Three-loop massive tadpoles and polylogarithms through weight six

Abstract

We evaluate the three-loop massive vacuum bubble diagrams in terms of polylogarithms up to weight six. We also construct the basis of irrational constants being harmonic polylgarithms of arguments $e^{ki\pi /3}$.

Comments: 26 pages, 4 ancillary files, v3: version published in JHEP: minor additions, file with results for massive three-loop form-factor integrals added