Maximum Wavelength of Confined Quarks and Gluons and Properties of Quantum Chromodynamics

TL;DR

This paper explores how confinement limits quark and gluon wavelengths, affecting their propagators, condensates, and the infrared behavior of QCD, with implications for various high-energy phenomena and phase structures.

Contribution

It introduces a model incorporating confinement effects into Dyson-Schwinger equations, modifying propagators and condensates, and discusses their impact on QCD phenomena and phase transitions.

Findings

Effective coupling remains finite in the infrared due to confinement.

Quark and gluon condensates are confined within hadrons, not in the vacuum.

Maximum wavelengths influence deep inelastic scattering, quarkonia decay, and phase structure.

Abstract

Because quarks and gluons are confined within hadrons, they have a maximum wavelength of order the confinement scale. Propagators, normally calculated for free quarks and gluons using Dyson-Schwinger equations, are modified by bound-state effects in close analogy to the calculation of the Lamb shift in atomic physics. Because of confinement, the effective quantum chromodynamic coupling stays finite in the infrared. The quark condensate which arises from spontaneous chiral symmetry breaking in the bound state Dyson-Schwinger equation is the expectation value of the operator $\bar q q$ evaluated in the background of the fields of the other hadronic constituents, in contrast to a true vacuum expectation value. Thus quark and gluon condensates reside within hadrons. The effects of instantons are also modified. We discuss the implications of the maximum quark and gluon wavelength for phenomena such as deep inelastic scattering and annihilation, the decay of heavy quarkonia, jets, and dimensional counting rules for exclusive reactions. We also discuss implications for the zero-temperature phase structure of a vectorial SU($N$) gauge theory with a variable number $N_f$ of massless fermions.