Effective Field Theories PDF
Preview Effective Field Theories
EffectiveFieldTheories Effectivefieldtheoriesareawidelyusedtoolinvariousbranchesofphysics.Thisbook provides a comprehensive discussion of the foundations and fundamentals of effec- tivefieldtheoriesofquantumchromodynamics(QCD)inthelightquarksectorwith anemphasisonthestudyofflavorsymmetriesandtheirrealizations.Inthiscontext, different types of effective field theories pertaining to various energy scales are con- sideredandselectedapplicationsaredevised.Thistextalsocoverstheformulationof effective field theories in a finite volume and its application in the analysis of lattice QCDdata.EffectiveFieldTheoriesisintendedforgraduatestudentsandresearchers inparticlephysics,hadronphysicsandnuclearphysics.Exercisesareincludedtohelp readersdeepentheirunderstandingofthetopicsdiscussedthroughout,withsolutions availabletolecturers. Ulf-G. Meißner is Professor in Theoretical Physics at Bonn University, Germany, and Director at the Institute for Advanced Simulation, Forschungszentrum Jülich, Germany. His research focuses on strong interaction physics, especially nuclear and particle physics. He was awarded the Lise Meitner Prize of the European Physical SocietyandtheDistinguishedScientistAwardoftheChineseAcademyofSciences. AkakiRusetsky works at the Helmholtz Institute for Radiation and Nuclear Physics at BonnUniversity,Germany.Hisresearchfocusesonstronginteractionphysics,effective fieldtheoriesandlatticefieldtheories.HereceivedtheVisitingScientistawardunder thePresident’sInternationalFellowshipInitiativeoftheChineseAcademyofSciences. Published online by Cambridge University Press Published online by Cambridge University Press Effective Field Theories ULF-G.MEIßNER BonnUniversity and ForschungszentrumJülich AKAKIRUSETSKY BonnUniversity Published online by Cambridge University Press UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom OneLibertyPlaza,20thFloor,NewYork,NY10006,USA 477WilliamstownRoad,PortMelbourne,VIC3207,Australia 314–321,3rdFloor,Plot3,SplendorForum,JasolaDistrictCentre,NewDelhi–110025,India 103PenangRoad,#05–06/07,VisioncrestCommercial,Singapore238467 CambridgeUniversityPressispartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learning,andresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781108476980 DOI:10.1017/9781108689038 ©CambridgeUniversityPress2022 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2022 AcataloguerecordforthispublicationisavailablefromtheBritishLibrary. ISBN978-1-108-47698-0Hardback Additionalresourcesforthispublicationatwww.cambridge.org/effectivefieldtheories. CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof URLsforexternalorthird-partyinternetwebsitesreferredtointhispublication anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate. Published online by Cambridge University Press Contents Preface pageix 1 BasicConcepts 1 1.1 Introduction 1 1.2 Warm-up:EffectiveTheoryforScatteringonthePotentialWell 2 1.3 IntegratingoutaHeavyScale:aModelatTreeLevel 13 1.4 TheModelatTreeLevel:Path-IntegralFormalism 17 1.5 EquationsofMotionandFieldRedefinitions 18 1.6 LightParticleMassatOneLoop 23 1.7 MatchingoftheQuarticCouplingatOneLoop 28 1.8 DependenceoftheEffectiveCouplingsontheHeavyMass 35 1.9 DecouplinginDifferentRenormalizationSchemes 38 1.10 FloatingCutoff 42 1.11 EmergentSymmetries 46 1.12 Trivialityoftheϕ4-Theory 52 1.13 RelevantDegreesofFreedomatLowMomenta 59 1.14 ConstructionPrinciplesofanEFT 60 1.15 LiteratureGuide 61 References 62 2 NonrelativisticEffectiveTheories 66 2.1 Introduction 66 2.2 Foldy–WouthuysenTransformation 67 2.3 ConstructionoftheNonrelativisticLagrangianforaScalarField 73 2.4 Symmetries 76 2.5 PerturbationTheory,MatchingandtheEffectiveRangeExpansion 81 2.6 Nucleon–NucleonScattering:theCaseofaLargeScatteringLength 91 2.7 RelativisticKinematics:Two-ParticleProcesses 94 2.8 CuspsinThree-ParticleDecays 99 2.9 DimersandtheFaddeevEquation 105 2.10 EfimovEffect 116 2.11 IncludingVirtualPhotonsinNonrelativisticTheories 121 2.12 SpectrumandDecaysofHadronicAtoms 143 2.13 LiteratureGuide 153 References 154 v Published online by Cambridge University Press vi Contents 3 Symmetries 161 3.1 Introduction 161 3.2 Euler–HeisenbergLagrangian 162 3.3 InteractionofLong-WavelengthPhotonswithAtoms 169 3.4 QCDFactsheet 170 3.5 ChiralSymmetryinQCD 174 3.6 WardIdentities 176 3.7 TheTriangleAnomaly 180 3.8 Anomalies:Point-SplitTechnique 188 3.9 FujikawaDeterminant 192 3.10 Non-AbelianAnomalies 197 3.11 Atiyah–SingerIndexTheorem 204 3.12 ChiralSymmetryandAnomaliesontheLattice 205 3.13 TraceAnomaly,DimensionalTransmutationandtheProtonMass 219 3.14 Low-EnergySpectrumofQCD:GoldstoneTheorem 224 3.15 Vafa–WittenTheorem 236 3.16 QuarkMassDependenceofHadronMasses 238 3.17 Soft-PionTechnique 242 3.18 Witten–VenezianoFormula 245 3.19 AnomalyMatching 247 3.20 SymmetriesandSpectrumof(Partially)QuenchedQCD 252 3.21 LiteratureGuide 256 References 257 4 Low-EnergyEffectiveFieldTheoryofQCD 263 4.1 Introduction 263 4.2 TheS-MatrixofCompositeParticles 265 4.3 Weinberg’sTheorem 275 4.4 Theσ-Model 277 4.5 Theσ-ModelwithNucleons 291 4.6 NonlinearRealizationofChiralSymmetry 299 4.7 ChiralPerturbationTheoryintheMesonSector:Lagrangianand GeneratingFunctional 304 4.8 Tree-LevelCalculations 309 4.9 ChiralPerturbationTheoryatOneLoop 316 4.10 ChiralLagrangianwithNucleons 337 4.11 ConsistentFormulationsofBaryonChiralPerturbationTheory 346 4.12 TheoreticalUncertainties 370 4.13 TheMeaningofLow-EnergyTheorems 373 4.14 IncludingElectromagneticandWeakInteractions 378 4.15 SplittingoftheStrongandtheElectromagneticInteractions 402 4.16 Wess–Zumino–WittenEffectiveAction 408 4.17 Theη0-MesonandLarge-NcChPT 413 4.18 InvarianceoftheChPTLagrangian 421 Published online by Cambridge University Press vii Contents 4.19 PartiallyQuenchedChPT 424 4.20 Theθ-Term,StrongCPViolationandAxions 431 4.21 LiteratureGuide 448 References 450 5 EffectiveTheoriesinaFiniteVolume 466 5.1 Introduction 466 5.2 TheMassofaStableParticleinaFiniteVolume 467 5.3 ScatteringStates:theLüscherEquation 476 5.4 MovingFrames,AngularMomentumandSpin 487 5.5 TwistedBoundaryConditions 499 5.6 Two-ParticleDecays 506 5.7 MultiparticleSystems:PerturbativeExpansionfortheEnergyLevels 513 5.8 Three-ParticleQuantizationCondition 522 5.9 Three-ParticleDecaysontheLattice 528 5.10 PhotonsinaFiniteVolume 533 5.11 TheChiralLimitinaFiniteVolume 542 5.12 LiteratureGuide 556 References 558 6 Exercises 565 AppendixA NotationsandConventions 599 A.1UnitsandMetric 599 A.2PauliMatrices 600 A.3Gell–MannMatrices 601 A.4DiracMatrices 602 A.5IsospinandSU(3)FlavorSymmetry 602 A.6SphericalHarmonics 603 A.7Clebsch–GordanCoefficients 604 A.8BesselFunctions 605 Index 606 Published online by Cambridge University Press Published online by Cambridge University Press Preface Effectivefieldtheories(EFTs)havebecomeapremiertoolinmanybranchesoftheoret- icalphysics,inparticularinnuclear,hadronicandparticlephysics.Itistheaimofthis book to present the foundations and applications of such an approach to the strong interactionswithintheverysuccessfulStandardModelofparticlephysics.Although wecoverawidevarietyoftopics,weconcentrateonapplicationsinhadronicandpar- ticlephysics.Furthermore,ouraimisnottoconsiderallpossibleEFTsinthesefields, but rather to discuss the physics related to the many fascinating phenomena emerg- ing in the light quark sector of Quantum Chromodynamics. We stress that we put a strongemphasisonthebasicsandthefoundationsoftheseEFTsandonlyworkout a few assorted applications. All this is based on a thorough discussion of the perti- nentsymmetriesandtheirrealizations,whichisonefundamentalcornerstoneofany EFT.NotableomissionsareheavyquarkEFTs,thewidefieldofnuclearphysics(with theexceptionoftheso-calledpionlessnuclearEFTcoveredhere)andalsotheStand- ardModelEFT,whichhasgainedprominenceinrecentyears.Wheneverpossible,we refer to appropriate books, reviews or papers. In any case, this book should enable the reader to work out an appropriately tailored EFT for any physical system under consideration.Furthermore,whenevernecessary,weexplaintheunderlyingquantum fieldtheoretical(QFT)toolsthatarerequiredtomasterEFTs.However,wehavenot madeanyattempttoprovideaself-containedQFTbook,asmanyexcellentbookson thissubjectareavailable. Thegenesisofthisbookisquiteinteresting.Itwasoriginallystartedbyoneofthe authors(UGM)atForschungszentrumJülichmorethantwodecadesagobutcametoa haltwhenhemovedtoBonnUniversityandtookoveranumberofadministrativeposi- tions.Inaway,thiswasfortunate,asovertheyearswefrequentlylecturedtogetheron coursesinTheoreticalHadronPhysics,AdvancedTheoreticalHadronPhysics,Effec- tiveFieldTheoriesandthelike,whichallowedustosharpenourviewonthesetopics, ultimatelyleadingtothebookinitspresentform. Many colleagues have contributed to our understanding of the topics discussed here, in particular Véronique Bernard, Bugra Borasoy, Gilberto Colangelo, Michael Döring, Gerhard Ecker, Evgeny Epelbaum, Jambul Gegelia, Feng-Kun Guo, Hans- WernerHammer,MartinHoferichter,BarryHolstein,MishaIvanov,NorbertKaiser, Joachim Kambor, Bastian Kubis, Valery Lyubovitskij, Maxim Mai, Ferenc Nieder- mayer, Jin-Yi Pang, Fernando Romero-López, Jacobo Ruiz de Elvira, Chien-Yeah SengandJia-JunWu.WeareespeciallygratefultoJürgGasserandHeiriLeutwyler forsharingtheirdeepinsights. ix https://doi.org/10.1017/9781108689038.001 Published online by Cambridge University Press x Preface WeespeciallythankFeng-Kun-GuoandBernardMetschforacarefulreadingofthe manuscript,Hans-WernerHammerforusefulremarksonEfimovphysicsandFabian Müllerforhelpwiththeexercises.Theyshouldnot,however,bemaderesponsiblefor anyerror. We are grateful for the support and patience of Simon Capelin, Sarah Lambert, Henry Cockburn, Vince Higgs and Arya Thampi from Cambridge University Press whowereinstrumentalinmakingthisbookpossible. WearealsogratefulforthehospitalityextendedbytheInstituteforTheoreticalPhys- icsandtheInstituteofHigh-EnergyPhysicsoftheChineseAcademyofSciences,the SchoolofPhysicsofPekingUniversityinBeijing,China,andtheInstituteforNuclear TheoryatSeattle,Washington,USA,wherepartsofthisbookwerewritten. This book could not have been completed without generous funding from the Deutsche Forschungsgemeinschaft, the Chinese Academy of Sciences, Volkswagen- Stiftung,EuropeanResearchCouncilandShotaRustaveliNationalScienceFounda- tionofGeorgia. https://doi.org/10.1017/9781108689038.001 Published online by Cambridge University Press
The list of books you might like
