Probing $J/ψ$ Production Mechanisms in Proton-Proton Collisions at SPD/NICA Energies

Abstract

We investigate inclusive $J/ψ$ production in proton-proton collisions at tens of GeV $\sqrt{s}$ energy, relevant for forthcoming measurements with the Spin Physics Detector (SPD) at NICA. Simulations are performed using the PEGASUS event generator with transverse-momentum-dependent (TMD) gluon densities, comparing the recent KMR-based KL$'2025$ and CCFM-based LLM$'2024$ parametrizations. Differential cross sections in rapidity and transverse momentum exhibit smooth, stable behavior under renormalization-scale variation, while factorization-scale dependence exposes limitations of the LLM$'2024$ set at low scales in contrast to KL$'2025$. Normalized $p_T$ spectra reveal distinct hardening patterns linked to the underlying gluon $k_T$ broadening in each model. The relative contributions of color-singlet and color-octet channels are also quantified, demonstrating the dominance of color-octet mechanisms in the SPD energy regime. These results provide the first detailed assessment of quarkonium production sensitivity to gluon TMDs near threshold, offering timely theoretical guidance for upcoming $J/ψ$ measurements at SPD/NICA.

Figures (5)

• Figure 1: Rapidity distributions ${d\sigma}/{dy}$ for inclusive $J/\psi$ production at $\sqrt{s}=9$, $18$, and $27~\mathrm{GeV}$ obtained using the KL$'2025$Kotikov:2025wft and LLM$'2024$Lipatov:2024xni gluon densities. The shaded bands represent the uncertainty from renormalization-scale variation. A clear broadening and enhancement of the distributions with increasing $\sqrt{s}$ reflect the expanding rapidity phase space and growing gluon–gluon luminosity at higher energies.
• Figure 2: Differential cross sections ${d\sigma}/{dp_T}$ for inclusive $J/\psi$ production in pp collisions at $\sqrt{s}=9$, $18$, and $27~\mathrm{GeV}$ using the KL$'2025$Kotikov:2025wft and LLM$'2024$Lipatov:2024xni gluon densities. The shaded bands indicate the uncertainty due to renormalization-scale variation. The comparison illustrates the evolution of the $p_T$ spectrum with increasing collision energy.
• Figure 3: Normalized differential cross sections $(1/\sigma)\, d\sigma/dp_T$ for $J/\psi$ production in $pp$ collisions at $\sqrt{s}=27~\mathrm{GeV}$ obtained using the KL$'2025$Kotikov:2025wft and LLM$'2024$Lipatov:2024xni gluon densities. The solid curves represent empirical fits to the simulated spectra with parameters shown in the legend. The distributions are normalized to emphasize differences in spectral shape between the two TMD sets.
• Figure 4: Relative contributions of different intermediate $c\bar{c}$ states to the total $J/\psi$ production cross section in $pp$ collisions as a function of $\sqrt{s}$ for the KL$'2025$Kotikov:2025wft and LLM$'2024$Lipatov:2024xni gluon densities. The dominance pattern $^3P_{2}^{[8]}$$>$$^3P_{0}^{[8]}$$>$$^1S_{0}^{[8]}$$>$$^3P_{1}^{[8]}$$>$$^3S_{1}^{[8]}$$>$$^3S_{1}^{[1]}$ persists across the entire SPD energy range, with minimal model dependence.
• Figure 5: Total inclusive $J/\psi$ production cross section in $pp$ collisions as a function of the center-of-mass energy $\sqrt{s}$, obtained with the KL$'2025$Kotikov:2025wft and LLM$'2024$Lipatov:2024xni gluon densities. The cross section increases with $\sqrt{s}$, reflecting the growth of gluon luminosity. The shifted power-law fit provides an excellent description for $\sqrt{s}\gtrsim12~\mathrm{GeV}$; the deviation at $\sqrt{s}=9~\mathrm{GeV}$ likely signals threshold or model-limit effects.