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arXiv · 0804.3478

U_A(1) anomaly and eta' mass from an infrared singular quark-gluon vertex

Reinhard Alkofer·Christian S. Fischer·Richard Williams
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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 $η^\prime$ 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 $\sim 1/k^4$. 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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Reinhard Alkofer, Christian S. Fischer, Richard Williams. 2008-09-08. U_A(1) anomaly and eta' mass from an infrared singular quark-gluon vertex. https://doi.org/10.1140/epja%2Fi2008-10646-x

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