Power corrections and Landau singularity

TL;DR

The paper investigates power corrections in QCD within a dispersive framework that regularizes the infrared running coupling to remove the Landau pole. It formalizes a split between perturbative and non-perturbative contributions, deriving both UV- and IR-origin power corrections through Borel-transform methods and dispersive integrals. It shows that IR regularization can induce perturbative power corrections that extend beyond traditional OPE expectations, and it discusses Minkowskian observables, with concrete implications for the tau hadronic width and lattice determinations of the gluon condensate. The work clarifies how short-distance power terms can arise naturally in this scheme and outlines how to interpret and disentangle these effects in phenomenology, while noting ambiguities connected to renormalons and the definition of a condensate.

Abstract

In the dispersive approach of Dokshitzer, Marchesini and Webber, standard power-behaved contributions of infrared origin are described with the notion of an infrared regular QCD coupling. I argue that their framework suggests the existence of non-standard contributions, arising from short distances (hence unrelated to renormalons and the operator product expansion), which appear in the process of removing the Landau singularity of the perturbative coupling. A natural definition of an infrared finite perturbative coupling is suggested within the dispersive method. Implications for the tau hadronic width and the lattice determination of the gluon condensate, where $O(1/Q^2)$ contributions can be generated, are pointed out.