Inclusive $J/ψ$ productions in pp collisions at $\sqrt{s}=$ 5.02, 7, and 13 TeV with the PACIAE model

TL;DR

This work tackles inclusive $J/\psi$ production in pp collisions at $\sqrt{s}=5.02$, 7, and 13 TeV, building a baseline for understanding nuclear modifications in heavier systems. The authors employ the PACIAE 4.0 model, which augments PYTHIA 8.3 with partonic and hadronic rescatterings and implements NRQCD channels (color-singlet and color-octet), cluster collapse, and non-prompt production from $b$-hadrons. They compare to mid- and forward-rapidity data, quantifying the relative contributions of NRQCD, cluster collapse, and non-prompt processes, and dissect NRQCD into direct production and feed-down from $\psi(2S)$ and $\chi_{c0,1,2}$ states across $p_{T}$, energy, and rapidity. They find NRQCD dominates the inclusive yield, with increasing cluster-collapse and non-prompt fractions at higher energies and forward rapidity, while hadronic rescattering modestly suppresses NRQCD and cluster-collapse yields; these results provide constraints on NRQCD long-distance matrix elements and highlight the role of rescattering in high-energy pp collisions.

Abstract

We investigate the inclusive $J/ψ$ production in proton-proton (pp) collisions at center-of-mass energies $\sqrt{s} = 5.02$, 7, and 13 TeV using the PACIAE 4.0 model. This model extends PYTHIA 8.3 by incorporating partonic and hadronic rescatterings before and after hadronization, respectively. Compared to our earlier study [K.-F. Ye et al., Phys. Rev. C 109, 035201 (2024)], which considered only the color-singlet processes, the present work includes both the color-singlet and color-octet contributions within the non-relativistic QCD (NRQCD) framework. In addition to NRQCD, we also consider the contributions from the cluster collapse and weak decays of $b$-hadrons. We find that the simulated inclusive $J/ψ$ transverse momentum differential cross sections agree well with the experimental data at both the middle and forward rapidities. We provide a quantitative analysis of the relative contributions for different production mechanisms and their energy and rapidity dependence in the inclusive $J/ψ$ production. Furthermore, we offer a quantification of the relative contributions of the various components and their energy and rapidity dependence in the NRQCD channels, including the direct production via the hard scattering and the feed-down from the decays of heavier charmonium states such as $ψ(2S)$, $χ_{c0}$, $χ_{c1}$, and $χ_{c2}$. Finally, we examine the effects of partonic and hadronic rescatterings and offer the quantitative estimate of their impact on the $J/ψ$ production. These results are entirely new and represent a significant step forward in understanding the mechanisms of the inclusive $J/ψ$ production in high-energy pp collisions.

Figures (5)

• Figure 1: Upper row panels: the $p_{\rm T}$-differential cross sections of $J/\psi$ from the inclusive process (downward triangles), the NRQCD (diamonds), the cluster collapse (upward triangles), and the non-prompt process (squares) at mid-rapidity in pp collisions at $\sqrt{s}=$ 5.02, 7, and 13 TeV in the PACIAE model. The solid circles are experimental data taken from Refs. Jpsi_5.02_midJpsi_7_midJpsi_13_mid. Middle row panels: the ratio between the experimental data and the inclusive $J/\psi$ results from the PACIAE model. Lower row panels: the fractions for the NRQCD, cluster collapse, and non-prompt components in the inclusive $J/\psi$ productions.
• Figure 2: Similar as that in Fig. \ref{['fig:all_ph_mid']}, but for the $p_{\rm T}$-differential inclusive $J/\psi$ cross sections at forward rapidity in pp collisions at $\sqrt{s}=$ 5.02, 7, and 13 TeV. The experimental data are taken from Refs. Jpsi_5.02_13_fwdJpsi_7_fwd.
• Figure 3: Upper panels: the $p_{\rm T}$-differential cross sections for $J/\psi$ from the direct production (circles) as well as the feed-down contributions from the decays of $\psi(2S)$ (squares), $\chi_{c0}$ (upward triangles), $\chi_{c1}$ (left triangles), and $\chi_{c2}$ (right triangles) at middle rapidity in pp collisions at $\sqrt{s}=$ 5.02, 7, and 13 TeV. The $p_{\rm T}$-differential cross sections for $J/\psi$ from the total NRQCD processes is represented by the empty diamonds. Lower panels: the fractions of different components in the NRQCD processes.
• Figure 4: Similar as that in Fig. \ref{['fig:NRQCD_13_TeV_mid']}, but for the $p_{\rm T}$-differential cross sections for $J/\psi$ from different NRQCD processes at forward rapidity in pp collisions at $\sqrt{s}=$ 5.02, 7, and 13 TeV.
• Figure 5: Panels (a) and (b): the $p_{\rm T}$-differential cross sections of $J/\psi$ from from the inclusive process (grey curves) as well as the NRQCD (red curves) , cluster collapse (green curves) and non-prompt (purple curves) processes at middle and forward rapidities in pp collisions at $\sqrt{s} =$ 13 TeV in the PACIAE model under different rescattering scenarios: both PRS and HRS included (solid curves), HRS only (dash-dotted curves), PRS only (dashed curves), and neither PRS nor HRS, the baseline (dotted curves). Panels (c) and (d) ((e) and (f), (g) and (h), (i) and (j)): the ratios of the spectra from the inclusive (NRQCD, cluster collapse, non-prompt) process with HRS-only (upward triangles), PRS-only (squares), and both PRS and HRS (circels) to this baseline.