Recently, we have developed a formalism to evaluate QCD loop diagrams with a
single virtual gluon using a running coupling constant at the vertices. This
corresponds to an all-order resummation of certain terms (the so-called
renormalon chains) in a perturbative series and provides a generalization of
the scale-setting prescription of Brodsky, Lepage and Mackenzie. In its
original form, the method is applicable to Green functions without external
gluons and to euclidean correlation functions. Here we generalize the approach
to the case of cross sections and inclusive decay rates, which receive both
virtual and real gluon corrections. We encounter nonperturbative ambiguities in
the resummation of the perturbative series, which may hinder the construction
of the operator product expansion in the physical region. The origin of these
ambiguities and their relation to renormalon singularities in the Borel plane
is investigated by introducing an explicit infrared cutoff. The ratios $R_{e^+
e^-}$ and $R_\tau$ are discussed in detail.Comment: 37 pages LaTeX, uses epsf, 8 figures. Largely revised version with an
  extended discussion and several new result

Neubert, Matthias

English

arXiv

Recently, we have developed a new formalism to evaluate QCD loop diagrams with a single virtual gluon using a running coupling constant at the vertices. It corresponds to an all-order resummation of certain terms (the so-called renormalon chains) in a perturbative series and provides a generalization of the scale-setting prescription of Brodsky, Lepage and Mackenzie. In its original form the method is applicable to Green functions without external gluons and to euclidean correlation functions. Here we generalize the approach to the case of cross sections and inclusive decay rates, which receive both virtual and real gluon corrections. We encounter non-perturbative ambiguities in the resummation of the perturbative series, which may hinder the standard construction of the operator product expansion. The ratios R_{e^+ e^-} and R_\tau are discussed in detail.Recently, we have developed a new formalism to evaluate QCD loop diagrams with a single virtual gluon using a running coupling constant at the vertices. It corresponds to an all-order resummation of certain terms (the so-called renormalon chains) in a perturbative series and provides a generalization of the scale-setting prescription of Brodsky, Lepage and Mackenzie. In its original form the method is applicable to Green functions without external gluons and to euclidean correlation functions. Here we generalize the approach to the case of cross sections and inclusive decay rates, which receive both virtual and real gluon corrections. We encounter non-perturbative ambiguities in the resummation of the perturbative series, which may hinder the standard construction of the operator product expansion. The ratios $R_{e~+ e~-}$ and $R_\tau$ are discussed in detail

Resummation of Renormalon Chains for Cross Sections and Inclusive Decay Rates

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