Two loop vertices and tree level multicollinear limits in QCD

Abstract

We present a summary of the methods required to solve loop-integrals and their reduction to Master Integrals. We then present the expansion in d = 4 - 2e of the Master Integrals required for the two loop massless vertex diagrams with three off-shell legs. The results are analytic and contain a new class of two-dimensional harmonic polylogarithms, which match onto the allowed phase-space boundary for the 1→2 process. These Master Integrals are relevant for the QCD corrections to Н → V*V* (where V = W,Z) and for two-loop studies of the triple gluon (and quark-gluon) vertex. We consider multi-parton collinear limits of QCD amplitudes at tree level. Using the MHV formalism we specify the underlying analytic structure of the resulting multi- collinear splitting functions. We adapt the MHV-rules to enable us to derive splitting functions without the need to evaluate the full amplitude. We derive general results for these splitting functions that are valid for specific numbers of negative helicity partons and an arbitrary number of positive helicity partons (or vice versa). Our method can be used to find splitting amplitudes with higher numbers of negative helicity partons. We present new results describing the collinear limits of up to six gluons and up to four partons. These results will have applications in the evaluation of higher order corrections to QCD cross-sections and jet evolution.