Two-loop quark self-energy in a new formalism (I) Overlapping divergences Original Research Article

A new integration technique for multi-loop Feynman integrals, called the matrix method, is developed and then applied to the divergent part of the overlapping two-loop quark self-energy function iΣ in the light-cone gauge n · Aa(x) = 0, n2 = 0. It is shown that the coefficient 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 course. It is worth noting that the original overlapping self-energy integral reduces eventually to 10 covariant and 38 noncovariant-gauge integrals. We were able to verify explicitly that the divergent parts of the 10 double covariant-gauge integrals agreed precisely with those currently used to calculate radiative corrections in the Standard Model.