Chiral QCD Baryon dynamics

arXiv:hep-ph/0007092v111Jul2000CHIRALQCD:BARYONDYNAMICS#1ULF-G.MEIßNERForschungszentrumJ¨ulich,Institutf¨urKernphysik(Theorie)D-52425J¨ulich,GermanyElectronicaddress:[e-mail]ofthechiralsymmetryofQCDforthestructureanddynamicsofthelow–lyingbaryons,withparticularemphasisonthenucleon.FZJ-IKP(TH)-2000-171AshortguidethroughthislongessayTherearemanyapproacheswhichrelatebaryonstructureandpropertiestoQCDinthenon–perturbativeregime,i.e.atenergies,wheretherunningcou-plingconstantαS(Q2)issufficientlylargetorenderconventionalperturba-tiontheorydoubtful.Inthisregime,quarksandgluonsareconfinedwithinhadrons.Inaddition,thelow–energydynamicsisseverelyconstrainedbythespontaneouslyandexplicitlybrokenchiralsymmetryofQCD.Toaccountforthesefacts,manymodelshavebeeninventedwhichemphasizeacertainas-pectoftheunderlyingtheory.Topickoneexample,letmejustpointoutthatthebagmodeldescribesbaryonsmadeofbagged(confined)quarksinasimpleandappealingpicture,withtheconfinementduetothedifferenceofthepressureinthevacuumandinthebaryonstate.However,insuchaframeworkonehasverylittlecontrolovertheapproximationsinvolved.An-othertypeofapproachescanbeconsideredmoreambitiousinthattheyonlytrytoimplementbasicprinciplesunderlyingQCDattheexpenseofsomeparameterswhichhavetobedeterminedfromdataandwhichparameterizeourignoranceofgoingdirectlyfromQCDtothebaryonstates.Oneoftheseapproachesarethesumrules,championnedbyBorisIoffeandhiscollabo-ratorsforbaryons.Here,thenon–perturbativevacuumstructureisgivenintermsofastringofquark,gluonandmixedcondensates,whicharematchedtotheoperatorproductexpansionofthen–pointfunctionunderconsideration.AdetaileddiscussionofthisframeworkcanbefoundinthecontributionbyColangeloandKhodjamiriantothisFestschrift.Inthisessay,Iwillbecon-cernedwithaverydifferentapproach.InacertainsenseitismoregeneralthanQCDsinceitsolelyexplorestheconsequencesofthespontaneouslyandexplicitlybrokenchiralsymmetryforthestructureanddynamicsofthelow–lyingbaryons.Theunderlyingframeworkisaneffectivefieldtheorybasedon#1EssayfortheFestschriftinhonorofBorisIoffe,toappearinthe“EncyclopediaofAnalyticQCD,”editedbyM.Shifman,tobepublishedbyWorldScientific.1asymptoticallyobservablestates,heretheGoldstonebosonsandthematterfields.ThebasicideasoftheGoldstonebosondynamicsarediscussedinde-tailbyHeiriLeutwylerinthisbook,soIwillfocusonthepictureofbaryonstructureatlowenergiesasitfollowsfromthechiralQCDdynamics.Thispicturecompletelymasksthequarkandgluondegreesoffreedomclearlyseenathighenergies,whichisnotthatsurprisingsinceinmanyphysicalsystemscollectiveexcitationsgovernthelowenergydynamics.TheGoldstonebosonsofQCDcanbethoughtoffassuchcollectiveexcitationsandthebaryonses-sentiallyassourcessurroundedbyacloudofthese.AsIwillshow,thismesoncloudpicturehasfar–reachingconsequencesforthebaryonstructureandiswellestablishedbynowthroughaseriesofprecisionexperiments.Inanycase,thisnon–perturbativeregimeofQCDismostchallengingtotheoristsanditisthereforenotsurprisingthattheprogressisslowbutsteady.Still,thefieldhasmaturedtoapointthattruelyquantitativetestsofchiralsymmetrybreakingcanbeperformed,asIwilldetailinthefollowingsections.Abasicdiscussionofhadroneffectivefieldtheory#2isgivenininsection3.Manyapplicationsforthetwo–andthree–flavorcasesarediscussedinsections4and5,respec-tively.NoattempttoachievecompletenessismadeandonlymaterialavailablebeforeJuly2000wasincluded.Beforeembarkingonanyoftheseissuesinde-tail,Iwillgiveaverypedestriantypeofintroductioninsection2tryingtooutlinethebasicideasandtheemergingpictureinafairlydescriptiveway.Thisshouldallowthebeginnertocatchtheessentialconceptswithoutbeingoverwhelmedbyheavymachinery.Thereadermoreinterestedinresultsorderivationsmightwanttoskipthissection.Moreprecisely,ashortreviewofthechiralsymmetryofQCDisgiveninsection2.2,followedbyadiscussiononhowonecanderivedynamicsfromsymmetryinsection2.3andsomeremarksonthephysicalpictureemergingforthestructureofthebaryonsinsection2.4.2Fromsymmetrytodynamics2.1SomeintroductoryremarksThespectrumofthelow–lyingmesonsrevealssomeinterestingfeatures.Start-ingatthemassoftherhomeson,Mρ≃770MeV,awholezooofscalar,vector,pseudoscalarandaxialstatesisobserved.Thesestatescomeinmul-tiplets(octetsornonets)organizedintermsofaflavorSU(3).Theaver-agemassoftheselowestmultipletsisMM≃1GeV.Below,thereareninepseudoscalarstateswhicharesuspiciouslylight,inparticularthethreepions(π+,π0,π−),Mπ/MM≃1/7,thekaons(K+,K−,K0,K0)andtheetawith#2Theterminus“hadroneffectivefieldtheory”meansnothingelsebutbaryonchiralper-turbationtheory.2MK≃Mη≃MM/2.Asexplainedbelow,thesenineparticlescanbeconsid-eredasthePseudo–GoldstonebosonsrelatedtothespontaneousbreakdownofthechiralsymmetryofQCD.DuetoGoldstone’stheorem,theirinteractionsvanishasthemomentumtransfergoestozero.Infact,thisstatementdoesnotonlyholdforinteractionsbetweenGoldstonebosons,likee.g.forlowenergyelasticpion–pionscattering,butalsoforGoldstonebosonsinteractingwith“matter”fields.Here,bymatterIdenoteanyparticlewhichisnotaGold-stoneboson,inparticularalsothenucleon.Asaconsequence,itfollowsthatthepion–nucleonintera