Energy Correlators from Partons to Hadrons: Unveiling the Dynamics of the Strong Interactions with Archival ALEPH Data

Abstract

Quantum Chromodynamics (QCD) is a remarkably rich theory exhibiting numerous emergent degrees of freedom, from flux tubes to hadrons. Their description in terms of the underlying quarks and gluons of the QCD Lagrangian remains a central challenge of modern physics. Colliders offer a unique opportunity to probe these phenomena experimentally: high energy partons produced from the QCD vacuum excite these emergent degrees, imprinting their dynamics in correlations in asymptotic energy flux. Decoding these correlations requires measurements with exceptional angular resolution, beyond that achieved in previous measurements. Recent progress has enabled precision calculations of energy flux on charged particles alone, allowing data-theory comparisons for measurements using high resolution tracking detectors. In this Letter, we resurrect thirty-year-old data from the ALEPH tracker, and perform a high angular resolution measurement of the two-point correlation of energy flux, probing QCD over three orders of magnitude in scale in a single measurement. Our measurement unveils for the first time the full spectrum of the correlator, including light-ray quasi-particle states, flux-tube excitations, and their transitions into confined hadrons. We compare our measurement with record precision theoretical predictions, achieving percent level agreement, and revealing interesting new phenomena in the confinement transitions. More broadly, we highlight the immense potential of this newly unlocked archival data set, the so called "recycling frontier", and emphasize synergies with ongoing and future collider experiments.

Figures (7)

• Figure 1: Correlation functions of local operators can be mapped to correlation functions of energy flow operators, $\mathcal{E}(\vec{n})$, illustrated as blue lines in the Penrose diagram. These functions characterize asymptotic fluxes, and are directly measurable at $e^+e^-$ colliders.
• Figure 2: Correlation functions of detector operators can be measured in particle colliders as correlations between pairs of hadrons at different angles. In the center, we illustrate a collision and its corresponding energy depositions in a detector. The Penrose diagrams illustrate the same collision and the corresponding configurations of detector operators.
• Figure 3: The energy flux in $e^{+}e^{-}$ collisions, and the corresponding EEC distribution, viewed with three angular resolutions: the first PLUTO measurement (1981), LEP measurements with hadronic calorimeters (1993), and our track based ALEPH measurement (2025). The two energy flow operators are illustrated as green dots.
• Figure 4: The energy correlator from partons to hadrons: A measurement of the EEC using archival data from the ALEPH tracker. Statistical error bars are shown as vertical lines and systematic error bars as purple boxes. ALEPH data is compared with state-of-the-art theoretical predictions, shown in light blue. Our re-analysis greatly extends both the precision, and angular range of the measurement, enabling a complete view of the dynamics of QCD.
• Figure 5: The EEC in the perturbative $z\sim 1/2$ region.