Non-local Lagrangians from Renormalons and Analyzable Functions

Abstract

We embed in a generalized Borel procedure the notion of renormalization and renormalons. While there are several efforts in literature to have a semi-classical understanding of the renormalons, here we argue that this is not the fundamental issue and show how to deal with the problem. We find that the effective Lagrangians describing the effects of renormalons are non-local in space but local in time. The quark-antiquark potential in QCD with an infinite number of fermions is also analyzed. The connection between the analyzable functions, the Callan-Symanzyk equation and the renormalons, provides an insight of a non-perturbative renormalization from the standard perturbative renormalization approach.

19 pages, 4 figures, references added, final version appearing in Annals of Physics

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Cited by in corpus (15)

• Resurgence of the Renormalization Group Equation
• Determination of perturbative QCD coupling from ALEPH $\tau$ decay data using pinched Borel-Laplace and Finite Energy Sum Rules
• Borel-Laplace Sum Rules with $\tau$ decay data, using OPE with improved anomalous dimensions
• Resurgence of the QCD Adler function
• Non-Wilsonian ultraviolet completion via transseries
• Lattice-motivated QCD coupling and hadronic contribution to muon $g-2$
• Renormalons in a scalar self interacting theory: thermal, thermomagnetic and thermoelectric corrections for all values of temperature
• Renormalons beyond the Borel plane
• Renormalons in quantum mechanics
• A consistent quantum field theory from dimensional reduction
• On Haag's theorem and renormalization ambiguities
• Resurgence and self-completion in renormalized gauge theories
• The QCD Adler function and the muon $g-2$ anomaly from renormalons
• Resurgent representation of the Adler function in the large-${\beta }_0$ approximation of QCD
• Gluon Mass Generation from Renormalons and Resurgence