Christoph Regner (Vienna): Renormalons, R‐evoultion and Renormalon Sum Rule

Perturbation series in QCD are generally known to be divergent and can at best be considered asymptotic. The asymptotic behaviour is caused by contributions from small and large loop momenta in perturbative calculations and manifests itself in poles of the
corresponding Borel transform. These poles are usually referred to as renormalons and
lead to ambiguities in the definition of perturbative series. In this talk we discuss the
implications of these ambiguities and investigate how well renormalon ambiguities can
be quantified. Furthermore it will be shown how the introduction of a new scale R can
be used to improve the poor convergence behaviour of perturbative series suffering
from renormalon ambiguities. From the solution of renormalization group equations
with respect to the scale R (R‐evolution), one can deduce an analytic all‐order
expression for the Borel transform of perturbative series that can be used as a test for
renormalon ambiguities. We will analyze this Borel transform in the context of the large‐
$\beta_0$ approximation.