Renormalons and Analytic Properties of the βfunction

Details Renormalons and Analytic Properties of the βfunction Renormalons and Analytic Properties of the βfunction

2005-10-03

arxiv.org/abs/hep-ph/0510033v1

J.Exp.Theor.Phys. 99 (2004) 474-479; Zh.Eksp.Teor.Fiz. 126 (2004) 542-548

Physics

High Energy Physics

High Energy Physics - Phenomenology

6 pages, PDF

Scientific paper

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.

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