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A Relativistic Description of Hadronic Decays of the Meson $pi_{1}$

The subject of this work is the analysis of hadronic decays of the exotic meson $\pi_{1}$ in a fully relativistic formalism, and comparison with the nonrelativistic results. The relativistic spin wave functions of mesons and hybrids are constructed based o

Arelativisticdescriptionofhadronicdecaysofthemesonπ1

NikodemPop lawski

arXiv:hep-ph/0507239v1 20 Jul 2005

NuclearTheoryCenter,IndianaUniversity,Bloomington,IN47405

Thisarticleisbasedontheauthor’sPh.D.thesiscurrentlybeingwrittenunderthesupervisionof

Prof.AdamSzczepaniak.

Abstract

Thesubjectofthisworkisanalysisofhadronicdecaysofexoticmesonπ1inafullyrelativistic

formalism,andcomparisonwiththenonrelativisticresults.TherelativisticspinwavefunctionsofmesonsandhybridsareconstructedbasedonunitaryrepresentationsoftheLorentzgroup.Theradialwavefunctionsareobtainedfromphenomenologicalconsiderationsofthemassop-erator.We ndthatdecaychannelsπ1→πb1andπ1→πf1arefavored,inagreementwithresultsobtainedusingothermodels,thusindicatingsomemodelindependenceoftheS+Pselectionrules.Wewillalsoreportone ectsofmeson nalstateinteractionsinexoticchannels.

1Introduction

Inaregionaround2GeVanewformofhadronicmatterisexpectedtoexistinwhichthegluonicdegreesoffreedomareexcited.InmesonsthesecanresultinresonanceswithexoticJPCquantumnumbers.Theadiabaticpotentialcalculationsshowπ1(1 +)asthelowestenergyexcitedgluoniccon guration[1].Thepresentmodelsofhybriddecays(forinstance[2,3])arenonrelativisticandthereforeoneshouldinvestigatecorrectionsarisingfromfullyrelativistictreatment.Thecaseofπ1isofaspecialinterestalsobecauseitsevidencehasbeenreportedbytheE852collaborationandnewexperimentalsearchesareplannedforJLabandGSI.

2Relativisticspinwavefunctionformesonsandhybrids

Forasystemofnon-interactingparticlesthespinwavefunctionisconstructedasanelementofanirreduciblerepresentationofthePoincaregroup.Wewillassumemu=md=m.Intherestframeofaquark-antiquarkpair

µµ

lq=(E(mq,q),q),lq¯, q), q),¯=(E(mq

thenormalizedspin-1wavefunction(JPC=1 )isgivenbytheClebsch-Gordancoe cientsand

canbewrittenintermsofDiracspinorsas

λqq¯Ψqq¯¯(q,lqq

=0,σq,σq¯)=

1

u¯(q,σq)γi 2mqq¯

2qi

c2004AmericanInstituteofPhysics

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