The Hadronization Impact on $J/\psi$ Energy Correlators: A Pythia8 Study from Partonic to Hadronic Observables

A comprehensive study of the $J/\psi$ energy correlator as a probe of non-perturbative hadronization in color-octet $c\bar{c}$ production is performed. The energy correlator measures the energy flow as a function of the angular distance ($\chi$) from the identified $J/\psi$ meson. Using the PYTHIA 8 Monte Carlo event generator, the correlator is computed at both parton and hadron levels. At high $J/\psi$ transverse momentum ($p_T > 7\ \text{GeV}/c$), the parton-level correlator in the $\cos\chi > 0$ region is dominated by soft gluon emission during the hadronization of the color-octet state, a contribution clearly distinguishable from other partonic sources, such as underlying multi-parton interactions. The transition to the hadron level, however, introduces substantial modifications, suppressing the correlator in this region by approximately an order of magnitude and underscoring the complexity of the hadronization mapping. Further analysis reveals that the hadron-level observable exhibits notable sensitivity to model parameters: increasing the mass splitting between colored $c\bar{c}$ pre-resonances and the $J/\psi$ meson from 0.2 to 0.8 GeV/$c^{2}$ enhances the correlator by up to $60\%$, while extending the color reconnection range yields a milder enhancement of about $10\%$. These findings demonstrate that precise measurements of the hadron level $J/\psi$ energy correlator, when interpreted within robust event-generator frameworks, can provide novel constraints on hadronization dynamics and help clarify the production mechanisms of $J/\psi$ state.