# QCD Technology: Light-Cone Quantization and Commensurate Scale Relations

## 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}{sub 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}{sub 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 relationsmore »

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center, Menlo Park, CA (US)

- Sponsoring Org.:
- USDOE Office of Energy Research (ER) (US)

- OSTI Identifier:
- 12479

- Report Number(s):
- SLAC-PUB-8240

TRN: US0401874

- DOE Contract Number:
- AC03-76SF00515

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 3 Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DECAY AMPLITUDES; DEGREES OF FREEDOM; EFFECTIVE CHARGE; FERMIONS; FORM FACTORS; FRAGMENTATION; GLUONS; HADRONS; LIGHT CONE; MATRIX ELEMENTS; PROTONS; QUANTIZATION; QUANTUM CHROMODYNAMICS; QUARKS; RENORMALIZATION; SCATTERING; SYMMETRY

### Citation Formats

```
Brodsky, Stanley J.
```*QCD Technology: Light-Cone Quantization and Commensurate Scale Relations*. United States: N. p., 1999.
Web. doi:10.2172/12479.

```
Brodsky, Stanley J.
```*QCD Technology: Light-Cone Quantization and Commensurate Scale Relations*. United States. doi:10.2172/12479.

```
Brodsky, Stanley J. Fri .
"QCD Technology: Light-Cone Quantization and Commensurate Scale Relations". United States. doi:10.2172/12479. https://www.osti.gov/servlets/purl/12479.
```

```
@article{osti_12479,
```

title = {QCD Technology: Light-Cone Quantization and Commensurate Scale Relations},

author = {Brodsky, Stanley J.},

abstractNote = {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}{sub 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}{sub 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.},

doi = {10.2172/12479},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1999},

month = {9}

}