Analysis note: measurement of energy-energy correlator in $e^{+}e^{-}$ collisions at $91$ GeV with archived ALEPH data

Abstract: Electron-positron ($e^+e^-$) collisions provide a clean environment for precision tests of Quantum Chromodynamics (QCD) due to the absence of hadronic initial-state effects. We present a novel analysis of archived ALEPH data from the Large Electron-Positron Collider at the $Z$ pole, leveraging energy-energy correlators (EECs) to study hadronic energy flow with unprecedented precision. The two-point EEC is measured as a function of the angular separation between particles spanning from the collinear to the back-to-back limits in a remarkably differential test of perturbative and non-perturbative QCD. The results are consistent with previous LEP measurements and provide significantly improved precision and finer angular binning resolution, especially at small angles and in the back-to-back limit. Comparisons with \textsc{pythia} 6 simulations show overall agreement, with deviations in key kinematic regions offering insights into hadronization. The measurement performed here connects to new opportunities for precision QCD studies in archived and future collider data.