%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 }