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 $e^{ki\pi /3}$.

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

References in corpus (5)

• Complete renormalization of QCD at five loops
• Iterated Binomial Sums and their Associated Iterated Integrals
• Analytic results for planar three-loop integrals for massive form factors
• Application of the DRA method to the calculation of the four-loop QED-type tadpoles
• "Sixth root of unity" and Feynman diagrams: hypergeometric function approach point of view

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