# High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles

Authors
Type
Published Article
Publication Date
Mar 21, 2005
Submission Date
Mar 21, 2005
Identifiers
DOI: 10.1088/1126-6708/2005/06/051
arXiv ID: hep-ph/0503209
Source
arXiv
In this article we present a high-precision evaluation of the expansions in $\e=(4-d)/2$ of (up to) four-loop scalar vacuum master integrals, using the method of difference equations developed by S. Laporta. We cover the complete set of QED-type' master integrals, i.e. those with a single mass scale only (i.e. $m_i\in\{0,m\}$) and an even number of massive lines at each vertex. Furthermore, we collect all that is known analytically about four-loop QED-type' masters, as well as about {\em all} single-mass-scale vacuum integrals at one-, two- and three-loop order.