N-jettiness Subtractions for NNLO QCD Calculations

TL;DR

This paper introduces a systematic subtraction method based on N-jettiness for precise NNLO QCD calculations, enabling fully differential results suitable for collider phenomenology and compatible with resummation and parton showers.

Contribution

The paper presents a new N-jettiness subtraction technique for NNLO QCD calculations that is systematic, physical observable-based, and applicable to arbitrary processes with massless partons.

Findings

Explicit NLO and NNLO subtraction formulas provided.

Successful application to Drell-Yan and Higgs production processes.

Method compatible with existing NNLO techniques for complex processes.

Abstract

We present a subtraction method utilizing the N-jettiness observable, Tau_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 Tau_N -> 0, and uses these to construct suitable Tau_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 Tau_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 method 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.