2-LOOP QUARK SELF-ENERGY IN A NEW FORMALISM .1. OVERLAPPING DIVERGENCES

A new integration technique for multi-loop Feynman integrals, called t he matrix method, is developed and then applied to the divergent part of the overlapping two-loop quark self-energy function i Sigma in the light-cone gauge n . A(a)(x) = 0, n(2) = 0. It is shown that the coeff icient of the double-pole term is strictly local, even off mass-shell, while the coefficient of the single-pole term contains local as well as nonlocal parts. On mass-shell, the single-pole part is local, of co urse. It is worth noting that the original overlapping self-energy int egral reduces eventually to 10 covariant and 38 noncovariant-gauge int egrals. We were able to verify explicitly that the divergent parts of the 10 double covariant-gauge integrals agreed precisely with those cu rrently used to calculate radiative corrections in the Standard Model. Our new technique is amazingly powerful, being applicable to massive and massless integrals alike, and capable of handling both covariant-g auge integrals and the more difficult noncovariant-gauge integrals. Pe rhaps the most important feature of the matrix method is the ability t o execute the 4 omega-dimensional momentum integrations in a single op eration, exactly and in analytic form. The method works equally well f or other axial-type gauges, notably the temporal gauge (n(2) > 0) and the pure axial gauge (n(2) < 0).