Single mass scale diagrams: construction of a basis for the $ϵ$-expansion

Abstract

Exploring the idea of Broadhurst on the ``sixth root of unity'' we present an ansatz for construction of a basis of transcendental numbers for the epsilon-expansion of single mass scale diagrams with two particle massive cut. As example, several new two- and three-loop master integrals are calculated.

Comments: 13 pages, LaTeX, two eps-figures. in v.3 misprint in epsilon-part of Eq.(10) is corrected