A new method for real radiation at next-to-next-to-leading order

Abstract

We propose a new method of computing real emission contributions to hard QCD processes. Our approach uses sector decomposition of the exclusive final-state phase space to enable extraction of all singularities of the real emission matrix elements before integration over any kinematic variable. The exact kinematics of the real emission process are preserved in all regions of phase space. Traditional approaches to extracting singularities from real emission matrix elements, such as phase space slicing and dipole subtraction, require both the determination of counterterms for double real emission amplitudes in singular kinematic limits and the integration of these contributions analytically to cancel the resulting singularities against virtual corrections. Our method addresses both of these issues. The implementation of constraints on the final-state phase space, including various jet algorithms, is simple using our approach. We illustrate our method using e + e − → jets at O(α 2 S ) as an example.

Constraints for the nuclear parton distributions from Z and W ± production at the LHC

“…The calculations are already reaching the NNLO accuracy [1] with the NNLO correction on top of the NLO one found rather small. This observation has given confidence to include the recent Tevatron measurements [2,3,4] for W ± and Z production to the latest global analyses of the free proton parton distribution functions (PDFs) [5,6,7].…”

“…The relevant expressions can be found for example from [1] or obtained from [23,24] with obvious change of couplings indicated below. In order to illustrate the ingredients and to exactly specify the computed quantity, we record here the leading order part of the cross-sections.…”

Measurement of the top pair production cross section in 8 TeV proton-proton collisions using kinematic information in thelepton+jetsfinal state with ATLAS

“…An alternative W þ jets sample simulated with SHERPA [30] with massive b=c quarks was produced to evaluate systematic uncertainties on W þ jets modeling. The V þ jets processes were normalized to the NNLO calculations [31,32].…”

CT10 next-to-next-to-leading order global analysis of QCD

“…Thus, there is a need for using cross sections calculated up to next-to-next-to-leading order (NNLO) in the strong coupling constant α s with parton distribution function sets that are also determined at NNLO. Complete calculations for this order in α s are available for the running coupling α s ðQÞ, PDF evolution in Q [11,12], matrix elements in deepinelastic scattering (DIS) [13][14][15][16][17][18][19], and vector boson production [20,21]. NNLO matrix elements are unknown for several other processes in the global analysis.…”