A numerical method for NNLO calculations

In the last decades, the interplay between increasing precision from the experimental side and NLO predictions becoming available from the theoretical side has led to impressive tests of the Standard Model. However, certain processes or observables in QCD should be known at NNLO in perturbation theory in order to match the experimental precision, and in the domain of electroweak interactions, many NLO processes still await for being calculated exactly. The calculation of radiative corrections for electroweak processes is mainly complicated by the presence of several mass scales, whereas in QCD the challenge comes from the presence of infrared singularities due to massless partons. If we have to deal with a combination of strong and electroweak interactions, i.e. with singularities and multi-scale problems, the situation is even more involved, and the complexity of the corresponding analytic calculations is enormous. On the other hand, the performance of computers is improving continuously, and in order to calculate cross sections one generally has to use numerical integration at some point in any case. All this points to the fact that a numerical evaluation of the ingredients needed to calculate cross sections beyond leading order, like loop integrals and certain phase space integrals, will be of increasing importance in the future. In this article I will first present a method which has been developed in [1] to evaluate IR (or UV) divergent multi-loop integrals by extracting the poles in 1/ǫ and calculating the pole coeffi-