We consider QCD radiative corrections to the production of $W$ and $Z$ bosons in hadron collisions. We present a fully exclusive calculation up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. To perform this NNLO computation, we use a recently proposed version of the subtraction formalism. The calculation includes the $\gamma \mathrm{\text{−}}Z$ interference, finite-width effects, the leptonic decay of the vector bosons, and the corresponding spin correlations. Our calculation is implemented in a parton level Monte Carlo program. The program allows the user to apply arbitrary kinematical cuts on the final-state leptons and the associated jet activity and to compute the corresponding distributions in the form of bin histograms. We show selected numerical results at the Fermilab Tevatron and the LHC.

We consider QCD radiative corrections to the production of colorless high-mass systems in hadron collisions. The logarithmically-enhanced contributions at small transverse momentum are treated to all perturbative orders by a universal resummation formula that depends on a single process-dependent hard factor. We show that the hard factor is directly related to the all-order virtual amplitude of the corresponding partonic process. The direct relation is universal (process-independent), and it is expressed by an all-order factorization formula that we explicitly evaluate up to the next-to-next-to-leading order (NNLO) in QCD perturbation theory. Once the NNLO scattering amplitude is available, the corresponding hard factor is directly determined: it controls NNLO contributions in resummed calculations at full next-to-next-to-leading logarithmic accuracy, and it can be used in applications of the qT subtraction formalism to perform fully-exclusive perturbative calculations up to NNLO. The universality structure of the hard factor and its explicit NNLO form are also extended to the related formalism of threshold resummation

We consider QCD radiative corrections to vector-boson production in hadron collisions. We present the next-to-next-to-leading order (NNLO) result of the hard-collinear coefficient function for the all-order resummation of logarithmically enhanced contributions at small transverse momenta. The coefficient function controls NNLO contributions in resummed calculations at full next-to-next-to-leading logarithmic accuracy. The same coefficient function is used in applications of the subtraction method to perform fully exclusive perturbative calculations up to NNLO.

We consider higher-order QCD corrections to Higgs boson production through gluon-gluon fusion in the large top quark mass limit in hadron collisions. We extend the transverse-momentum (q _T ) subtraction method to next-to-next-to-next-to-leading order (N³LO) and combine it with the NNLO Higgs-plus-jet calculation to numerically compute differential infrared-safe observables at N³LO for Higgs boson production in gluon fusion. To cancel the infrared divergences, we exploit the universal behaviour of the associated q _T distributions in the small-q _T region. We document all the necessary ingredients of the transverse-momentum subtraction method up to N³LO. The missing third-order collinear functions, which contribute only at q _T = 0, are approximated using a prescription which uses the known result for the total Higgs boson cross section at this order. As a first application of the third-order q _T subtraction method, we present the N³LO rapidity distribution of the Higgs boson at the LHC.

We consider QCD radiative corrections to the production of colorless high-mass systems in hadron collisions. We show that the recent computation of the soft-virtual corrections to Higgs boson production at N3LO [1] together with the universality structure of soft-gluon emission can be exploited to extract the general expression of the hard-virtual coefficient that contributes to threshold resummation at N3LL accuracy. The hard-virtual coefficient is directly related to the process-dependent virtual amplitude through a universal (process-independent) factorization formula that we explicitly evaluate up to three-loop order. As an application, we present the explicit expression of the soft-virtual N3LO corrections for the production of an arbitrary colorless system. In the case of the Drell–Yan process, we confirm the recent result of Ref. [2]

We present high-accuracy QCD predictions for the transverse-momentum ($q_T$) distribution and fiducial cross sections of Drell–Yan lepton pairs produced in hadronic collisions. At small values of $q_T$ we resum to all perturbative orders the logarithmically enhanced contributions up to next-to-next-to-next-to-leading logarithmic (${\mathrm{N}}^3\mathrm{LL}$) accuracy, including all the next-to-next-to-next-to-leading order (${\mathrm{N}}^3\mathrm{LO}$) [i.e., $\mathcal{O}({\alpha }_S^3)$] terms. Our resummed calculation has been implemented in the public numerical program DYTurbo, which produces fast and precise predictions with the full dependence on the final-state lepton kinematics. We consistently combine our resummed results with the known $\mathcal{O}({\alpha }_S^3)$ fixed-order predictions at large values of $q_T$ thus also obtaining full ${\mathrm{N}}^3\mathrm{LO}$ accuracy for fiducial cross sections. We show numerical results at LHC energies discussing the reduction of the perturbative uncertainty with respect to lower-order calculations.