Leading-Color Two-Loop QCD Corrections for Three-Jet Production at Hadron Colliders

TL;DR

The paper delivers the complete set of leading-color two-loop QCD corrections for three-jet production at hadron colliders, enabling NNLO predictions. It achieves this by analytically continuing Euclidean-region five-parton amplitudes to the physical region using a pentagon-function basis and a small number of finite-field evaluations, producing analytic generating remainders and a robust C++ library (FivePointAmplitudes) for stable, efficient evaluation. The work includes explicit two-loop partial-remainder matrices, comprehensive channel accounting, and extensive validation: symmetry checks, cross-validation with BlackHat, and explicit scale-dependence tests. This provides a ready-to-use framework for precision QCD studies of multi-jet events at the LHC and beyond, bridging theoretical amplitudes and phenomenology.

Abstract

We present the complete set of leading-color two-loop contributions required to obtain next-to-next-to-leading-order (NNLO) QCD corrections to three-jet production at hadron colliders. We obtain analytic expressions for a generating set of finite remainders, valid in the physical region for three-jet production. The analytic continuation of the known Euclidean-region results is determined from a small set of numerical evaluations of the amplitudes. We obtain analytic expressions that are suitable for phenomenological applications and we present a C++ library for their efficient and stable numerical evaluation.

Figures (3)

• Figure 1: Characteristic Feynman diagrams which contribute to $\mathcal{A}^{(2)[j]}$ for representative channels with no external quark lines, a single quark line and two external quark lines, for $j=0$ (left column), $j=1$ (middle column) and $j=2$ (right column).
• Figure 2: Schematic representation for the two kinds of contributions to $H^{(2)}$: the square of one-loop amplitudes, and the interference between tree-level and two-loop amplitudes.
• Figure 3: Logarithmic distribution of correct digits (see \ref{['eq:correct-digits']}) on samples of 110k points for each of the channels. The blue line corresponds to evaluation in double precision. The orange line represents evaluation with the rescue system enabled. The gray dashed line is the cumulative distribution of the latter. The rescue system's thresholds are the same as in \ref{['tab:rescue-data']}. Average core time for evaluation on a single phase-space point with rescue system enabled as measured when evaluating all sample points in parallel using all 32 threads of Intel(R) Xeon(R) Silver 4216 CPU @ 2.10GHz.