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

TL;DR

The paper introduces the J/ψ-energy correlator as a novel probe of non-perturbative hadronization in color-octet cc̄ to J/ψ transitions, analyzed in the J/ψ rest frame with a $p_T$-weighted energy-flow observable. Using PYTHIA 8 with NRQCD, it compares parton-level and hadron-level correlators, finding that soft gluon emission from hadronization contributes in the region $cos χ > 0$ at high $p_T^{J/ψ}$, but the hadronization process reshapes and largely suppresses this signal at the hadron level by about an order of magnitude. The correlator shows notable sensitivity to hadronization parameters: increasing the mass splitting between pre-resonances and J/ψ from $0.2$ to $0.8$ GeV/$c^{2}$ enhances the hadron-level signal by up to ~60%, while expanding the color reconnection range yields ~10% enhancements, with overall changes constrained within ~10% for CR variations. These results demonstrate that hadron-level measurements, properly interpreted through generator-based mappings, can constrain hadronization dynamics and clarify J/ψ production mechanisms within NRQCD.

Abstract

A comprehensive study of the $J/ψ$ 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 ($χ$) from the identified $J/ψ$ meson. Using the PYTHIA 8 Monte Carlo event generator, the correlator is computed at both parton and hadron levels. At high $J/ψ$ transverse momentum ($p_T > 7\ \text{GeV}/c$), the parton-level correlator in the $\cosχ> 0$ 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 $J/ψ$ 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 $J/ψ$ energy correlator, when interpreted within robust event-generator frameworks, can provide novel constraints on hadronization dynamics and help clarify the production mechanisms of $J/ψ$ state.

Figures (4)

• Figure 1: Top panel: differential cross sections for $J/\psi$ production in $pp$ collisions at $\sqrt{s}= 500$ GeV STAR_pT. The black circles represent the experimental data from RHIC-STAR experiment, while the colored symbols show the PYTHIA results for different $J/\psi$ components: inclusive (blue circles), prompt (green squares), and non-prompt (red diamonds). Bottom panel: ratio of the simulated inclusive $J/\psi$ PYTHIA result to the experiment data.
• Figure 2: $J/\psi$-energy correlator at parton level for events with $^{3}S_{1}^{[8]}\rightarrow J/\psi + gluon$ process, including contribution from: Underlying-event (UE, red diamonds), hard-scattered partons produced in association with the $c\bar{c}$ pair via $q\bar{q}/gg/qg \rightarrow c \bar{c}^{[8]} + g/q$ (Hard (w/c $c\bar{c}$),blue circles), and soft partons emitted during the $c\bar{c}$ hadronization process (Hadr. soft, green squares). Results are shown in three $J/\psi$$p_{T}$ intervals: $0 < p_{\mathrm{T}}^{J/\psi} < 2.5$ GeV/$c$ (left), $2.5 < p_{\mathrm{T}}^{J/\psi} < 7$ GeV/$c$ (middle), and $7 < p_{\mathrm{T}}^{J/\psi} < 15$ GeV/$c$ (right). Kinematic requirements of $-1 < y^{J/\psi} < 1$, $-1 < \eta^X < 1$, and $p_T^X > 0.2$ GeV/$c$ are applied.
• Figure 3: $J/\psi$-energy correlator at the hadron and parton level for events with $c\bar{c}(^{3}S_{1}^{[8]})\rightarrow J/\psi + gluon$ process. Contributions are shown from all pre-hadonization partons (Pre-hadr.(total) partons), primary hadrons (Primay hadron, red circle), inclusive hadrons that additionally include hadron decay contributions (inclusive hadron, blue triangles), and soft partons released during the $c\bar{c}$ hadronization process (Hadr. soft,green squares). Results are presented in three $J/\psi$$p_{T}$ intervals: $0 < p_{\mathrm{T}}^{J/\psi} < 2.5$ GeV/$c$ (left), $2.5 < p_{\mathrm{T}}^{J/\psi} < 7$ GeV/$c$ (middle), and $7 < p_{\mathrm{T}}^{J/\psi} < 15$ GeV/$c$ (right). Kinematic requirements of $-1 < y^{J/\psi} < 1$, $-1 < \eta^X < 1$, and $p_T^X > 0.2$ GeV/$c$ are applied.
• Figure 4: The hadron level $J/\psi$ energy correlator as a function of $cos \chi$ for the directly produced $J/\psi$ production in pp collisions at $\sqrt{s}=500$ GeV. The $J/\psi$ is selected with $|y^{J/\psi}|<1$ and $7 < p_{T}^{J/\psi} < 15$ GeV/$c$. Associated charged particles $X$ satisfy $-1 < \eta^X < 1$, and $p_T^X > 0.2$ GeV/$c$. (a) The top panel shows the dependence on the color-octet $c\bar{c}$ mass splitting parameter 0.2 (blue circles), 0.4 (green squares), 0.6 (red diamonds), and 0.8 (magenta triangles) GeV/$c^{2}$. The bottom panel shows the ratio of each distribution to the default case of 0.2 GeV/$c^{2}$. (b) The top panel shows the dependence on the color reconnection range parameter R = 0 (blue circles), 0.5 (green squares), 1.8 (red diamonds), 3.6 (magenta triangles), and 5.4(purple pentagon), with Onia:massSplit fixed at 0.2 GeV/$c^{2}$. The bottom panel shows the ratio of each distibution to the $R=0$ case.