Reduction of a Class of Three-Loop Vacuum Diagrams to Tetrahedron Topologies

J. -M. Chung; B. K. Chung

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Reduction of a Class of Three-Loop Vacuum Diagrams to Tetrahedron Topologies

J. -M. Chung·B. K. Chung

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Abstract

We obtain finite parts (as well as $ε$-pole parts) of massive three-loop vacuum diagrams with three-point and/or four-point interaction vertices by reducing them to tetrahedron diagrams with both massive and massless lines, whose finite parts were given analytically in a recent paper by Broadhurst. In the procedure of reduction, the method of integration-by-parts recurrence relations is employed. We use our result to compute the $\bar{\rm MS}$ effective potential of the massive $ϕ^4$ theory.

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J. -M. Chung, B. K. Chung. 2001-01-19. Reduction of a Class of Three-Loop Vacuum Diagrams to Tetrahedron Topologies. https://arxiv.org/abs/hep-th/0101098

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