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We provide an update on a long-term project that aims at evaluating massive vacuum integrals at the five-loop frontier, with high precision and in various space-time dimensions. A number of applications are sketched, mainly concerning the determination of anomalous dimensions, for quantum field theories in four, three and two dimensions.
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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 $e^{k i pi/3}$.
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