Three-Jet Production in Electron-Positron Collisions at Next-to-Next-to-Leading Order Accuracy

We introduce a completely local subtraction method for fully differential predictions at next-to-next-to-leading order (NNLO) accuracy for jet cross sections and use it to compute event shapes in three-jet production in electron-positron collisions. We validate our method on two event shapes, thrust and $C$ parameter, which are already known in the literature at NNLO accuracy and compute for the first time oblateness and the energy-energy correlation at the same accuracy.

Figure 1

The NNLO coefficient of the weighted $\tau =1-T$ distribution. The lower panels show the predictions of Ref. [7], denoted as SW, (middle panel) and those of Ref. [6], denoted as GGGH, (lower panel) normalized to ours, as well as the relative uncertainties of the numerical integrations (shaded band around the line at one). Also shown in the middle panel are the predictions of MadGraph5_aMC@NLO, denoted as MG5, for $\tau >1/3$.

Figure 2

The same as Fig. 1 for the $C$ parameter, with the middle panel showing also the predictions of Ref. [3], denoted as NT, for $C_{\mathrm{par}}>3/4$.

Figure 3

Weighted distributions of oblateness $O$ at LO, NLO, and NNLO accuracy in perturbative QCD. The bands represent the dependence on the renormalization scale varied in the range ${\xi }_R\equiv \mu /{\mu }_0\in [0.5,2]$ around the default scale ${\mu }_0=\sqrt{Q^2}$. The lower panel shows the relative scale dependence (band) at NNLO accuracy and the relative uncertainty of the integrations (error bars).

Figure 4

Distributions of energy-energy correlation EEC at LO, NLO, and NNLO accuracy in perturbative QCD. The bands and the lower panel are like in Fig. 3.

Figure 5

Distribution of the NNLO coefficient for oblateness $O$. The error bars represent the statistical uncertainty of the Monte Carlo integrations.

Figure 6

Same as Fig. 5 for energy-energy correlation.