Two-loop quark self-energy in a new formalism; 2, Renormalization of the quark propagator in the light-cone gauge

For pt.I see ibid., vol.440, p.537-602, 1995. The complete two-loop correction to the quark propagator, consisting of the spider, rainbow, gluon bubble and quark bubble diagrams, is evaluated in the non-covariant light-cone gauge (LCG), n.A/sup a/(x)=0, n/sup 2/=0. (The overlapping self-energy diagram had already been computed.) The chief technical tools include the powerful matrix integration technique, the n*/sub mu /-prescription for the spurious poles of (q.n)/sup -1/, 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 /sub 2/ contains both covariant and non-covariant components, and is a local function of the external momentum p, even off the mass-shell, as all non-local divergent terms cancel exactly. Consequently, both the quark mass and field renormalizations are local. The structure of Sigma /sub 2/ implies a quark mass counterterm of the form delta m(LCG)=m alpha /sub s/C/sub F/(3+ alpha /sub s/W)+O( alpha /sub s//sup 3/), alpha /sub s/ identical to g/sup 2/ Gamma ( epsilon )(4 pi )/sup epsilon -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 (1987). (44 refs).