From Moments to Functions in Quantum Chromodynamics

TL;DR

This paper demonstrates how to derive the analytic forms of single-scale quantities in QCD, such as anomalous dimensions and Wilson coefficients, from a finite set of moments using large-scale recursions and computer algebra.

Contribution

It introduces a method to compute the full analytic expressions of QCD quantities from a finite number of moments at 3-loop order.

Findings

Successfully derived anomalous dimensions and Wilson coefficients from moments

Implemented large-scale recursions with computer algebra

Extended calculations to 3-loop order in unpolarized deep inelastic scattering

Abstract

Single-scale quantities, like the QCD anomalous dimensions and Wilson coefficients, obey difference equations. Therefore their analytic form can be determined from a finite number of moments. We demonstrate this in an explicit calculation by establishing and solving large scale recursions by means of computer algebra for the anomalous dimensions and Wilson coefficients in unpolarized deeply inelastic scattering from their Mellin moments to 3-loop order.