Quantum Scaling in Energy Correlators Beyond the Confinement Transition

Abstract

We study the QCD scaling behavior of the small-angle Energy-Energy Correlator (EEC), focusing on the transition between its perturbative pre-confinement and non-perturbative post-confinement regimes. Applying the light-ray Operator Product Expansion (OPE), we develop a formalism that describes the scaling of the EEC with the input energy $Q$ in the transition and the post-confinement region, where the latter quantum scaling is determined by the $J=5$ DGLAP anomalous dimension. A key result of our work is a novel connection between the light-ray OPE and the dihadron fragmentation function (DFF), where we show that the non-perturbative OPE coefficients correspond to moments of the DFF. This finding establishes a new paradigm for studying hadronization. Our theoretical predictions are validated against Monte Carlo simulations for both $e^+e^-$ and $pp$ collisions, showing excellent agreement. The potential role of the quantum scaling in the precision determination of $\alpha_s$ is also discussed.