Renormalon-inspired resummations for vector and scalar correlators- estimating the uncertainty in {alpha}_{s}({m}_{τ}²) and and {α}({M}_{Z}²)

We perform an all-orders resummation of the QCD Adler D-function for the vector correlator, in which the portion of perturbative coefficients involving the leading power of b, the first beta-function coefficient, is resummed. To avoid a renormalization scale dependence when we match the resummation to the exactly known NLO and NNLO results, we employ the Complete Renormalization Group Improvement (CORGI) approach. These fixed-order and resummed CORGI results are analytically continued by numerically performing a contour integral to obtain corresponding fixed and all-orders ``contour-improved'' results for the e+e- R-ratio ands its tau decay analogue R_{\tau}. The difference between these fixed-order and all-order results is used to estimate the uncertainty in the extraction of {alpha}_{s}({M}_{Z}^{2}} from R_{\tau} measurements, and that in the QED coupling {\alpha}({M}_{Z}^{2}) due to hadronic corrections related to R. Analogous resummations for the scalar correlator are performed, and used to assess the uncertainty in the Higgs decay width to a heavy quark pair. We point out that CORGI fixed-order contour-improved results for R and the Higgs decay width, can be given explicitly in terms of the Lambert-W function and hypergeometric functions, avoiding the need for numerical integration.