Jet production in the CoLoRFulNNLO method: Event shapes in electron-positron collisions

We present the CoLoRFulNNLO method to compute higher order radiative corrections to jet cross sections in perturbative QCD. We apply our method to the computation of event shape observables in electron-positron collisions at NNLO accuracy and validate our code by comparing our predictions to previous results in the literature. We also calculate for the first time jet cone energy fraction at NNLO.

Figure 1

Perturbative predictions for the thrust ($\tau \equiv 1-T$) and heavy jet mass ($\rho$) distributions at LO, NLO and NNLO accuracy. The bands represent the renormalization scale uncertainty of our predictions corresponding to the range ${\xi }_R\in [0.5,2]$ around the central value of ${\mu }_0=\sqrt{Q^2}$. The lower panels show the ratio of the (updated but unpublished—see text) predictions of Ref. [6] (SW) and EERAD3 [96] (GGGH) to CoLoRFulNNLO (this work). The bands on the lower panels show the relative scale uncertainty of our NNLO results.

Figure 2

Same as Fig. 1 for total ($B_T$) and wide ($B_W$) jet broadening.

Figure 3

Same as Fig. 1 for the $C$-parameter ($C_{\mathrm{par}}$) and the two-to-three jet transition parameter ($y_{23}$) in the Durham clustering algorithm.

Figure 4

The $OC(O)$ coefficients of the thrust, heavy jet mass, total and wide jet broadening, $C$-parameter and two-to-three jet transition variable $y_{23}$ distributions. Lower panels show the ratio of the (updated but unpublished—see text) predictions of Ref. [6] (SW) and EERAD3 [96] (GGGH) to CoLoRFulNNLO (this work). The shaded bands on the lower panels represent the relative statistical uncertainties of our predictions due to Monte Carlo integrations.

Figure 5

The distribution of jet cone energy fraction (JCEF) at LO, NLO and NNLO accuracy in perturbative QCD. The bands represent the variation of the renormalization scale in the range ${\xi }_R=\mu /{\mu }_0\in [0.5,2]$ around the central value of ${\mu }_0=\sqrt{Q^2}$. The lower panel shows the relative scale dependence at NNLO accuracy.

Figure 6

The distribution of the NNLO coefficient for jet cone energy fraction (JCEF). The error bars represent the statistical uncertainty of the Monte Carlo integrations.