Renormalons and Analytic Properties of the \beta function
High Energy Physics - Phenomenology
2014-11-18 v1 Astrophysics
Disordered Systems and Neural Networks
Statistical Mechanics
High Energy Physics - Theory
Abstract
The presence or absense of renormalon singularities in the Borel plane is shown to be determined by the analytic properties of the Gell-Mann - Low function \beta(g) and some other functions. A constructive criterion for the absense of singularities consists in the proper behavior of the \beta function and its Borel image B(z) at infinity, \beta(g)\sim g^\alpha and B(z)\sim z^\alpha with \alpha\le 1. This criterion is probably fulfilled for the \phi^4 theory, QED and QCD, but is violated in the O(n)-symmetric sigma model with n\to\infty.
Cite
@article{arxiv.hep-ph/0510033,
title = {Renormalons and Analytic Properties of the \beta function},
author = {I. M. Suslov},
journal= {arXiv preprint arXiv:hep-ph/0510033},
year = {2014}
}
Comments
6 pages, PDF