Vector Mesons on the Light Front

We apply the light-front quantization to the Nambu--Jona-Lasinio model with the vector interaction, and compute vector meson's mass and light-cone wavefunction in the large N limit. Following the same procedure as in the previous analyses for scalar and ps

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aSACLAY-T03/115hep-ph/0308096VectorMesonsontheLightFrontK.Naitoa,1,S.Maedanb,2andK.Itakurac,d,3aMemeMediaLaboratory,HokkaidoUniversity,Sapporo060-8628,JapanbDepartmentofPhysics,TokyoNationalCollegeofTechnology,Tokyo193-0997,JapancRIKENBNLResearchCenter,BrookhavenNationalLaboratory,Upton,NY11973,USAdServicedePhysiqueTh´eorique,CEA/Saclay,F91191Gif-sur-YvetteCedex,France4AbstractWeapplythelight-frontquantizationtotheNambu–Jona-Lasiniomodelwiththevectorinteraction,andcomputevectormeson’smassandlight-conewavefunctioninthe

largeNlimit.Followingthesameprocedureasinthepreviousanalysesforscalarandpseudo-scalarmesons,wederivethebound-stateequationsofaqq¯systeminthevectorchannel.Weincludethelowestordere ectsofthevectorinteraction.Theresultingtransverseandlongitudinalcomponentsofthebound-stateequationlookdi erentfromeachother.Buteventuallyafterimposinganappropriatecuto ,one ndsthesetwoareidentical,givingthesamemassandthesame(spin-independent)light-conewavefunction.Massofthevectormesondecreasesasoneincreasesthestrengthofthevectorinteraction.

We apply the light-front quantization to the Nambu--Jona-Lasinio model with the vector interaction, and compute vector meson's mass and light-cone wavefunction in the large N limit. Following the same procedure as in the previous analyses for scalar and ps

Thelight-cone(LC)wavefunctionofahadronisoneofthemostusefulquantitiesforde-scribingthehadronstructureintermsofitsunderlyingdegreesoffreedom[1].Ingeneral,itcontainsinformationaboutsoftdynamicsamongquarks,antiquarksandgluons,andonecancomputevariousscatteringprocessesinvolvinghadronsininitial/ nalstates,bycombiningitwiththehardpartofthediagrams.Di ractivevectormesonproductionisoneofthetypicalex-amplesofsuchprocesses[2].Tocomputetheamplitudeofdi ractiveelectro/photoproductionofavectormesonforawiderangeofkinematics,oneneedstoknowtheLCwavefunctionofavectormesonwithnon-perturbativeinformation.InthisLetter,wearegoingtodiscussthisLCwavefunctionofthevectormesoninasimplemodel.Asanotherinterestingexample,E791ex-perimentatFermilab[3]hasrecentlyattemptedtodeterminetheLCwavefunction(squared)ofpionsthroughthedi ractivepiondissociationprocess(dijetsproduction)accordingtoRef.[4].AlthoughitisarguedthatdeterminationofthepionLCwavefunctionfromtheexperimentaldataisactuallyquitehard[5],itisstilltruethatonecannotcomputetheamplitudeofthisprocesswithoutknowingthepionLCwavefunction.Similarexperimentsarepossibleinthedi-jetsproductionfromavirtualphoton,where,accordingtothevectormesondominancemodel,thevectormesoncontributionformsthehadronicpartofthephotonwavefunction.

Perturbativecalculationsprovideuswiththesocalled”asymptotic”formoftheLCwave-functions.Forexample,theasymptoticformofthepionLCwavefunctionisknownaswellasthevectormeson’sone[6,7].However,http://doc.guandang.nettticesimula-tioncancomputethe rstfewmomentsofmeson’sdistributionfunction,butatpresenttheyarenotsu cienttodeterminetheLCwavefunctionitself.Therefore,itisveryimportanttodevelopanon-perturbativetechniquewhichallowsustodirectlyobtaintheLCwavefunction.Clearly,themoststraightforwardandnaturalframeworkistheHamiltonianformalisminthelight-front(LF)quantization[8,1].BeforechallengingtheproblemintherealQCD,oneshouldbeabletolearnmuchfromtheanalysesofsimplermodelssuchastheNambu–Jona-Lasinio(NJL)model.Indeed,thismodelwasrecentlystudiedbytwooftheauthorswithintheLFquantization[9,10]andwefollowthesameproceduretogettheLCwavefunctionsofvectormesons.Asiswellknown,thereisaparadoxicalsituationintheLFquantization.IthasbeenaskedhowonecandescribespontaneoussymmetrybreakinginaformalismhavingonlyatrivialFockvacuum.ThiswasansweredinRef.[9]withintheNJLmodelwithNcomponentfermions¯i/LNJL=Ψ( m0)Ψ+1

±γγΨ2andψ+iscalled”good”5)isnotadynamicalvariableandissubjecttoaconstraintequation,

aswewillseebelow.This”fermionicconstraint”isanonlinearequationintheNJLmodelandleadstothe”gapequation”forthechiralcondensateifoneadoptsanappropriatecuto .Namely,usingtheparityinvariantcuto |p±|<Λ,onegetsM m0

4π2 2 M2

M2 ,(1)

i122,vµ=(v+,v ,v⊥),v=(v+,v⊥,v⊥)and ±= / x±.

Weuseµ,νforLorentzindicesoffourvectors,i,jfortransversecoordinates1,2,andα,βforspinorindices.¯ isthedynamicalmassofthefermion.WhenthecouplingconstantwhereM=m0 G1 ΨΨ =GNΛ2/4π2islargerthanthecriticalvalueG (critical)=1/2,thegapequationhasaG111

We apply the light-front quantization to the Nambu--Jona-Lasinio model with the vector interaction, and compute vector meson's mass and light-cone wavefunction in the large N limit. Following the same procedure as in the previous analyses for scalar and ps

non-zerosolutioneveninthechirallimitm0→0.Thismeansthatthefermionicconstraintallowsfor”symmetric”and”broken”solutionscorrespondingtothoseofthegapequation.Ifoneselectsthe”broken”solution,andsubstitutingittothecanonicalHamiltonian,oneobtainsthe”broken”Hamiltonian.Thisgovernsthedynamicsinthebrokenphaseandiscompletelydi erentfromtheHamiltonianwiththe”symmetric”solution.InRef.[9],thefermioniccon-straintwassolvedbyusingthe1/Nexpansion[Indeed,Eq.(1)istheleadingorderresult],andtheyobtainedtheHamiltonianinbothsymmetricandbrokenphases.Theyalsosolvedthebound-stateequationsforthescalarandpseudo-scalarmesons6andobtainedtheirLCwave-functionsandmasses,aswellasthePCACandGORrelations.

Onecanofcourseapplythesameprocedureforvectorstates,butweknowthattheNJLmodelLNJLdoesnotallowforaboundstateinthevec …… 此处隐藏：16814字，全部文档内容请下载后查看。喜欢就下载吧 ……