Subtraction Terms for Hadronic Production Processes at Next-to-Next-to-Leading Order

TL;DR

The paper tackles NNLO calculations for hadronic single-inclusive production by proposing an analytic subtraction scheme based on the dipole formalism to tame infrared divergences across real and virtual contributions. It extends the NLO subtraction structure to NNLO using a hierarchy of counter-terms ($d\alpha^{(0)}_{n+2}$, $d\beta^{(0)}_{n+2}$, $d\gamma^{(0)}_{n+2}$, $d\alpha^{(1)}_{n+1}$) and exact matrix elements evaluated at shifted phase-space points, ensuring cancellation while preserving exclusive information. A key innovation is incorporating rapidity distributions through convolutions with tilde{Γ} kernels, enabling differential predictions alongside total rates. The approach yields a practical, analytic pathway to NNLO parton-level Monte Carlo calculations for processes like Drell-Yan, vector boson, and Higgs production, with potential generalization to other simple processes and kinematic observables.

Abstract

I describe a subtraction scheme for the next-to-next-to-leading order calculation of single inclusive production at hadron colliders. Such processes include Drell-Yan, W^{+/-}, Z and Higgs Boson production. The key to such a calculation is a treatment of initial state radiation which preserves the production characteristics, such as the rapidity distribution, of the process involved. The method builds upon the Dipole Formalism and, with proper modifications, could be applied to deep inelastic scattering and e^+ e^- annihilation to hadrons.