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\$.
%0 Journal Article
%1 Broadhurst1993Twoloop
%A Broadhurst, D. J.
%A Fleischer, J.
%A Tarasov, O. V.
%D 1993
%J Zeitschrift f�r Physik C Particles and Fields
%K condensate, tools
%N 2
%P 287--301
%R 10.1007/bf01474625
%T Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension
%U http://dx.doi.org/10.1007/bf01474625
%V 60
%X 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\$.
@article{Broadhurst1993Twoloop,
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.
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\$.},
added-at = {2019-02-23T22:09:48.000+0100},
archiveprefix = {arXiv},
author = {Broadhurst, D. J. and Fleischer, J. and Tarasov, O. V.},
biburl = {https://www.bibsonomy.org/bibtex/2db3c06d86e900d56611a0d7de16f1af9/cmcneile},
citeulike-article-id = {10349956},
citeulike-linkout-0 = {http://arxiv.org/abs/hep-ph/9304303},
citeulike-linkout-1 = {http://arxiv.org/pdf/hep-ph/9304303},
citeulike-linkout-2 = {http://dx.doi.org/10.1007/bf01474625},
day = 27,
doi = {10.1007/bf01474625},
eprint = {hep-ph/9304303},
interhash = {4b52cd7dae9a57c9f1c10beb3cd78e1b},
intrahash = {db3c06d86e900d56611a0d7de16f1af9},
issn = {0170-9739},
journal = {Zeitschrift f�r Physik C Particles and Fields},
keywords = {condensate, tools},
month = apr,
number = 2,
pages = {287--301},
posted-at = {2015-08-25 11:22:01},
priority = {2},
timestamp = {2019-02-23T22:15:27.000+0100},
title = {{Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension}},
url = {http://dx.doi.org/10.1007/bf01474625},
volume = 60,
year = 1993
}