Charmonium Production at High Energy in the k_T-Factorization Approach

TL;DR

The paper investigates high-energy charmonium production using the $k_T$-factorization framework combined with leading-order NRQCD. It fits Tevatron $p_T$ distributions with three unintegrated gluon densities to extract NRQCD NMEs for $J/\psi$, $\psi'$, and $\chi_{cJ}$, then uses these NMEs to predict $J/\psi$ production in $\gamma\gamma$, $\gamma p$, and DIS $ep$ collisions, including direct and resolved photon processes. The results show color-singlet channels often dominate at HERA and LEP2, with color-octet contributions constrained by Tevatron fits, and overall predictions agree with data within a factor of ~2, underscoring the importance of kt effects. The work also outlines the need for NLO calculations in the $k_T$-factorization framework to reduce theoretical uncertainties and to fully establish the relative role of kt-factorization versus collinear NRQCD.

Abstract

We study charmonium production at high-energy colliders (Tevatron, HERA, and LEP2) in the framework of the k_T-factorization approach and the factorization formalism of non-relativistic quantum chromodynamics at leading order in the strong-coupling constant alpha_s and the relative velocity v. The transverse-momentum distributions of direct and prompt J/psi-meson production measured at the Fermilab Tevatron are fitted to obtain the non-perturbative long-distance matrix elements for different choices of unintegrated gluon distribution functions in the proton. Using the matrix elements thus obtained, we predict charmonium production rates in gamma-gamma, gamma-p, and deep-inelastic e-p collisions including the contributions from both direct and resolved photons. The results are compared with the known ones obtained in the conventional parton model and with recent experimental data from HERA and LEP2.

Figures (10)

• Figure 1: Contributions to the $p_T$ distribution of prompt $J/\psi$ hadroproduction in $p\overline{p}$ scattering with $\sqrt{S}=1.96$ TeV and $|y|<0.6$ from the relevant color-octet states compared with CDF data from Tevatron run II CDFII. All distributions are normalized to unity at their peaks.
• Figure 2: Contributions to the $p_T$ distribution of direct $J/\psi$ hadroproduction in $p\overline{p}$ scattering with $\sqrt{S}=1.8$ TeV and $|y|<0.6$ from the partonic subprocesses (1) $R + R\rightarrow J/\psi[^{3}S_1^{(8)}]$, (2) $R + R\rightarrow J/\psi[^{1}S_0^{(8)},^{3}P_J^{(8)}]$, (3) $R + R\rightarrow J/\psi[^{3}S_1^{(1)}]+g$, and (4) their sum compared with CDF data from Tevatron run I CDFI. The theoretical results are obtained with the (a) JB JB, (b) JS JS, or (c) KMR KMR unintegrated gluon distribution functions. The decay branching fraction $B(J/\psi \to \mu^+ + \mu^-)$ is included.
• Figure 3: Contributions to the $p_T$ distribution of $J/\psi$ mesons from $\psi^\prime$ decays in hadroproduction in $p\overline{p}$ scattering with $\sqrt{S}=1.8$ TeV and $|y|<0.6$ from the partonic subprocesses (1) $R + R\rightarrow \psi^\prime[{^3S}_1^{(8)}]$, (2) $R + R\rightarrow \psi^\prime[{^1S}_0^{(8)},{^3P}_J^{(8)}]$ (this contribution actually vanished), (3) $R + R\rightarrow \psi^\prime[{^3S}_1^{(1)}]+g$, and (4) their sum compared with CDF data from Tevatron run I CDFI. The theoretical results are obtained with the (a) JB JB, (b) JS JS, or (c) KMR KMR unintegrated gluon distribution functions. The decay branching fraction $B(J/\psi \to \mu^+ + \mu^-)$ is included.
• Figure 4: Contributions to the $p_T$ distribution of $J/\psi$ mesons from $\chi_{cJ}$ decays in hadroproduction in $p\overline{p}$ scattering with $\sqrt{S}=1.8$ TeV and $|y|<0.6$ from the sum of the partonic subprocesses $R + R\rightarrow \chi_{cJ}[^{3}P_J^{(1)}]$ and $R + R\rightarrow \chi_{cJ}[^{3}S_1^{(8)}]$, the latter of which being quite unimportant, compared with CDF data from Tevatron run I CDFI. The theoretical results are obtained with the JB JB, JS JS, or KMR KMR unintegrated gluon distribution functions. The decay branching fraction $B(J/\psi \to \mu^+ + \mu^-)$ is included.
• Figure 5: Contributions to the $p_T$ distribution of prompt $J/\psi$ hadroproduction in $p\overline{p}$ scattering with $\sqrt{S}=1.96$ TeV and $|y|<0.6$ from (1) direct production, (2) $\psi^\prime$ decays, (3) $\chi_{cJ}$ decays, and (4) their sum compared with CDF data from Tevatron run II CDFII. The theoretical results are obtained with the (a) JB JB, (b) JS JS, or (c) KMR KMR unintegrated gluon distribution functions. The decay branching fraction $B(J/\psi \to \mu^+ + \mu^-)$ is included.