Abstract
We present a subtraction method utilizing the N -jettiness observable, T N , to perform QCD calculations for arbitrary processes at next-to-next-to-leading order (NNLO). Our method employs soft-collinear effective theory (SCET) to determine the IR singular contributions of N -jet cross sections for T N → 0, and uses these to construct suitable T N -subtractions. The construction is systematic and economic, due to being based on a physical observable. The resulting NNLO calculation is fully differential and in a form directly suitable for combining with resummation and parton showers. We explain in detail the application to processes with an arbitrary number of massless partons at lepton and hadron colliders together with the required external inputs in the form of QCD amplitudes and lower-order calculations. We provide explicit expressions for the T N -subtractions at NLO and NNLO. The required ingredients are fully known at NLO, and at NNLO for processes with two external QCD partons. The remaining NNLO ingredient for three or more external partons can be obtained numerically with existing NNLO techniques. As an example, we employ our results to obtain the NNLO rapidity spectrum for Drell-Yan and gluon-fusion Higgs production. We discuss aspects of numerical accuracy and convergence and the practical implementation. We also discuss and comment on possible extensions, such as more-differential subtractions, necessary steps for going to N3LO, and the treatment of massive quarks.
Highlights
The precise knowledge of QCD corrections is a key ingredient for interpreting the data from collider experiments
The inclusive QCD cross section for the production of a final state X can, if the hard scale Q associated with X is large enough, be obtained in terms of a perturbatively calculable partonic cross section convolved with parton distribution functions (PDFs)
The decomposition of the T0 spectrum into singular and nonsingular components is shown in figures 3 and 5 for Drell-Yan and Higgs production, respectively, where we separately show the O(αs) (NLO) and O(αs2) corrections, counted relative to the leading order (LO) Born cross section
Summary
The precise knowledge of QCD corrections is a key ingredient for interpreting the data from collider experiments. (It has been suggested that this method can be applied to compute heavy-quark pair production at NNLO [48, 49].) Our N -jettiness subtraction method generalizes this to arbitrary numbers of QCD partons in the initial and final state It employs the N -jettiness global event shape [50] as the physical N -jet resolution variable. In this work we give a general description of how N -jet resolution variables, and N -jettiness, can be used as subtraction terms to compute fixed-order cross sections. We demonstrate that this naturally leads to subtraction terms for fixed-order calculations, and show how these can be used in phase-space slicing, as done in refs.
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