Energy-Energy Correlators in $e^+e^-$ and Deep Inelastic Scattering

We study energy-energy correlators (EECs) in $e^+e^-$ annihilation and deep inelastic lepton-hadron scattering (DIS), focusing on aspects of nonperturbative physics in these observables. We introduce the EEC jet functions and investigate the infrared (IR) behavior of both small-angle EECs and angle-integrated EECs by performing explicit one-loop calculations. The factorization and universality of the EECs in these processes are demonstrated. A matching scheme is proposed to smoothly connect kinematic regions where different scaling behaviors with jet energy are observed. In combination with the next-to-leading order correction, this matching provides a good description of the EEC data and PYTHIA simulations in high-energy $e^+e^-$ annihilation. Predictions for DIS processes for future electron-ion collider kinematics are also presented.