UA(1) anomaly and $ eta^{{prime}}_{}$ -mass from an infrared singular quark-gluon vertex |
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Authors: | R. Alkofer C. S. Fischer R. Williams |
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Affiliation: | 1.Graz University, Universit?tsplatz 5,Graz,Austria;2.Institut für Kernphysik,TU Darmstadt,Darmstadt,Germany;3.Gesellschaft für Schwerionenforschung mbH,Darmstadt,Germany |
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Abstract: | The U A(1) problem of QCD is inevitably tied to the infrared behaviour of quarks and gluons with its most visible effect being the -mass. A dimensional argument of Kogut and Susskind showed that the mixing of the pseudoscalar flavour-singlet mesons with gluons can provide a screening of the Goldstone pole in this channel if the full quark-quark interaction is strongly infrared singular as ∼ 1/k 4 . We investigate this idea using previously obtained results for the Landau gauge ghost and gluon propagator, together with recent determinations for the singular behaviour of the quark-gluon vertex. We find that, even with an infrared vanishing gluon propagator, the singular structure of the quark-gluon vertex for certain kinematics is apposite for yielding a non-zero screening mass. |
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Keywords: | KeywordHeading" >PACS 11.30.Rd Chiral symmetries 11.30.Fs Global symmetries (e.g., baryon number, lepton number) 12.38.Lg Other nonperturbative calculations 14.40.Aq IEq3" > /content/6686156qt7374124/10050_2008_730_Article_IEq3.gif" alt=" $ pi$" align=" middle" border=" 0" > , K , and IEq4" > /content/6686156qt7374124/10050_2008_730_Article_IEq4.gif" alt=" $ eta$" align=" middle" border=" 0" > mesons |
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