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The Four-Jet Rate in Electron-Positron Annihilation at Order $α_s^4$

Xuan Chen, Dmitry Chicherin, Elliot Fox, Nigel Glover, Matteo Marcoli, Vasily Sotnikov, Huiting Sun, Hantian Zhang, Simone Zoia

Abstract

We compute for the first time the production rate for four jets in electron-positron annihilation at next-to-next-to-leading order. Our calculation exhibits the highest final-state jet multiplicity considered at this perturbative accuracy to date. The cancellation of infrared singularities is achieved in the antenna subtraction scheme, relying particularly on generalized antenna functions. The evaluation of the two-loop virtual corrections is enabled by the construction of a new basis of transcendental special functions tailored to four-particle decay kinematics. Our results are compared with LEP data, finding improved agreement with respect to the next-to-leading order calculation. In the region where perturbative predictions are most reliable, we observe a significant reduction of theory uncertainties, which now fall below the experimental ones.

The Four-Jet Rate in Electron-Positron Annihilation at Order $α_s^4$

Abstract

We compute for the first time the production rate for four jets in electron-positron annihilation at next-to-next-to-leading order. Our calculation exhibits the highest final-state jet multiplicity considered at this perturbative accuracy to date. The cancellation of infrared singularities is achieved in the antenna subtraction scheme, relying particularly on generalized antenna functions. The evaluation of the two-loop virtual corrections is enabled by the construction of a new basis of transcendental special functions tailored to four-particle decay kinematics. Our results are compared with LEP data, finding improved agreement with respect to the next-to-leading order calculation. In the region where perturbative predictions are most reliable, we observe a significant reduction of theory uncertainties, which now fall below the experimental ones.
Paper Structure (7 sections, 6 equations, 2 figures)

This paper contains 7 sections, 6 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Calculation
  3. Two-loop corrections
  4. Results
  5. Conclusions and Outlook
  6. Acknowledgments
  7. One-mass pentagon functions in the decay channel

Figures (2)

  • Figure 1: Fixed-order predictions for the four-jet rate compared to data from the ALEPH experiment ALEPH:2003obs (black) at $\sqrt{s}=91.2$ GeV. Predictions are shown at LO (green), NLO (blue) and NNLO (red). In the inserted frame, we zoom in the $y_{\mathrm{cut}}\in[10^{-3},10^{-1}]$ region and use a logarithmic scale on the $y$-axis. Colored bands represent theory uncertainties obtained by varying the renormalization scale. The ratio to NLO-accurate predictions is shown in the middle frame. In the bottom frame, NNLO results without the two-loop finite remainder (dashed black line) are compared with the complete NNLO predictions (red), both normalized to NLO results (blue).
  • Figure 2: Fixed-order predictions for the four-jet rate compared to data from the ALEPH experiment ALEPH:2003obs (black) at several center-of-mass energies. Predictions are shown at NLO (blue) and NNLO (red). Colored bands represent theory uncertainties obtained by varying the renormalization scale.