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

Abstract: We investigate the inclusive $J/ψ$ productions in proton-proton 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. Several $J/ψ$ production mechanisms are considered: the leading-order non-relativistic QCD (NRQCD) color-singlet and color-octet contributions, the cluster collapse mechanism, and the non-prompt $J/ψ$ from $b$-hadron decays. The simulated inclusive $J/ψ$ transverse momentum ($p_{\rm T}$) differential cross sections agree well with the experimental data at both the middle and forward rapidities. For the $J/ψ$ yield, the dominant contribution comes from the NRQCD channel, while the cluster collapse and non-prompt processes provide relatively minor contributions. A decomposition of the NRQCD component, comprising direct production from the parton hard scattering and feed-down from $ψ(2S)$, $χ<em>{c0}$, $χ</em>{c1}$, and $χ<em>{c2}$, reveals that at low (high) $p</em>{\rm T}$ the dominant contributions come from the direct production and $χ<em>{c2}$ ($χ</em>{c1}$) feed-down. The $ψ(2S)$ feed-down fraction is 8-9$\%$, while the $χ_{c0}$ contribution is around 2-3$\%$. The influence of the partonic and hadronic rescatterings is also examined. The partonic rescattering exhibits negligible impact on the $J/ψ$ yields across all production mechanisms. In contrast, the hadronic rescattering suppresses the $J/ψ$ productions from both the NRQCD and cluster collapse mechanisms, while leaving the non-prompt $J/ψ$ yield almost unaffected.