A first next-to-next-to-leading order study of three-jet production at the LHC

TL;DR

This work delivers the first NNLO QCD predictions for three-jet production and $R_{3/2}$ at the LHC, advancing perturbative precision for a complex $2\to3$ process with five colored partons. Using the sector-improved residue subtraction scheme and a leading-color approximation for the two-loop term, the authors obtain NNLO cross sections and differential distributions, demonstrating significantly reduced scale dependence relative to NLO. The results show nuanced NNLO corrections across jet observables and establish $R_{3/2}$ as a high-precision probe for $\alpha_s$, while highlighting substantial computational demands and paving the way for future phenomenological studies and methodological refinements. An erratum later corrects a color-factor miscalibration, modestly increasing the NNLO contribution and clarifying the relative size of subleading-color effects.

Abstract

Multi-jet rates at hadron colliders provide a unique possibility for probing Quantum Chromodynamics (QCD), the theory of strong interactions. By comparing theory predictions with collider data, one can directly test perturbative QCD, extract fundamental parameters like the strong coupling $α_s$ and search for physics beyond the Standard Model. In this work we calculate, for the first time, the next-to-next-to-leading (NNLO) QCD corrections to typical three-jet observables and to differential three-to-two jet ratios. We demonstrate that the inclusion of the NNLO corrections significantly reduces the dependence of those observables on the factorization and renormalization scales. Besides its phenomenological value, this proof-of-principle computation represents a milestone in perturbative QCD.

Figures (5)

• Figure 1: The three panels show the $i$th leading jet transverse momentum $p_T(j_i)$ for $i=1,2,3$ for the production of (at least) three jets. LO (green), NLO (blue) and NNLO (red) are shown for the central scale (solid line). 3-point scale variation is shown as a coloured band. The grey band corresponds to the uncertainty from Monte Carlo integration.
• Figure 2: The observable $H_T$ in two-jet production for two different central scale choices. Scale variation corresponds to 3-point variation. The colours are the same as in fig. \ref{['fig:pTi']}.
• Figure 3: As in fig. \ref{['fig:HT_2j']} but for three-jet production.
• Figure 4: The top two panels show $R_{3/2}(p_T(j_1))$ (in absolute and as ratio to NLO) and the bottom two panels $R_{3/2}(H_T)$. The colours are the same as in fig. \ref{['fig:pTi']}.
• Figure 5: The three panels show $R_{3/2}(H_T,y^*)$, in each panel a different slice in $y^*$ as ratio to NLO. The colours are the same as in fig. \ref{['fig:pTi']}.