We investigate the energy-energy correlator (EEC) of hadrons produced on the same side in $e^+e^-$ annihilation or in leading jets in $pp$ collisions. We observe a remarkable universality of the correlator. Using a non-perturbative transverse momentum dependent (TMD) fragmentation function to model the transition from the ``free-hadron" region to the perturbative collinear region, we are able to describe the near-side shapes and peaks over a wide range of energy for both the $e^+e^-$ annihilation and the $pp$ jet substructure measurements in terms of just two parameters. We present further predictions for the ratio of the projected three-point energy correlator to the EEC. The excellent agreement between our calculations and the experimental data may provide new insights into the role of non-perturbative physics for EECs, and suggests the possibility of exploring non-perturbative TMDs using theoretical tools developed for the energy correlators.
Comment: 6+4 pages, 5+7 figures