Abstract
We present the analytic formula for the Energy-Energy Correlation (EEC) in electron-positron annihilation computed in perturbative QCD to next-to-next-to-next-to-leading order (N3LO) in the back-to-back limit. In particular, we consider the EEC arising from the annihilation of an electron-positron pair into a virtual photon as well as a Higgs boson and their subsequent inclusive decay into hadrons. Our computation is based on a factorization theorem of the EEC formulated within Soft-Collinear Effective Theory (SCET) for the back-to-back limit. We obtain the last missing ingredient for our computation — the jet function — from a recent calculation of the transverse-momentum dependent fragmentation function (TMDFF) at N3LO. We combine the newly obtained N3LO jet function with the well known hard and soft function to predict the EEC in the back-to-back limit. The leading transcendental contribution of our analytic formula agrees with previously obtained results in mathcal{N} = 4 supersymmetric Yang-Mills theory. We obtain the N = 2 Mellin moment of the bulk region of the EEC using momentum sum rules. Finally, we obtain the first resummation of the EEC in the back-to-back limit at N3LL′ accuracy, resulting in a factor of ∼ 4 reduction of uncertainties in the peak region compared to N3LL predictions.
Highlights
In the quest of understanding the nature of the strong interaction, the study of QCD radiation produced in high-energy electron-positron collisions provides a powerful lens into the behavior of Quantum Chromodynamics (QCD)
We present the analytic formula for the Energy-Energy Correlation (EEC) in electron-positron annihilation computed in perturbative QCD to next-to-next-to-nextto-leading order (N3LO) in the back-to-back limit
We show that thanks to the resummation of large logarithms up to N3LL and the inclusion of fixed-order boundary terms at N3LO, we achieve a ∼ 4-fold reduction of uncertainty compared to previous results obtained at lower accuracy
Summary
In the quest of understanding the nature of the strong interaction, the study of QCD radiation produced in high-energy electron-positron collisions provides a powerful lens into the behavior of Quantum Chromodynamics (QCD). In N = 4 sYM, the factorization of the EEC in both its forward and back-to-back limit has been explored up to four loops by using the operator product expansion for light-ray operators [41], and by relating the EEC to four-point correlation functions of conserved currents [23] Note that these factorization theorems contain the full distributional structures, and their fixed-order expansions start at O(αs0). We obtain the three-loop jet functions from our results for the transverse-momentum dependent fragmentation functions (TMDFFs) calculated in the companion paper [42],2 and present the full singular structure of the EEC at N3LO in QCD in the back-to-back limit.
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