QCD Technology: Light-Cone Quantization and Commensurate Scale Relations

TL;DR

This paper reviews theoretical tools like light-cone quantization, effective charge, conformal symmetry, and commensurate scale relations to analyze both perturbative and non-perturbative aspects of quantum chromodynamics, enhancing understanding of hadron structure and interactions.

Contribution

It introduces and discusses the application of light-cone wavefunctions, effective charge, conformal symmetry, and commensurate scale relations as novel tools for QCD analysis.

Findings

Light-cone wavefunctions encode hadron properties in terms of quark and gluon degrees of freedom.

Effective charge $ extalpha_V$ provides a physical coupling with analytic mass dependence.

Conformal symmetry leads to relations between observables even without scale invariance.

Abstract

I discuss several theoretical tools which are useful for analyzing perturbative and non-perturbative problems in quantum chromodynamics, including (a) the light-cone Fock expansion, (b) the effective charge $\alpha_V$, (c) conformal symmetry, and (d) commensurate scale relations. Light-cone Fock-state wavefunctions encode the properties of a hadron in terms of its fundamental quark and gluon degrees of freedom. Given the proton's light-cone wavefunctions, one can compute not only the quark and gluon distributions measured in deep inelastic lepton-proton scattering, but also the multi-parton correlations which control the distribution of particles in the proton fragmentation region and dynamical higher twist effects. Light-cone wavefunctions also provide a systematic framework for evaluating exclusive hadronic matrix elements, including timelike heavy hadron decay amplitudes and form factors. The $\alpha_V$ coupling, defined from the QCD heavy quark potential, provides a physical expansion parameter for perturbative QCD with an analytic dependence on the fermion masses which is now known to two-loop order. Conformal symmetry provides a template for QCD predictions, including relations between observables which are present even in a theory which is not scale invariant. Commensurate scale relations are perturbative QCD predictions based on conformal symmetry relating observable to observable at fixed relative scale. Such relations have no renormalization scale or scheme ambiguity.