Determination ofαs(Mτ2)from improved fixed order perturbation theory

Abstract

We revisit the extraction of ${\ensuremath{\alpha}}_{s}({M}_{\ensuremath{\tau}}^{2})$ from the QCD perturbative corrections to the hadronic $\ensuremath{\tau}$ branching ratio, using an improved fixed-order perturbation theory based on the explicit summation of all renormalization-group accessible logarithms, proposed some time ago in the literature. In this approach, the powers of the coupling in the expansion of the QCD Adler function are multiplied by a set of functions ${D}_{n}$, which depend themselves on the coupling and can be written in a closed form by iteratively solving a sequence of differential equations. We find that the new expansion has an improved behavior in the complex energy plane compared to that of the standard fixed-order perturbation theory (FOPT), and is similar but not identical to the contour-improved perturbation theory (CIPT). With five terms in the perturbative expansion we obtain in the $\overline{\mathrm{MS}}$ scheme ${\ensuremath{\alpha}}_{s}({M}_{\ensuremath{\tau}}^{2})=0.338\ifmmode\pm\else\textpm\fi{}0.010$, using as input a precise value for the perturbative contribution to the hadronic width of the $\ensuremath{\tau}$ lepton reported recently in the literature.