Dynamical mass generation in continuum quantum chromodynamics

TLDR

The study uses gauge‑invariant Schwinger‑Dyson equations derived from a resummation of Feynman graphs, essential for multiplicative renormalizability in light‑cone gauge, and notes that similar ambiguities are reduced in three‑dimensional QCD where quark confinement is linked to a vortex condensate supported by the mass gap. The authors investigate the emergence of a mass gap and effective gluon mass in continuum QCD via specialized Schwinger‑Dyson equations. They close the equations by solving a Ward identity, exact in the infrared but ambiguous in the ultraviolet, within the resummed, gauge‑invariant framework. Numerical results indicate an effective gluon mass of 500 ± 200 MeV and a 0⁺ glueball mass roughly twice that.

Abstract

We study the formation of a mass gap, or effective gluon mass (and consequent dimensionful parameters such as the string tension, glueball mass, $〈\mathrm{Tr}{{G}_{\ensuremath{\mu}\ensuremath{\nu}}}^{2}〉$, correlation lengths) in continuum QCD, using a special set of Schwinger-Dyson equations. These equations are derived from a resummation of the Feynman graphs which represent certain gauge-invariant color-singlet Green's functions, and are themselves essentially gauge invariant. This resummation is essential to the multiplicative renormalizability of QCD in the light-cone gauge, which we adopt for technical reasons. We close the dynamical equations by "solving" a Ward identity, a procedure which, while exact in the infrared regime, is subject to ambiguities and corrections in the ultraviolet regime which are beyond the scope of the present work. (These ambiguities are less prominent for QCD in three dimensions, which we discuss also.) As discussed in an earlier work, quark confinement arises from a vortex condensate supported by the mass gap. Numerical calculations of the mass gap are presented, suggesting an effective gluon mass of 500\ifmmode\pm\else\textpm\fi{}200 MeV and a ${0}^{+}$ glueball mass of about twice this value.