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

In this article we present a high-precision evaluation of the expansions in ǫ = (4−d)/2 of (up to) fourloop 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-, twoand three-loop order.