Analytical Computation of Energy-Energy Correlation at Next-to-Leading Order in QCD

The energy-energy correlation (EEC) between two detectors in $e^{+}{e}^{-}$ annihilation was computed analytically at leading order in QCD almost 40 years ago, and numerically at next-to-leading order (NLO) starting in the 1980s. We present the first analytical result for the EEC at NLO, which is remarkably simple, and facilitates analytical study of the perturbative structure of the EEC. We provide the expansion of the EEC in the collinear and back-to-back regions through next-to-leading power, information which should aid resummation in these regions.

Figure 1

Analytical results for ${\sin }^2(\chi )B$ are compared with numerical results from Event2 [13, 14]. The Event2 prediction is obtained after sampling over $10^{10}$ points, with the internal CUTOFF set to ${10}^{-14}$. Error bars represent Event2 statistical uncertainties.