Coherence Phenomena in Charmonium Production off Nuclei at the Energies of RHIC and LHC

TL;DR

The paper tackles the puzzle of charmonium suppression in proton–nucleus and nucleus–nucleus collisions at RHIC/LHC by developing a light-cone dipole framework that incorporates coherence and formation effects via LC Green functions. It reveals that gluon shadowing, amplified by higher Fock components, is a dominant source of suppression at high energies and that the expected x2 scaling emerges once energy-loss mechanisms fade with energy. The approach unifies limiting high- and low-energy regimes and demonstrates clear deviations from QCD factorization, providing parameter-free predictions that match SPS data and yield distinctive RHIC/LHC signatures, including a sharp xF dependence and a zero–xF peak in AA. The work also systematically extends to χ-state production, feed-down to J/ψ, and gluon radiation processes, establishing a comprehensive baseline for interpreting heavy-ion results and guiding future direct J/ψ/ψ′ studies.

Abstract

In the energy range of RHIC and LHC the mechanisms of nuclear suppression of charmonia are expected to be strikingly different from what is known for the energy of the SPS. One cannot think any more of charmonium produced on a bound nucleon which then attenuates as it passes through the rest of the nucleus. The coherence length of charmonium production substantially exceeds the nuclear radius in the new energy range. Therefore the production amplitudes on different nucleons, rather than the cross sections, add up and interfere, i.e. shadowing is at work. So far no theoretical tool has been available to calculate nuclear effects for charmonium production in this energy regime. We develop a light-cone Green function formalism which incorporates the effects of the coherence of the production amplitudes and of charmonium wave function formation, and is the central result of this paper. We found a substantial deviation from QCD factorization, namely, gluon shadowing is much stronger for charmonium production than it is in DIS. We predict for nuclear effects $x_2$ scaling which is violated at lower energies by initial state energy loss which must be also included in order to compare with available data. In this paper only the indirect J/Psi originating from decay of P-wave charmonia are considered. The calculated x_F-dependence of J/Psi nuclear suppression is in a good accord with data. We predict a dramatic variation of nuclear suppression with x_F in pA and a peculiar peak at x_F=0 in AA collisions at RHIC.

Figures (12)

• Figure 1: Perturbative QCD mechanism of production of the $\chi$ states in a gluon-nucleon collision.
• Figure 2: The incident gluon converts onto a $\bar{c}c$ pair long in advance of the nucleus. The pair propagates and attenuates with the absorption cross section $\sigma_3(r_T)$ (see the text) up to the point where it converts into a colorless $\bar{c}c$ pair with quantum numbers of $\chi$. Then it continues propagating through the nucleus, and is attenuated with the cross section $\sigma_{\bar{q}q}(r_T)$.
• Figure 3: The incident gluon can either produce the colorless $\bar{c}c$ pair with quantum numbers of $\chi$ at the point $z$ ( a), or it produces diffractively a color-octet $\bar{c}c$ with the quantum numbers of the gluon at the point $z_1$ which is then converted into a color singlet state at $z$ ( b). Propagation of a color-singlet or octet $\bar{c}c$ is described by the Green functions $G_{\bar{c}c}^{(1)}$ and $G_{\bar{c}c}^{(8)}$, respectively.
• Figure 4: Nuclear transparency for $\chi$ production off lead as function of energy of the charmonium, or $x_2$ (the upper scale). The solid curve includes both effects of coherence and formation, while the dashed curve corresponds to $l_c=0$. Since transparency scales in $x_2$ according to (\ref{['scaling']}), values of $x_2$ are shown on the top axis.
• Figure 5: Tungsten to beryllium cross section ratio as function of Feynman $x_F$ for $J/\Psi$ production at proton energy $800\,GeV$. The thin solid curve represents contribution of initial state quark shadowing and finals state $\bar{c}c$ attenuation for $\chi$ production. The dotted curve includes also gluon shadowing. The dashed curve is corrected for gluon enhancement at large $x_2$ (small $x_F$) using the prescription from ekr. The final solid curve is also corrected for energy loss and for $\chi\to J/\Psi\gamma$ decay. Experimental points are from the E866 experiment e866.