Numerical integration of one-loop Feynman diagrams forN-photon amplitudes

In the calculation of cross sections for infrared-safe observables in highenergy collisions at next-to-leading order, one approach is to perform all ofthe integrations, including the virtual loop integration numerically. One woulduse a subtraction scheme that removes infrared and collinear divergences fromthe integrand in a style similar to that used for real emission graphs. Thenone would perform the loop integration by Monte Carlo integration along withthe integrations over final state momenta. In this paper, we have explored howone can perform the numerical integration. We have studied the N-photonscattering amplitude with a massless electron loop in order to have a case witha singular integrand that is not, however, so singular as to require thesubtractions. We report results for N = 4, N = 5 with left-handed couplings,and N=6.Comment: 30 pages including 5 figures. This is a revised version that is close to the published versio