We present the computational framework Matrix [1] which allows us to evaluate fully differential cross sections for a wide class of processes at hadron colliders in next-tonext-to-leading order (NNLO) QCD. The processes we consider are 2 → 1 and 2 → 2 hadronic reactions involving Higgs and vector bosons in the final state. All possible leptonic decay channels of the vector bosons are included for the first time in the calculations, by consistently accounting for all resonant and non-resonant diagrams, off-shell effects and spin correlations. We briefly introduce the theoretical framework Matrix is based on, discuss its relevant features and provide a detailed description of how to use Matrix to obtain NNLO accurate results for the various processes. We report reference predictions for inclusive and fiducial cross sections of all the physics processes considered here and discuss their corresponding uncertainties. Matrix features an automatic extrapolation procedure that allows us, for the first time, to control the systematic uncertainties inherent to the applied NNLO subtraction procedure down to the few permille level (or better).

We present a novel method to combine QCD calculations at next-to-next-toleading order (NNLO) with parton shower (PS) simulations, that can be applied to the production of heavy systems in hadronic collisions, such as colour singlets or a tt pair. The NNLO corrections are included by connecting the MiNLO method with transversemomentum resummation, and they are calculated at generation time without any additional reweighting, making the algorithm considerably efficient. Moreover, the combination of different jet multiplicities does not require any unphysical merging scale, and the matching preserves the structure of the leading logarithmic corrections of the Monte Carlo simulation for parton showers ordered in transverse momentum. We present proof-of-concept applications to hadronic Higgs production and the Drell-Yan process at the LHC.

We consider QCD radiative corrections to W + W − production at the LHC and present the first fully differential predictions for this process at next-to-next-to-leading order (NNLO) in perturbation theory. Our computation consistently includes the leptonic decays of the W bosons, taking into account spin correlations, off-shell effects and nonresonant contributions. Detailed predictions are presented for the different-flavour channel pp → µ + e − ν µνe + X at √ s = 8 and 13 TeV. In particular, we discuss fiducial cross sections and distributions in the presence of standard selection cuts used in experimental W + W − and H → W + W − analyses at the LHC. The inclusive W + W − cross section receives large NNLO corrections, and, due to the presence of a jet veto, typical fiducial cuts have a sizeable influence on the behaviour of the perturbative expansion. The availability of differential NNLO predictions, both for inclusive and fiducial observables, will play an important role in the rich physics programme that is based on precision studies of W + W − signatures at the LHC.

Novel contributions to the total inclusive cross section for Higgs-Strahlung in the Standard Model at hadron colliders are evaluated. Although formally of order α 2 s , they have not been taken into account in previous NNLO predictions. The terms under consideration are induced by Higgs radiation off top-quark loops and thus proportional to the top-quark Yukawa coupling. At the Tevatron, their effects to WH production are below 1% in the relevant Higgs mass range, while for ZH production, we find corrections between about 1% and 2%. At the LHC, the contribution of the newly evaluated terms to the cross section is typically of the order of 1%-3%. Based on these results, we provide updated predictions for the total inclusive Higgs-Strahlung cross section at the Tevatron and the LHC.