# 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

NikodemPop lawski

arXiv:hep-ph/0507239v1 20 Jul 2005

NuclearTheoryCenter,IndianaUniversity,Bloomington,IN47405

Thisarticleisbasedontheauthor’sPh.D.thesiscurrentlybeingwrittenunderthesupervisionof

Abstract

1Introduction

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