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

Abstract

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 Münz in the dimensional regularization scheme. All pole terms in ε=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)].

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

References in corpus (3)

• The Standard Model Effective Potential at Two Loops
• Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models
• Compact analytical form for a class of three-loop vacuum Feynman diagrams

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