& P^{2}\geq \frac{\eta ^{2}}{4}
\end{array}\right. \nonumber \\ & &  \nonumber \\
B(P^{2}) & = & \left\{
\begin{array}{cl}
(\eta ^{2}-4P^{2})^{\frac{1}{2}}, &
\; \; \; \; \; \; \; \; \; \; \; \; P^{2}\leq \frac{\eta ^{2}}{6} \\
\frac{4m_D^3}{P^2}, &  \; \; \; \; \; \; \; \; \; \; \; P^{2}\geq
\frac{\eta ^{2}}{6}
\end{array}\right. , \label{4.2}\end{aligned}$$ where the quantity $m_D$ has been referred to previously as the “dynamical-quark mass"[@pagels79; @cahill85], which sets the scale for dynamical chiral symmetry breaking. Its value is determined here by demanding that the function $B$ and its first derivative match at the point $\eta ^2/6$, and is thus given by $m_D=[24\sqrt{3}]^{-1/3}\eta \approx 0.29\eta $. For $\eta \sim 1$ GeV, a dynamical-quark mass of $m_D\sim 290$ MeV is obtained, which is consistent with the notion of a constituent-quark mass. In Ref.[@pagels79], using evidence from $e^+e^-$ annihilation, the dynamical mass is estimated to be $m_D\approx 244$ MeV. These arguments place constraints on the range of the parameter $\eta $, which is thereby fixed at $5$ fm$^{-1}$ ($\approx 1$ GeV) for the remainder of this work. The ansatz (\[4.2\]) encompasses the expected behavior of the solutions to the Schwinger-Dyson equation (\[SDE\]) on the real axis[@conchi], and is here taken 