Compact analytical form for a class of three-loop vacuum Feynman diagrams

Abstract

We present compact, fully analytical expressions for singular parts of a class of three-loop diagrams which cannot be factorized into lower-loop integrals. As a result of the calculations we obtain the analytical expression for the three-loop effective potential of the massive O(N) \phi^4 model presented recently by J.-M.Chung and B.K.Chung, Phys.Rev. D56, 6508 (1997).