Renormalons and Analytic Properties of the βfunction
arXiv:hep-ph/0510033 · doi:10.1134/1.1809674
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 β(g) and some other functions. A constructive criterion for the absense of singularities consists in the proper behavior of the βfunction and its Borel image B(z) at infinity, β(g)\sim g^αand B(z)\sim z^αwith α\le 1. This criterion is probably fulfilled for the ϕ^4 theory, QED and QCD, but is violated in the O(n)-symmetric sigma model with n\to\infty.
6 pages, PDF