Abstract

In this article we present a high-precision evaluation of the expansions in ϵ = (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. mi ∊ {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 all single-mass-scale vacuum integrals at one-, two- and three-loop order.

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