$\tau$ Decay and the QCD infrared fixed point

Abstract

We apply the optimization procedure based on the Principle of Minimal Sensitivity to the third-order calculation of $R_{\tau}$. Since the effective couplant remains finite, freezing to a value $\alpha_s/\pi = 0.26$ at low energies, we can actually evaluate the defining integral of $R_{\tau}$ and compare the optimized perturbation theory result to that of the optimized result obtained after the integral has been evaluated using contour techniques. The good agreement shows that the optimization procedure is consistent and suggests that the infrared fixed point is meaningful.