Direct extraction of ∆(_MS) from e(^+)e jet observables

Abstract

We demonstrate a renormalisation group improved formulation of QCD perturbation theory. At next-to-leading order (NLO) and beyond this permits a direct extraction of the QCD dimensional transmutation parameter, A(_ms) that typifies the one parameter freedom of the theory in the limit of massless quarks. We apply this to a variety of experimental data on e(^+)e" jet observables at NLO. We take into consideration data from PETRA, PEP, TRISTAN, SLC and LEP 1 and 2. In this procedure there is no need to mention, let alone to arbitrarily vary, the unphysical renormalization scale µ, and one avoids the spurious and meaningless "theoretical error" associated with standard a(_8) determinations. An attempt is made to estimate the importance of uncalculated next-to-NLO and higher order perturbative corrections, and power corrections, by studying the scatter in the values of ∆(_MS) obtained for different observables. We also consider large infrared logarithm resummations in these jet observables and present results for the particular cases of the four-jet rate to a next-to-leading logarithm approximation and the distributions for the four-jet variables, "light hemisphere mass" and "narrow jet broadening" to a next-to-next-to-leading logarithm approximation in the perturbative expansion. We apply a simple power correction to these variables and obtain remarkably good fits to the data.