Ultraviolet-improved gauge technique and the effective quark propagator in QCD

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Abstract
The gauge technique linearizes the Schwinger-Dyson equation by replacing the full vertex with a longitudinal vertex, satisfying the Ward identity. We show how to improve the standard gauge-technique treatment which is nonrenormalizable, by adding a conserved transverse vertex to the longitudinal vertex thereby removing all overlapping divergences from the Schwinger-Dyson equation in QCD. The improved gauge technique preserves multiplicative renormalizability and gauge covariance. Such a modified version of the gauge technique is used to solve the Schwinger-Dyson equation for the effective quark propagator of QCD, S(p), in the ultraviolet regime. For nonzero current-quark mass m, a solution is found that agrees with renormalization-group analysis, while a similar solution appears for the m=0 case corresponding to dynamical chiral-symmetry breaking [i.e., a nonzero dynamical quark mass M(p)].