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

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

1993-04-27

arxiv.org/abs/hep-ph/9304303v1

Z.Phys.C60:287-302,1993

Physics

High Energy Physics

High Energy Physics - Phenomenology

25 pages, OUT--4102--43, BI--TP/92--57

Scientific paper

10.1007/BF01474625

In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, 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. Pad\'{e} 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 $d$, and achieve highly accelerated convergence of its expansions in powers of $q^2/m^2$ or $m^2/q^2$, for $d=4$.

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