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We describe a general method of calculating the fully differential cross section for the production of jets at next-to-leading order in a hadron collider. This method is based on a 'crossing' of next-to-leading order calculations with all partons in the final state. The method introduces universal crossing functions that allow a modular approach to next-to-leading order calculations for any process with initial state partons. These techniques are applied to the production of jets in association with a vector boson including all decay correlations of the final state observables.

We establish an efficient polynomial-complexity algorithm for one-loop calculations, based on generalized D-dimensional unitarity. It allows automated computations of both cut-constructible and rational parts of one-loop scattering amplitudes from on-shell tree amplitudes. We illustrate the method by (re)-computing all four-, five-and six-gluon scattering amplitudes in QCD at one-loop.

We present a simple formalism for the evolution of timelike jets in which tree-level matrix element corrections can be systematically incorporated, up to arbitrary parton multiplicities and over all of phase space, in a way that exponentiates the matching corrections. The scheme is cast as a shower Markov chain which generates one single unweighted event sample, that can be passed to standard hadronization models. Remaining perturbative uncertainties are estimated by providing several alternative weight sets for the same events, at a relatively modest additional overhead. As an explicit example, we consider Z → qq evolution with unpolarized, massless quarks and include several formally subleading improvements as well as matching to tree-level matrix elements through α 4 s . The resulting algorithm is implemented in the publicly available Vincia plugin 1 to the Pythia8 event generator.

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We present a simple formalism for parton-shower Markov chains. As a first step towards more complete 'uncertainty bands', we incorporate a comprehensive exploration of the ambiguities inherent in such calculations. To reduce this uncertainty, we then introduce a matching formalism which allows a generated event sample to simultaneously reproduce any infrared safe distribution calculated at leading or next-to-leading order in perturbation theory, up to sub-leading corrections.To enable a more universal definition of perturbative calculations, we also propose a more general definition of the hadronization cutoff. Finally, we present an implementation of some of these ideas for final-state gluon showers, in a code dubbed VINCIA.

We present the implementation of several colorsinglet final-state processes at Next-to-Next-to Leading Order (NNLO) accuracy in QCD to the publicly available parton-level Monte Carlo program MCFM. Specifically we discuss the processesDecays of the unstable bosons are fully included, resulting in a flexible fully differential Monte Carlo code. The NNLO corrections have been calculated using the non-local N -jettiness subtraction approach. Special attention is given to the numerical aspects of running MCFM for these processes at this order. We pay particular attention to the systematic uncertainties due to the power corrections induced by the N -jettiness regularization scheme and the evaluation time needed to run the hybrid openMP/MPI version of MCFM at NNLO on multiprocessor systems.

We use the recently proposed jettiness-subtraction scheme to provide the complete calculation of Higgs boson production in association with a jet in hadronic collisions through next-to-nextto-leading order in perturbative QCD. This method exploits the observation that the N -jettiness event-shape variable completely describes the singularity structure of QCD when final-state colored particles are present. Our results are in agreement with a recent computation of the gg and qg partonic initial states based on sector-improved residue subtraction. We present phenomenological results for both fiducial cross sections and distributions at the LHC.