Paper
Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension
Authors
Abstract
In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small , in dimensions, using identities derived from integration by parts. Expansions are given, in terms of hypergeometric series, for all gluon diagrams and for all but one of the quark diagrams; expansions of the latter are obtained from differential equations. Padé approximants to truncations of the expansions are shown to be of great utility. As an application, we obtain the two-loop photon self-energy, for all , and achieve highly accelerated convergence of its expansions in powers of or , for .