  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.
