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UA(1) anomaly and \( \eta^{{\prime}}_{}\) -mass from an infrared singular quark-gluon vertex

  • Regular Article - Theoretical Physics
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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 \( \eta^{{\prime}}_{}\) -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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Authors and Affiliations

  1. Graz University, Universitätsplatz 5, A-8010, Graz, Austria

    R. Alkofer

  2. Institut für Kernphysik, TU Darmstadt, Schlossgartenstrasse 9, 64289, Darmstadt, Germany

    C. S. Fischer & R. Williams

  3. Gesellschaft für Schwerionenforschung mbH, Planckstr. 1, D-64291, Darmstadt, Germany

    C. S. Fischer

Authors
  1. R. Alkofer
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  2. C. S. Fischer
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  3. R. Williams
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Correspondence to R. Williams.

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Communicated by A. Schäfer

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Alkofer, R., Fischer, C.S. & Williams, R. UA(1) anomaly and \( \eta^{{\prime}}_{}\) -mass from an infrared singular quark-gluon vertex. Eur. Phys. J. A 38, 53–60 (2008). https://doi.org/10.1140/epja/i2008-10646-x

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