Prompt production of $J/ψ$ in the soft gluon resummation approach using the ICEM

TL;DR

This work addresses prompt $J/psi$ production at small transverse momentum by combining a Soft Gluon Resummation–based TMD factorization with an Improved Color Evaporation Model for hadronization, and fixes the intermediate-$p_T$ region by matching to fixed-order Collinear Factorization through Inverse-Error Weighting. The analysis uses LO CPM and LL-LO SGR, with a single phenomenological parameter $F^{J/psi}$ that is fitted across energies and then used to predict SPD NICA results; the hadronization and shape of the $p_T$ spectra are controlled by $F^{J/psi}$ and the nonperturbative Sudakov. Numerical results show good agreement with data from $\sqrt{s}=15$ GeV to 13 TeV, with the energy dependence of $F^{J/psi}$ captured by a power-like form, and the SPD NICA predictions obtained (with $F^{J/psi}$ from the fit) largely align with NRQCD expectations within uncertainties. Overall, the study provides a coherent framework to describe heavy quarkonium production across the full $p_T$ range and offers testable predictions for upcoming experiments, while highlighting the LO–NLO uncertainties and potential refinements from higher-order corrections.

Abstract

In the article, we study prompt $J/ψ$ production at small transverse momentum within the Transverse Momentum Dependent (TMD) factorization. The Soft Gluon Resummation (SGR) approach is used for modelling of TMD PDFs. The hadronization process of heavy charm quarks is described with the Improved Color Evaporation model (ICEM). In order to obtain spectra of $J/ψ$ at the arbitrary transverse momenta, fixed-order calculations within the collinear parton model (CPM) are also applied and further matched with the TMD calculations using the Inverse-Error Weighting (InEW) scheme. We present results of calculations for a wide range of collision energy with the fitting of the relevant nonperturbative parameter of the ICEM. Predictions for the SPD NICA experiment are also provided alongside comparison with the result of calculation using nonrelativistic QCD (NRQCD) framework.

Figures (8)

• Figure 1: The cross section of $J/\psi$ production versus transverse momentum at $\sqrt{s} = 13$ TeV (left panel) and $\sqrt{s} = 7$ TeV (right panel). The experimental data were taken from the LHCb LHCb:2015foc and CMS CMS:2010nis Collaborations
• Figure 2: The cross section of $J/\psi$ production versus transverse momentum at $\sqrt{s} = 5$ TeV (left panel) and $\sqrt{s} = 1.96$ TeV (right panel). The experimental data were taken from the LHCb LHCb:2021pyk and CDF CDF:2004jtw Collaborations
• Figure 3: The cross section of $J/\psi$ production versus transverse momentum at $\sqrt{s} = 200$ GeV. The experimental data were taken from the PHENIX Collaboration PHENIX:2011gyb
• Figure 4: The cross section of $J/\psi$ production versus transverse momentum at $\sqrt{s} = 200$ GeV. The experimental data were taken from the PHENIX Collaboration PHENIX:2011gyb
• Figure 5: The cross section of $J/\psi$ production versus transverse momentum at $\sqrt{s} = 200$ GeV (left panel) and $\sqrt{s} = 63$ GeV. The experimental data were taken from the PHENIX PHENIX:2011gyb and ISR Clark:1978mg Collaborations