Dispersive Approach to Power-Behaved Contributions in QCD Hard Processes

TL;DR

The paper develops a dispersive, universal approach to capture power-suppressed, non-perturbative contributions in QCD hard processes by introducing an infrared-finite effective coupling $ ext{a}_{ ext{eff}}(ic^2)$. Observables receive dispersively generated power corrections that are expressed as (log-)moment integrals of $ ext{a}_{ ext{eff}}$, with leading terms determined by one-loop diagrams featuring a small gluon mass and process-dependent characteristic functions. The authors systematically analyze quark-dominated processes (including $e^+e^-$ annihilation, DIS structure functions, and Drell-Yan) and derive explicit leading power terms in $1/Q^{2p}$ or $1/Q$ for various observables, all written in terms of universal moments $A_{2p}, A'_{2p}, A''_{2p}$. This framework aims to test and constrain the low-scale behavior of QCD dynamics from inclusive observables, offering a unified treatment of non-perturbative effects across multiple processes. Overall, the work provides a first-principles-inspired method to quantify and test confinement-inspired power corrections in a broad class of hard QCD processes through a dispersive coupling formalism.

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 analyse 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 τhadronic 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).