N-jettiness subtractions for NNLO QCD calculations

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 N 3 LO, and the treatment of massive quarks.

A complete basis of helicity operators for subleading factorization

“…Subtraction schemes based on factorization theorems include the recently introduced N -jettiness subtraction scheme [137][138][139], based on the N -jettiness event shape [140], as well as the SCET based subtraction scheme for NNLO semileptonic top quark decays of ref. [141].…”

NNLO QCD predictions for fully-differential top-quark pair production at the Tevatron

“…This has been possible thanks to the development of subtraction schemes [62][63][64][65][66][67][68][69][70], slicing methods [60,61,71] and the calculation of several two-to-two virtual amplitudes [72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91]. As far as top-quark pair production is concerned, besides our own calculation [10,92] only partial results are known at the differential level [93,94]; there is also progress at the level of total crosssection [95] obtained with slicing methods.…”

Drell-Yan production atNNLL′+NNLOmatched to parton showers

“…The fact that the NNLL 0 resummation reproduces all singular terms of the full FO result to Oðα 2 s Þ implies that the resummed expanded result in dσ nons ≥1 =dΦ 1 acts precisely as a differential NNLO T 0 -subtraction [43] (see also Ref. [44]).…”

“…As discussed in detail in Ref. [43], the cancellation can be made more local by considering more-differential resummations (e.g. utilizing the results of Refs.…”

“…At NNLL 0 accuracy, we need the boundary conditions at two-loop order, and the evolution to three (two) loops in the cusp (noncusp) anomalous dimensions. All required expressions are known in the literature [43,[57][58][59][60][61][62][63][64][65] and we do not reproduce them here.…”