We discuss a modification of the next-to-next-to-leading order (NNLO) subtraction scheme based on the residue-improved sector decomposition that reduces the number of double-real emission sectors from five to four. In particular, a sector where energies and angles of unresolved particles vanish in a correlated fashion is redundant and can be discarded. This simple observation allows us to formulate a transparent iterative subtraction procedure for double-real emission contributions, to demonstrate the cancellation of soft and collinear singularities in an explicit and (almost) process-independent way and to write the result of a NNLO calculation in terms of quantities that can be computed in four space-time dimensions. We illustrate this procedure explicitly in the simple case of gluonic corrections to the Drell–Yan process of annihilation into a lepton pair. We show that this framework leads to fast and numerically stable computation of QCD corrections.

Abstract:We present an implementation of the vector boson pair production processes ZZ, W + W − and W Z within the POWHEG framework, which is a method that allows the interfacing of NLO calculations to shower Monte Carlo programs. The implementation is built within the POWHEG BOX package. The Z/γ * interference, as well as singly resonant contributions, are properly included. We also considered interference terms arising from identical leptons in the final state. As a result, all contributions leading to the desired four-lepton system have been included in the calculation, with the sole exception of the interference between ZZ and W + W − in the production of a pair of same-flavour, oppositely charged fermions and a pair of neutrinos, which we show to be fully negligible. Anomalous trilinear couplings can be also set in the program, and we give some examples of their effect at the LHC. We have made the relevant code available at the POWHEG BOX web site.

We compute the next-to-leading-order QCD corrections to the production of two Z-bosons in the annihilation of two gluons at the LHC. Being enhanced by a large gluon flux, these corrections provide a distinct and, potentially, the dominant part of the N 3 LO QCD contributions to Z-pair production in proton collisions. The gg → ZZ annihilation is a loop-induced process that receives the dominant contribution from loops of five light quarks, that are included in our computation in the massless approximation. We find that QCD corrections increase the gg → ZZ production cross section by Oð50%-100%Þ depending on the values of the renormalization and factorization scales used in the leading-order computation and the collider energy. The large corrections to the gg → ZZ channel increase the pp → ZZ cross section by about 6% to 8%, exceeding the estimated theoretical uncertainty of the recent next-to-next-to-leading-order QCD calculation.

We present analytic formulas that describe fully-differential production of color-singlet final states in qq and gg annihilation, including all the relevant partonic channels, through NNLO QCD. We work within the nested soft-collinear scheme which allows for fully local subtraction of infrared divergences. We demonstrate analytic cancellation of soft and collinear poles and present formulas for finite parts of all integrated subtraction terms. These results provide an important building block for calculating NNLO QCD corrections to arbitrary processes at hadron colliders within the nested soft-collinear subtraction scheme.