  We use a novel method to calculate analytically the QCD instanton prefactor
due to a quark field carrying a small mass parameter $m$. In the SU(2)
instanton background of size $\rho$, the spinor effective action $\Gamma^F$ (in
the minimal subtraction scheme), which gives rise to the prefactor $\exp
(-\Gamma^F)$, is shown to have the small-$m \rho$ behavior
  \Gamma^F = -\ln (m /\mu) - \ln (\mu\rho)/3 -2 \alpha(1/2) -(m \rho)^2 \{\ln
(m \rho /2) +\gamma+1/2\} -2 (m \rho)^4 \{-\ln ^2(m \rho)/4+\ln (m \rho)
(1/2-\gamma +\ln 2)/2+C \} +O((m \rho)^6), where $\gamma=0.577216...$,
$\alpha(1/2)=0.145873...$, and our numerically evaluated value for the constant
$C$ is $C=-0.382727...$. A good agreement between this form and the numerically
exact calculation is found if $(m \rho) \lesssim 0.8$.
