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.
Cite
@article{arxiv.1902.05847,
title = {Non-local Lagrangians from Renormalons and Analyzable Functions},
author = {Alessio Maiezza and Juan Carlos Vasquez},
journal= {arXiv preprint arXiv:1902.05847},
year = {2019}
}
Comments
19 pages, 4 figures, references added, final version appearing in Annals of Physics