Next-to-Next-to-Leading Order Study of Three-Jet Production at the LHC

Multijet 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 ${\alpha }_s$, and search for physics beyond the standard model. In this work we calculate, for the first time, the next-to-next-to-leading order (NNLO) QCD corrections to typical three-jet observables and to differential three-to-two jet ratios. The calculation is complete apart from the three-jet double virtual contributions which are included in the leading-color approximation. 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.

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). Three-point scale variation is shown as a colored 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 three-point variation. The colors are the same as in Fig. 1.

Figure 3

As in Fig. 2 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 colors are the same as in Fig. 1.

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 colors are the same as in Fig. 1.