A global analysis of Energy-Energy Correlation data: determination of $α_S$ and non-perturbative QCD parameters

Abstract

We present a comprehensive global analysis of Energy-Energy Correlation (EEC) data in electron-positron annihilation into hadrons, spanning a wide range of center-of-mass energies ($7.7\,\,\text{GeV}\!\leq\!\sqrt{s}\!\leq\! 91.2\,\,\text{GeV})$. In the back-to-back (two-jet) region, we resum to all orders the logarithmically-enhanced contributions up to next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. The resummed results are consistently matched to fixed-order calculations up to $\mathcal{O}(α_S^3)$. Our resummation formalism also incorporates dominant heavy-quark mass effects and models non-perturbative power corrections by means of an analytic dispersive approach. A simultaneous fit yields an excellent description of experimental data across all energies, enabling a precise determination of the strong coupling, $α_S(m_Z^2) = 0.119 \pm 0.002$, as well as the non-perturbative parameters, including those characterizing the Collins--Soper evolution kernel. Our analysis includes, for the first time in a global fit, datasets from the ALEPH and AMY collaborations.

Figures (12)

• Figure 1: Comparison between experimental data and theoretical predictions (blue bands) for the EEC distribution at the $Z$-boson resonance from OPAL Coll. (top left and top right), DELPHI Coll. (middle left and right), L3 Coll. (bottom left) and SLD Coll. (bottom right). The uncertainty bands represent the theoretical uncertainties estimated through scale variations. The lower panels show the ratio of the theoretical results to the experimental data.
• Figure 2: Comparison between the recent reanalysis of archived experimental data from ALEPH Coll. at $\sqrt{s}=91.2\,\text{GeV}$ and our theoretical predictions (blue bands). The EEC distribution is shown as a function of $\chi$ (left panel) and as a function of $z$ on logarithmic scales (right panel), the latter emphasizing the back-to-back region where resummation and non-perturbative effects are most prominent. The uncertainty bands represent the theoretical uncertainties estimated through scale variations. The lower panels show the ratio of the theoretical results to the experimental data.
• Figure 3: Comparison between experimental data and theoretical predictions (blue bands) for the EEC distribution from TOPAZ Coll. at $\sqrt{s} = 59.5$ GeV (left) and $\sqrt{s} = 53.3$ GeV (right). The uncertainty bands represent the theoretical uncertainties estimated through scale variations. The lower panels show the ratio of the theoretical results to the experimental data.
• Figure 4: Comparison between experimental data and theoretical predictions (blue bands) for the EEC distribution from AMY Coll. at $\sqrt{s} = 58.0$ GeV. The uncertainty bands represent the theoretical uncertainties estimated through scale variations. The lower panels show the ratio of the theoretical results to the experimental data.
• Figure 5: Comparison between experimental data and theoretical predictions (blue bands) for the EEC distribution from the TASSO Coll. at $\sqrt{s} = 43.5$ GeV (top left), $\sqrt{s} = 34.8$ GeV (top right), $\sqrt{s} = 22$ GeV (bottom left), and $\sqrt{s} = 14$ GeV (bottom right). The uncertainty bands represent the theoretical uncertainties estimated through scale variations. The lower panels show the ratio of the theoretical results to the experimental data.