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

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

2001-01-16

arxiv.org/abs/hep-th/0101098v2

J.Korean Phys.Soc. 38 (2001) 60-64

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, no figure, typos in Eq.(3) and Eq.(7) corrected

Scientific paper

We obtain finite parts (as well as $\epsilon$-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 $\phi^4$ theory.

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