Dispersive approach to power-behaved contributions in QCD hard processes

Abstract

We consider power-behaved contributions to hard processes in QCD arising from non-perturbative effects at low scales which can be described by introducing the notion of an infrared-finite effective coupling. Our method is based on a dispersive treatment which embodies running coupling effects in all orders. The resulting power behaviour is consistent with expectations based on the operator product expansion, but our approach is more widely applicable. The dispersively generated power contributions to different observables are given by (log-)moment integrals of a universal low-scale effective coupling, with process-dependent powers and coefficients. We analyze a wide variety of quark-dominated processes and observables, and show how the power contributions are specified in lowest order by the behaviour of one-loop Feynman diagrams containing a gluon of small virtual mass. We discuss both collinear-safe observables (such as the e + e − total cross section and τ hadronic width, DIS sum rules, e + e − event shape variables and the Drell-Yan K-factor) and collinear divergent quantities (such as DIS structure functions, e + e − fragmentation functions and the Drell-Yan cross section).