Non-perturbative comparison of QCD effective charges

Abstract

We study the non-perturbative behavior of two versions of the QCD effective charge, one obtained from the pinch technique gluon self-energy, and one from the ghost-gluon vertex. Despite their distinct theoretical origin, due to a fundamental identity relating various of the ingredients appearing in their respective definitions, the two effective charges are almost identical in the entire range of physical momenta, and coincide exactly in the deep infrared, where they freeze at a common finite value. Specifically, the dressing function of the ghost propagator is related to the two form factors in the Lorentz decomposition of a certain Green's function, appearing in a variety of field-theoretic contexts. The central identity, which is valid only in the Landau gauge, is derived from the Schwinger-Dyson equations governing the dynamics of the aforementioned quantities. The renormalization procedure that preserves the validity of the identity is carried out, and various relevant kinematic limits and physically motivated approximations are studied in detail. A crucial ingredient in this analysis is the infrared finiteness of the gluon propagator, which is inextricably connected with the aforementioned freezing of the effective charges. Some important issues related to the consistent definition of the effective charge in the presence of such a gluon propagator are resolved. We finally present a detailed numerical study of a special set of Schwinger-Dyson equations, whose solutions determine the non-perturbative dynamics of the quantities composing the two effective charges.

34 pages, 14 figures

References in corpus (10)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Constraints on the IR behavior of the gluon propagator in Yang-Mills theories
• Gribov no-pole condition, Zwanziger horizon function, Kugo-Ojima confinement criterion, boundary conditions, BRST breaking and all that
• Building the Full Fermion-Photon Vertex of QED by Imposing Multiplicative Renormalizability of the Schwinger-Dyson Equations for the Fermion and Photon Propagators
• Gauge-invariant truncation scheme for the Schwinger-Dyson equations of QCD
• Power-law running of the effective gluon mass
• Kugo-Ojima color confinement criterion and Gribov-Zwanziger horizon condition
• Gluon mass and freezing of the QCD coupling
• Effective gluon mass and infrared fixed point in QCD

Cited by in corpus (1)

• Decoupling and scaling solutions in Yang-Mills theory with the Gribov horizon