Title:

RSinvariant resummations of QCD perturbation theory

We propose a renormaloninspired resummation of QCD perturbation theory based on approximating the renormalization scheme (RS) invariant effective charge (EC) beta function coefficients by the portion containing the highest power of b = (11N'2N(_f))/6, the first betafunction coefficient, for SU(N) QCD with N(_f) quark flavours. This can be accomplished using exact largeN(_f) allorders results. The resulting resummation is RSinvariant and the exact nexttoleading order (NLO) and nexttoNLO (NNLO) coefficients in any RS are included. This improves on a previously employed naive leading6 resummation which is RSdependent. The RSinvariant resummation is used to assess the reliability of fixedorder perturbation theory for the e(^+)e(^) Rratio, hadronic taudecay ratio R(_r), and Deep Inelastic Scattering (DIS) sum rules, by comparing it with the exact NNLO results in the EC RS. For R and R(_r), where largeorder perturbative behaviour is dominated by a leading ultraviolet renormalon singularity, the comparison indicates fixedorder perturbation theory to be very reliable. For DIS sum rules, which have a leading infrared renormalon singularity, the performance is rather poor. We show that QCD Minkowski observables such as the R and R(_r) are completely determined by the EC betafunction, p(x), corresponding to the Euclidean QCD vacuum polarization Adler Dfunction, together with the NLO perturbative coefficient of D. An efficient numerical algorithm is given for evaluating R, Rr from a weighted contour integration of D(se(^10)) around a circle in the complex squared energy .splane, with p(x) used to evolve in s around the contour. The difference between the R, R(_r) constructed using the NNLO and leadingb resummed versions of pi(x) provides an estimate of the uncertainty due to the uncalculated higher order corrections. We estimate that at LEP energies ideal data on the Rratio could determine a(_s)(M(_2)(_Z)) to threesignificant figures. For R(_r) we estimate a theoretical uncertainty δa(_s)(m(^2)(_r)) ~ 0.001, corresponding to δa(_s)(m(^2)(_r)) ~ 0.002. This encouragingly small uncertainty is much less than has recently been deduced from comparison with the analogous naive allorders resummation, which we demonstrate to be extremely RS dependent and hence misleading.
