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The Energy-Energy Correlation at Next-to-Leading Order in QCD, Analytically

Lance J. Dixon, Ming-xing Luo, Vladyslav Shtabovenko, Tong-Zhi Yang, Hua Xing Zhu

Abstract

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 EEC in the collinear and back-to-back regions through to next-to-leading power, information which should aid resummation in these regions.

The Energy-Energy Correlation at Next-to-Leading Order in QCD, Analytically

Abstract

The energy-energy correlation (EEC) between two detectors in 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 EEC in the collinear and back-to-back regions through to next-to-leading power, information which should aid resummation in these regions.

Paper Structure

This paper contains 2 sections, 25 equations, 5 figures.

Table of Contents

  1. Analytical results for remaining color coefficients
  2. Validation of individual color components

Figures (5)

  • Figure 1: Analytical results for $\sin^2(\chi) B$ are compared with numerical results from Event2Catani:1996jhCatani:1996vz. The Event2 prediction is obtained after sampling over 10 billion points, with the internal CUTOFF set to $10^{-14}$. Error bars represent Event2 statistical uncertainties.
  • Figure 2: Representative cut diagrams for real corrections to the EEC at NLO.
  • Figure 3: Comparison with Event2 for the $B_{C_F}$, $B_{C_A}$ and $B_{N_f}$ contributions.
  • Figure 4: Comparison with Event2 for the $C_F^2$ coefficient in the region where $B_{C_F}$ is close to zero.
  • Figure 5: Comparison with Event2 for the identical-quark interference terms.