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

D. J. Broadhurst·J. Fleischer·O. V. Tarasov
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Abstract

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. 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 $d$, 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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D. J. Broadhurst, J. Fleischer, O. V. Tarasov. 1993-04-27. Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension. https://doi.org/10.1007/bf01474625

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