All-orders renormalon resummations for some QCD observablest

Abstract

Exact large- N f results for the QCD Adler D-function and Deep Inelastic Scattering sum rules are used to resum to all orders the portion of QCD perturbative coefficients containing the highest power of b = 1 6 (11 N-2N f) , for SU ( N) QCD with N f quark flavours. These terms correspond to renormalon singularities in the Borel plane and are expected asymptotically to dominate the coefficients to all orders in the 1/ N f expansion. Remarkably, we note that this is already apparent in comparisons with the exact next-to-leading order (NLO) and next-to-NLO (NNLO) perturbative coefficients. The ultra-violet (UV) and infra-red (IR) renormalon singularities in the Borel transform are isolated and the Borel sum (principal value regulated for IR) performed. Resummed results are also obtained for the Minkowski quantities related to the D-function, the e + e − R-ratio and the analogous τ-lepton decay ratio, R τ . The renormalization scheme dependence of these partial resummations is discussed and they are compared with the results from other groups and with exact fixed-order perturbation theory at NNLO. Prospects for improving the resummation by including more exact details of the Borel transform are considered.