ar X iv : h ep - p h / 98 05 43 2 v 4 2 3 A pr 1 99 9 Calculation of a Class of Three - Loop Vacuum Diagrams with Two Different Mass Values

Using the method of Chetyrkin, Misiak, and Münz 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. In particular, this specific mass ratio is of great interest in relation to the three-loop effective potential of the O(N) φ4 theory. All pole terms in ǫ = 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 10, 2491 (1974)]. PACS number(s): 11.10.Gh Typeset using REVTEX Electronic address: [email protected] Electronic address: [email protected] 1