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Four-Jet Rate in Electron-Positron Annihilation at Order $α_{s}^{4}$

Xuan Chen ¹, Dmitry Chicherin ², Elliot Fox³, Nigel Glover ^3,4, Matteo Marcoli ³, Vasily Sotnikov ⁵, Huiting Sun ¹, Hantian Zhang ⁴, and Simone Zoia ⁵

¹School of Physics, Shandong University, Jinan, Shandong 250100, China
²LAPTh-CNRS-USMB, 9 chemin de Bellevue, 74940 Annecy, France
³Institute for Particle Physics Phenomenology, Department of Physics, University of Durham, Durham DH1 3LE, United Kingdom
⁴Theoretical Physics Department, CERN, 1211 Geneva 23, Switzerland
⁵Physik-Institut, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland

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Phys. Rev. Lett. 136, 251901 – Published 23 June, 2026

DOI: https://doi.org/10.1103/xxg6-yd47

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.

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Phys. Rev. Lett. 136, 251901– Published 23 June, 2026

Vol. 136, Iss. 25 — 26 June 2026

Received 4 March 2026
Revised 11 May 2026
Accepted 21 May 2026

DOI: https://doi.org/10.1103/xxg6-yd47

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Four-Jet Rate in Electron-Positron Annihilation at Order $α_{s}^{4}$

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Four-Jet Rate in Electron-Positron Annihilation at Order αs4

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Four-Jet Rate in Electron-Positron Annihilation at Order $α_{s}^{4}$