Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension

In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small q, in d 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 selfenergy, for all d, and achieve highly accelerated convergence of its expansions in powers of q/m or m/q, for d = 4. OUT–4102–43 BI–TP/92–57 April 1993 ) [email protected] ) [email protected] ) Supported by Bundesministerium für Forschung and Technologie; on leave of absence from the Joint Institute for Nuclear Research, 141980 Dubna, Russia