Contour-improved versus fixed-order perturbation theory in hadronic τ decays

Abstract

The hadronic decay rate of the τ lepton serves as one of the most precise determinations of the QCD coupling αs. The dominant theoretical source of uncertainty at present resides in the seeming disparity of two approaches to improving the perturbative expansion with the help of the renormalisation group, namely fixed-order and contour-improved perturbation theory. In this work it is demonstrated that in fact both approaches yield identical results. However, the fixed-order series is found to oscillate around the contour-improved result with an oscillation frequency of approximately six perturbative orders, approaching it until about the 30th order, after which the expansion reveals its asymptotic nature. © SISSA 2005.