hence the self-energy functions, for complex values of their arguments. The solution of the Schwinger-Dyson equation in the complex plane is a challenging problem in itself[@burden92; @conchi], and is being pursued elsewhere for forms such as that in (\[4.1\])[@burdencon]. Although these solutions are crucial to a comprehensive study of the present problem, reasonable approximations are available. The analytic solutions given in (\[3.2\]) for the self-energy functions obtained using the simple model two-point function (\[3.1\]) are useful in this regard. It is shown, for example, in Ref.[@PCR89] that the solutions to (\[2.2\]) and (\[2.3\]) for the self-energy amplitudes obtained using (\[4.1\]), display behavior similar to the simple model solutions of (\[3.2\]) on the real axis with the exception of an additional tail on the scalar amplitude, $B$, attributed to the ultraviolet contribution in (\[4.1\]). Others have argued on both theoretical and experimental grounds that the asymptotic form of the scalar contribution to the self energy should behave as $B(P^2)\sim 4m^3_D/P^2$, which, in the Landau gauge, is exact within a logarithm[@pagels79]. The self-energy functions used in the numerical work here are thus modeled as $$\begin{aligned}
A(P^{2}) & = & \left\{
\begin{array}{cl}
2, & P^{2}\leq \frac{\eta ^{2}}{4} \\
\frac{1}{2}\left[ 1+\left(1+\frac{2\eta ^{2}}{P^{2}}\right)
^{\frac{1}{2}}\right] , 