  The precise quark mass dependence of the one-loop effective action in an
instanton background has recently been computed [arXiv:hep-th/0410190]. The
result interpolates smoothly between the previously known extreme small and
large mass limits. The computational method makes use of the fact that the
single instanton background has radial symmetry, so that the computation can be
reduced to a sum over partial waves of logarithms of radial determinants, each
of which can be computed numerically in an efficient manner. The bare sum over
partial waves is divergent and must be regulated and renormalized. In this
paper we provide more details of this computation, including both the
renormalization procedure and the numerical approach. We conclude with
comparisons of our precise numerical results with a simple interpolating
function that connects the small and large mass limits, and with the leading
order of the derivative expansion.
