Freezing of the QCD coupling constant and solutions of Schwinger-Dyson equations

We compare phenomenological values of the frozen QCD running coupling constant $\left({\alpha }_s\right)$ with two classes of infrared finite solutions obtained through nonperturbative Schwinger-Dyson equations. We use these same solutions with frozen coupling constants as well as their respective nonperturbative gluon propagators to compute the QCD prediction for the asymptotic pion form factor. Agreement between theory and experiment on ${\alpha }_s\mathrm{}\left(0\right)\mathrm{}$ and $F_{\pi }{(Q}^2)$ is found only for one of the Schwinger-Dyson equation solutions.