Two loop vertices and tree level multicollinear limits in QCD

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

Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations

The antenna subtraction method handles real radiation contributions in higher order corrections to jet observables. The method is based on antenna functions, which encapsulate all unresolved radiation between a pair of hard radiator partons. To apply this method to compute hadron collider observables, initial-initial antenna functions with both radiators in the initial state are required. In view of extending the antenna subtraction method to next-to-next-to-leading order (NNLO) calculations at hadron colliders, we derive the one-loop initial-initial antenna functions in unintegrated and integrated form.Comment: 24 page

Two-loop master integrals for qq‾→VV q\overline{q}\to VV : the planar topologies

The two-loop QCD corrections to vector boson pair production at hadron colliders involve a new class of Feynman integrals: two-loop four-point functions with two off-shell external legs. We describe their reduction to a small set of master integrals by solving linear relations among them. We then use differential equations in the external invariants to compute all master integrals that are relevant to planar Feynman amplitudes. Our results are expressed analytically in terms of generalized harmonic polylogarithms. The calculation relies heavily on techniques that exploit the algebraic structure of these functions, which we describe in detail

Antenna subtraction at NNLO with hadronic initial states: initial-final configurations

We extend the antenna subtraction method to include initial states containing one hadron at NNLO. We present results for all the necessary subtraction terms, antenna functions, for the master integrals required to integrate them over the relevant phase space and finally for the integrated antennae themselves. Where applicable, our results are cross-checked against the known NNLO coefficient functions for deep inelastic scattering processes