Calculation of a Class of Three-Loop Vacuum Diagrams with Two Different Mass Values

Details Calculation of a Class of Three-Loop Vacuum Diagrams with Two Different Mass Values Calculation of a Class of Three-Loop Vacuum Diagrams with Two Different Mass Values

1998-05-23

arxiv.org/abs/hep-ph/9805432v4

Phys.Rev. D59 (1999) 105014

Physics

High Energy Physics

High Energy Physics - Phenomenology

RevTex, 15 pages, 4 postscript figures, minor corrections in K(c), Appendix B removed, typos corrected, acknowledgements chang

Scientific paper

10.1103/PhysRevD.59.105014

We calculate analytically a class of three-loop vacuum diagrams with two different mass values, one of which is one-third as large as the other, using the method of Chetyrkin, Misiak, and M\"{u}nz in the dimensional regularization scheme. All pole terms in \epsilon=4-D (D being the space-time dimensions in a dimensional regularization scheme) plus finite terms containing the logarithm of mass are kept in our calculation of each diagram. It is shown that three-loop effective potential calculated using three-loop integrals obtained in this paper agrees, in the large-N limit, with the overlap part of leading-order (in the large-N limit) calculation of Coleman, Jackiw, and Politzer [Phys. Rev. D {\bf 10}, 2491 (1974)].

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