Two-loop quark self-energy in a new formalism: (II) Renormalization of the quark propagator in the light-cone gauge Original Research Article

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·Aa(x)=0, n2=0. (The overlapping self-energy diagram had already been computed.) The chief technical tools include the powerful matrix integration technique, the n∗μ-prescription for the spurious poles of (q·n)−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 Σ2 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 Σ2 implies a quark mass counterterm of the form δm(lcg)=mα̃sCF(3+α̃sW)+O(α̃s3), α̃s≡g2Γ(ϵ)(4π)ϵ−2, with W depending only on the dimensional regulator ϵ, and on the numbers of colors and flavors. It turns out that δm(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.