Real Radiation at Next-to-Next-to-Leading Order in QCD: $e^{+}{e}^{-}\to 2$ Jets through $O\left({\alpha }_s^2\right)$

We present a calculation of the differential two-jet cross section in $e^{+}{e}^{-}$ annihilation through next-to-next-to-leading order (NNLO) in the strong coupling constant ${\alpha }_s$. The calculation is performed using a new method for dealing with real radiation suggested recently by us. For the first time, the two-jet event rate is computed directly, without any reference to the inclusive cross section $e^{+}{e}^{-}\to \mathrm{\text{hadrons}}$. We also calculate the energy distribution of the leading jet in $e^{+}{e}^{-}\to 2$ jets and find significant modifications of the shape of this distribution at NNLO.

Figure 1

Bin-integrated energy distribution for $y_{\mathrm{c}\mathrm{u}\mathrm{t}}=0.1$. The fractions of events in each energy bin are shown. The dotted histogram denotes the LO result, the dashed histogram the NLO result, and the solid histogram the NNLO result.