Perturbative relations between $e^{+}{e}^{-}$ annihilation and $\tau$ decay observables including resummation effects

Abstract

By exploiting the analyticity properties of the two-point current-current correlator we obtain numerical predictions for the $e^{+}{e}^{-}$ moments in terms of the $\tau$ decay rate. We perform a partial resummation of the pertinent perturbative series expansion by solving the renormalization group equation for Adler's function. Our predictions are renormalization scheme independent but depend on the order of the perturbative $\beta$-function expansion. The analysis involves the unknown five-loop coefficient $k_3$ for which we give some new estimates.

10 pages, LaTeX, 2 postscript figures

References in corpus (5)

• The four-loop beta-function in Quantum Chromodynamics
• Renormalization group analysis of the tau-lepton decay within QCD
• Resummation analysis of the $\tau$ decay width using the four-loop $\beta$-function
• New high order relations between physical observables in perturbative QCD
• QCD Tests from Tau Decays

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