High-precision e-expansions of massive four-loop vacuum bubbles
arXiv:hep-ph/0210336 · doi:10.1016/S0370-2693(02)02910-6
Abstract
In this paper we calculate at high-precision the expansions in e=(4-D)/2 of the master integrals of 4-loop vacuum bubble diagrams with equal masses, using a method based on the solution of systems of difference equations. We also show that the analytical expression of a related on-shell 3-loop self-mass master integral contains new transcendental constants made up of complete elliptic integrals of first and second kind.
7 pages, 2 figures, LaTex, to be published in Physics Letters B