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

Y. Schroder·A. Vuorinen
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Abstract

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.

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Y. Schroder, A. Vuorinen. 2005-03-21. High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles. https://doi.org/10.1088/1126-6708%2F2005%2F06%2F051

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