld.Thereareaconsiderablevarietyoftechniques,ofdifferingrigor,whichareusedbyparticlephysiciststoaccomplishthis.Wepresenthere thosewhichhavebecomeindispensabletools.Inaddition,weattempttoconvey theinsightsand‘conventionalwisdom’whichhavebeendevelopedthroughoutthe field.Thisbookcanonlybeanintroductiontotherichescontainedinthesubject, hopefullyprovidingafoundationandamotivationforfurtherexplorationbyits readers.
Inwritingthebook,wehavebecomealltoopainfullyawarethateachtopic, indeedeachspecificreaction,hasanextensiveliteratureandphenomenology,and thatthereisalimitationtothedepththatcanbepresentedcompactly.Weemphasizeapplications,notfundamentals,ofquantumfieldtheory.Proofsofformaltopicslikerenormalizabilityorthequantizationofgaugefieldsarelefttootherbooks, asisthetopicofpartonphenomenology.Inaddition,thestudybycomputerof latticefieldtheoryisanextensiveandrapidlychangingdiscipline,whichwedo notattempttocover.Althoughitwouldbetemptingtodiscusssomeofthemany stimulatingideas,amongthemsupersymmetry,grandunification,andstringtheory,whichattempttodescribephysicsbeyondtheStandardModel,limitationsof spacepreventusfromdoingso.
Althoughthisbookbeginsgently,wedoassumethatthereaderalreadyhassome familiaritywithquantumfieldtheory.Asanaidtothosewholackfamiliaritywith path-integralmethods,weincludeapresentation,inAppendixA,whichtreatsthis
subjectinanintroductorymanner.Inaddition,weassumeaknowledgeofthebasic phenomenologyofparticlephysics.
Wehaveconstructedthematerialtobeofusetoawidespectrumofreaders whoareinvolvedwiththephysicsofelementaryparticles.Certainlyitcontains materialofinteresttoboththeoristandexperimentalistalike.Giventhetrendto incorporatetheStandardModelinthestudyofnuclei,weexpectthebooktobe ofusetothenuclearphysicscommunityaswell.Eventhestudentbeingtrainedin themathematicsofstringtheorywouldbewelladvisedtolearntherolethatsigma modelsplayinparticletheory.
Thisisagoodplacetostresssomeconventionsemployedinthisbook.Chaptersareidentifiedwithromannumerals.Incross-referencingequations,weinclude thechapternumberifthereferencedequationisinachapterdifferentfromthe pointofcitation.TheMinkowskimetricis gμν = diag {1, 1, 1, 1}.Throughout,weusethenaturalunits = c = 1,andchoose e> 0sothattheelectronhaselectriccharge e .WeemployrationalizedHeaviside–Lorentzunits,and thefine-structureconstantisrelatedtothechargevia α = e 2 /4π .Thecouplingconstantsforthe SU(3)c × SU(2)L × U(1) gaugestructureoftheStandardModel aredenotedrespectivelyas g3 ,g2 ,g1 ,andweemploycoupling-constantphase conventionsanalogoustoelectromagnetismfortheotherabelianandnonabelian covariantderivativesoftheStandardModel.Thechiralprojectionoperatorforlefthandedmasslessspinone-halfparticlesis (1 + γ5 )/2,andinanalyzingsystemsin d dimensions,weemploytheparameter ≡ (4 d)/2.Whatismeantbythe‘Fermi constant’isdiscussedinSect.V–2.
Amherst,MA,2013
I InputstotheStandardModel ThisbookisabouttheStandardModelofelementaryparticlephysics.Ifweset thebeginningofthemoderneraofparticlephysicsin1947,theyearthepionwas discovered,thentheensuingyearsofresearchhaverevealedtheexistenceofaconsistent,self-containedlayerofreality.Theenergyrangewhichdefinesthislayerof realityextendsuptoabout1TeVor,intermsoflength,downtodistancesoforder 10 17 cm.TheStandardModelisafield-theoreticdescriptionofstrongandelectroweakinteractionsattheseenergies.Itrequirestheinputofasmanyas28independentparameters.1 TheseparametersarenotexplainedbytheStandardModel; theirpresenceimpliestheneedforanunderstandingofNatureatanevendeeper level.Nonetheless,processesdescribedbytheStandardModelpossessaremarkableinsulationfromsignalsofsuchNewPhysics.Althoughthestronginteractions remainacalculationalchallenge,theStandardModel(generalizedfromitsoriginal formtoincludeneutrinomass)wouldappeartohavesufficientcontenttodescribe allexistingdata.2 Thusfar,itisatheoreticalstructurewhichhasworkedsplendidly.
I–1Quarksandleptons TheStandardModelisan SU(3) × SU(2) × U(1) gaugetheorywhichisspontaneouslybrokenbytheHiggspotential.TableI–1displaysmassdeterminations [RPP12]ofthe Z 0 and W ± gaugebosons,theHiggsboson H 0 ,andtheexisting masslimitonthephoton γ
IntheStandardModel,thefundamentalfermionicconstitutentsofmatterarethe quarksandtheleptons.Quarks,butnotleptons,engageinthestronginteractions asaconsequenceoftheircolorcharge.Eachquarkandleptonhasspinone-half.
1 Therearesixleptonmasses,sixquarkmasses,threegaugecouplingconstants,threequark-mixingangles andonecomplexphase,threeneutrino-mixinganglesandasmanyasthreecomplexphases,aHiggsmass andquarticcouplingconstant,andthe QCD vacuumangle.
2 Admittedly,atthistimethesourcesof darkmatter andof darkenergy areunknown.
Particle
TableI–1. Bosonmasses.
Mass(GeV/c 2 )
γ< 1 × 10 27
W ±
Z 0
H 0
80 385 ± 0 015
91.1876 ± 0.0021
126.0 ± 0.4
Collectively,theydisplayconventionalFermi–Diracstatistics.Noattemptismade intheStandardModeleithertoexplainthevarietyandnumberofquarksandleptonsortocomputeanyoftheirproperties.Thatis,theseparticlesaretakenatthis levelastrulyelementary.Thisisnotunreasonable.Thereisnoexperimentalevidenceforquarkorleptoncompositeness,suchasexcitedstatesorformfactors associatedwithintrinsicstructure.
Quarks Therearesixquarks,whichfallintotwoclassesaccordingtotheirelectricalcharge Q.The u,c,t quarkshave Q = 2e/3andthe d,s,b quarkshave Q =− e/3, where e istheelectricchargeoftheproton.The u,c,t and d,s,b quarks areeigenstatesofthehamiltonian(‘masseigenstates’).However,becausetheyare believedtobepermanentlyconfinedentities,somethoughtmustgointoproperly definingquarkmass.Indeed,severaldistinctdefinitionsarecommonlyused.We deferadiscussionofthisissueandsimplynotethatthevaluesinTableI–2provide
TableI–2. Thequarks.
FlavorMassa (GeV/c 2 )Charge I3
u(2.55+0 75 1 05 ) × 10 3 2e/31/20000
d(5.04+0 96 1 54 ) × 10 3 e/3 1/20000
s 0.105+0.025 0.035 e/30 1000
c 1.27+0.07 0.11 2e/300100
b 4.20+0 17 0 07 e/3000 10
t 173.4 ± 1.6 2e/300001
a The t -quarkmassisinferredfromtopquarkevents.Allothersaredeterminedin MS renormalization(cf.Sect.II–1)atscales mu,d,s (2GeV/c 2 ), mc (mc ) and mb (mb ) respectively.
TableI–3. Theleptons.
FlavorMass(GeV/c 2 )Charge Le Lμ Lτ
νe < 0.2 × 10 8
0100
e 5 10998928(11) × 10 4 e100
νμ < 1.9 × 10 4 0010
μ 0 1056583715(35) e010
ντ < 0 0182 0001
τ 1 77682(16) e001
anoverviewofthequarkmassspectrum.Ausefulbenchmarkforquarkmassesis theenergyscale QCD ( severalhundredMeV)associatedwiththeconfinement phenomenon.Relativeto QCD ,the u,d,s quarksarelight,the b,t quarksare heavy,andthe c quarkhasintermediatemass.Thedynamicalbehavioroflight quarksisdescribedbythechiralsymmetryofmasslessparticles(cf.Chap.VI) whereasheavyquarksareconstrainedbytheso-calledHeavyQuarkEffective Theory(cf.Sect.XIII–3).Eachquarkissaidtoconstituteaseparate flavor,i.e. sixquarkflavorsexistinNature.The s,c,b,t quarkscarryrespectivelythe quantumnumbersofstrangeness(S ),charm(C ),bottomness(B ),andtopness(T ).
The u,d quarksobeyan SU (2)symmetry(isospin)andaredistinguishedbythe three-componentofisospin(I3 ).Theflavorquantumnumbersofeachquarkare displayedinTableI–2.
Leptons Therearesixleptonswhichfallintotwocategoriesaccordingtotheirelectrical charge.Thechargedleptons e,μ,τ have Q =− e andtheneutrinos νe ,νμ ,ντ have Q = 0.Leptonsarealsoclassifiedintermsofthreeleptontypes:electron (νe ,e),muon (νμ ,μ),andtau (ντ ,τ).Thisfollowsfromthestructureofthecharged weakinteractions(cf.Sect.II–3)inwhichthesecharged-lepton/neutrinopairsare coupledto W ± gaugebosons.Associatedwitheachleptontypeisaleptonnumber Le ,Lμ ,Lτ .TableI–3summarizesleptonproperties.
Atthistime,thereisonlyincompleteknowledgeofneutrinomasses.Information onthemassparameters mνe ,mνμ ,mντ isobtainedfromtheirpresenceinvarious weaktransitionamplitudes.Forexample,thesinglebetadecayexperiment 3 H → 3 He + e + ν e issensitivetothemass mνe .Inlikemanner,oneconstrainsthemasses mνμ and mντ inprocessessuchas π + → μ+ + νμ and τ → 2π + π + + ντ respectively.ExistingboundsonthesemassesaredisplayedinTableI–3.
Itisknownexperimentallythatuponcreationtheneutrinos {να }≡ (νe .νμ ,ντ ) willnotpropagateindefinitelybutwillinsteadmixwitheachother.Thismeansthat thebasisofstates {να } cannotbeeigenstatesofthehamiltonian.Diagonalization oftheleptonichamiltonianiscarriedoutinSect.VI–2andyieldsthebasis {νi }≡ {ν1 ,ν2 ,ν3 } ofmasseigenstates.Informationontheneutrinomasseigenvalues m1 ,m2 ,m3 isobtainedfromneutrinooscillationexperimentsandcosmological studies.Oscillationexperiments(cf.Sects.VI–3,VI–4)aresensitivetosquaredmassdifferences.3 Throughoutthebook,weadheretothefollowingrelations,
Fromthecompilationin[RPP12],thesquared-massdifference | m2 32 | deduced fromthestudyofatmosphericandacceleratorneutrinosgives
whereasdatafromsolarandreactorneutrinosimplyasquared-massdifference roughly31timessmaller,
Thustheneutrinos ν1 and ν2 formaquasi-doublet.Onespeaksofa normal or inverted neutrinomassspectrum,respectively,forthecases4
Sincethelargestneutrinomass mlgst ,beit m2 or m3 ,cannotbelighterthanthe masssplittingofEq.(1.2),wehavethebound mlgst > 0.049eV.Finally,acombinationofcosmologicalinputscanbeemployedtoboundtheneutrinomasssum 3 i = 1 mi ,theprecisebounddependingonthechoseninputdataset.Inoneexample[deP etal.12],photometricredshiftsmeasuredfromalargegalaxysample,cosmicmicrowavebackground(CMB)dataandarecentdeterminationoftheHubble parameterareusedtoobtainthebound
whereasdatafromtheCMBcombinedwiththatfrombaryonacousticoscillations yields[Ad etal. (Planckcollab.)13]
AfurtherdiscussionoftheneutrinomassspectrumappearsinSect.VI–4.
3 Onlytwoofthemassdifferencescanbeindependent,so m2 12 + m2 23 + m2 31 = 0.
4 Thereisalsothepossibilityofa quasi-degenerate neutrinomassspectrum(m1 m2 m3 ),whichcanbe thoughtofasalimitingcaseofboththenormalandinvertedcasesinwhichtheindividualmassesare sufficientlylargetodwarfthe | m2 32 | splitting.
