TVID 2 computes all master integrals for planar three-loop self-energy diagrams with two closed fermion loops using at most two-dimensional numerical integrations.
Three-loop vacuum integrals with arbitrary masses
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abstract
Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, only results for integrals with one and two independent mass scales are known, but in the electroweak Standard Model and many extensions thereof, one often encounters more mass scales of comparable magnitude. For this reason, a numerical approach for the evaluation of three-loop vacuum integrals with arbitrary mass pattern is proposed here. Concretely, one can identify a basic set of three master integral topologies. With the help of dispersion relations, each of these can be transformed into one-dimensional or, for the most complicated case, two-dimensional integrals in terms of elementary functions, which are suitable for efficient numerical integration.
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TVID 2: Evaluation of planar-type three-loop self-energy integrals with arbitrary masses
TVID 2 computes all master integrals for planar three-loop self-energy diagrams with two closed fermion loops using at most two-dimensional numerical integrations.