QCD effective charge from the three-gluon vertex of the background-field method

Abstract

In this article we study in detail the prospects of determining the infrared finite QCD effective charge from a special kinematic limit of the vertex function corresponding to three background gluons. This particular Green's function satisfies a QED-like Ward identity, relating it to the gluon propagator, with no reference to the ghost sector. Consequently, its longitudinal form factors may be expressed entirely in terms of the corresponding gluon wave function, whose inverse is proportional to the effective charge. After reviewing certain important theoretical properties, we consider a typical lattice quantity involving this vertex, and derive its exact dependence on the various form factors, for arbitrary momenta. We then focus on the particular momentum configuration that eliminates any dependence on the (unknown) transverse form factors, projecting out only the desired quantity. A preliminary numerical analysis indicates that the effective charge is relatively insensitive to the numerical uncertainties that may afflict future simulations of the aforementioned lattice quantity. The numerical difficulties associated with a parallel determination of the dynamical gluon mass are briefly discussed.

32 pages, 5 figures

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• QCD Running Couplings and Effective Charges
• Renormalization group analysis of the gluon mass equation
• Nonperturbative Ball-Chiu construction of the three-gluon vertex
• Gluon mass generation in the presence of dynamical quarks
• Three-gluon running coupling from lattice QCD at $N_f=2+1+1$: a consistency check of the OPE approach
• On the self-consistency of off-shell Slavnov-Taylor identities in QCD
• Gluon dynamics from an ordinary differential equation
• Hadronic bound-states in SU(2) from Dyson--Schwinger Equations
• Four-gluon vertex from the Curci-Ferrari model at one-loop order
• Gluon and Ghost Dynamics from Lattice QCD