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

TL;DR

This paper explores how the infrared behavior of quark-gluon interactions in QCD can explain the eta' meson mass and the U_A(1) anomaly, emphasizing the role of a singular quark-gluon vertex.

Contribution

It demonstrates that a singular quark-gluon vertex can provide the necessary screening mass for the U_A(1) problem, even with a vanishing gluon propagator.

Findings

Infrared singular quark-gluon vertex contributes to eta' mass

Screening of Goldstone pole explained by vertex singularity

Results align with Landau gauge propagator data

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 $\sim 1/k^4$. 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.