Numerical evaluation of multi-loop integrals by sector decomposition

In a recent paper [Nucl. Phys. B 585 (2000) 741] we have presented an automated subtraction method for divergent multi-loop/leg integrals in dimensional regularisation which allows for their numerical evaluation, and applied it to diagrams with massless internal lines. Here we show how to extend this algorithm to Feynman diagrams with massive propagators and arbitrary propagator powers. As applications, we present numerical results for the master 2-loop 4-point topologies with massive internal lines occurring in Bhabha scattering at two loops, and for the master integrals of planar and non-planar massless double box graphs with two off-shell legs. We also evaluate numerically some two-point functions up to 5 loops relevant for beta-function calculations, and a 3-loop 4-point function, the massless on-shell planar triple box. Whereas the 4-point functions are evaluated in non-physical kinematic regions, the results for the propagator functions are valid for arbitrary kinematics. (C) 2004 Elsevier B.V. All rights reserved.