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Analytic structure in the coupling constant plane in perturbative QCD

Irinel Caprini·Jan Fischer
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Abstract

We investigate the analytic structure of the Borel-summed perturbative QCD amplitudes in the complex plane of the coupling constant. Using the method of inverse Mellin transform, we show that the prescription dependent Borel-Laplace integral can be cast, under some conditions, into the form of a dispersion relation in the a-plane. We also discuss some recent works relating resummation prescriptions, renormalons and nonperturbative effects, and show that a method proposed recently for obtaining QCD nonperturbative condensates from perturbation theory is based on special assumptions about the analytic structure in the coupling plane that are not valid in QCD.

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Irinel Caprini, Jan Fischer. 2003-10-14. Analytic structure in the coupling constant plane in perturbative QCD. https://doi.org/10.1103/physrevd.68.114010

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