Two-Loop Quark Self-Energy in a New Formalism (II): Renormalization of the Quark Propagator in the Light-Cone Gauge

Abstract

The complete two-loop correction to the quark propagator, consisting of the spider, rainbow, gluon bubble and quark bubble diagrams, is evaluated in the noncovariant light-cone gauge (lcg). (The overlapping self-energy diagram had already been computed.) The chief technical tools include the powerful matrix integration technique, the n^*-prescription for the spurious poles of 1/qn, and the detailed analysis of the boundary singularities in five- and six-dimensional parameter space. It is shown that the total divergent contribution to the two-loop correction Sigma_2 contains both covariant and noncovariant components, and is a local function of the external momentum p, even off the mass-shell, as all nonlocal divergent terms cancel exactly. Consequently, both the quark mass and field renormalizations are local. The structure of Sigma_2 implies a quark mass counterterm of the form $\delta m (lcg) = m\tilde\alpha_s C_F(3+\tilde\alpha_sW) + {\rm O} (\tilde\alpha_s^3)$, $\tilde\alpha_s = g^2\Gamma(\eps)(4\pi)^{\eps -2}$, with W depending only on the dimensional regulator epsilon, and on the numbers of colors and flavors. It turns out that \delta m(lcg) is identical to the mass counterterm in the general linear covariant gauge. Our results are in agreement with the Bassetto-Dalbosco-Soldati renormalization scheme.