The renormalised quark Dyson-Schwinger equation is studied in the limit of
the renormalised current heavy quark mass m_R --> infinity. We are particularly
interested in the analytic pole structure of the heavy quark propagator in the
complex momentum plane. Approximations in which the quark-gluon vertex is
modelled by either the bare vertex or the Ball-Chiu Ansatz, and the Landau
gauge gluon propagator takes either a gaussian form or a gaussian form with an
ultraviolet asymptotic tail are used.Comment: 21 pages Latex and 5 postscript figures. The original version of this
paper has been considerably extended to include a formalism dealing with the
renormalised heavy quark Dyson-Schwinger equation and uses a more realistic
Ansatz for the gluon propagator
