Collinear limit of the energy-energy correlator in $e^+ e^-$ collisions: transition from perturbative to non-perturbative regimes

Abstract

We study the collinear limit of the energy-energy correlator (EEC) in $e^+e^-$ collisions, focusing on the transition from the perturbative QCD regime at relatively large angles to the non-perturbative region at small angles. To describe this transition, we introduce a non-perturbative jet function and perform a global analysis at NNLO+NNLL accuracy using experimental data spanning center-of-mass energies from $Q = 29.0$ to $91.2$ GeV. This marks the first accurate description of the EEC across the entire near-side region ($0^\circ<\chi<90^\circ$) within a unified theoretical framework. Our analysis also provides, for the first time, a quantitative extraction of the non-perturbative contribution to the EEC quark jet function, identifying a characteristic transition scale around $2.3$ GeV - distinct from the scale observed in EEC-in-jet measurements in $pp$ collisions at the LHC, which are dominated by gluon jets. These results offer the first evidence for flavor dependence (quark vs. gluon) in the EEC and provide new insights into the interplay between perturbative and non-perturbative QCD dynamics.