NNLO hard functions in massless QCD

TL;DR

This work delivers the complete NNLO hard functions for all 2→2 massless QCD processes by extracting UV-renormalized, color-decomposed helicity amplitudes and performing IR renormalization within a color-space framework. The authors organize the results into four-quark, two-quark-two-gluon, and four-gluon channels, providing analytic color-basis expressions, RG anomalous dimensions, and benchmark numerical values, with cross-checks against existing fixed-order results. Analytic results are made available electronically along with a Mathematica interface to facilitate practical use in high-precision resummations. The findings enable boundary terms for RG evolution to NNLO accuracy and are poised to support advanced resummations (e.g., NNLL' and beyond) in dijet and boosted-top observables at hadron colliders.

Abstract

We derive the hard functions for all 2->2 processes in massless QCD up to next-to-next-to-leading order (NNLO) in the strong coupling constant. By employing the known one- and two-loop helicity amplitudes for these processes, we obtain analytic expressions for the ultraviolet and infrared finite, minimally subtracted hard functions, which are matrices in color space. These hard functions will be useful in carrying out higher-order resummations in processes such as dijet and highly energetic top-quark pair production by means of soft-collinear effective theory methods.