Photoproduction of Charmonia and Total Charmonium-Proton Cross Sections

TL;DR

The paper develops a parameter-free light-cone dipole framework to simultaneously predict elastic photoproduction of charmonia and charmonium–nucleon total cross sections. It uses factorization in impact parameters, realistic charmonium rest-frame wave functions derived from four potentials, Melosh spin rotation for the light-cone boost, and universal dipole cross sections (GBW and KST). The inclusion of spin effects, especially the Melosh rotation, is crucial for matching the observed psi' production and the psi'–J/psi ratio; the approach accurately describes data across a wide range of energy and photon virtuality. It also yields state-dependent, energy-growing charmonium–nucleon cross sections and discusses nuclear suppression via formation and coherence lengths, with results aligning with experimental observations across multiple nuclei and energies.

Abstract

Elastic virtual photoproduction cross sections gamma^*p -> J/psi(psi')p and total charmonium-nucleon cross sections for J/psi, psi' and chi states are calculated in a parameter free way with the light-cone dipole formalism and the same input: factorization in impact parameters, light-cone wave functions for the gamma^* and the charmonia, and the universal phenomenological dipole cross section which is fitted to other data. The charmonium wave functions are calculated with four known realistic potentials, and two models for the dipole cross section are tested. Very good agreement with data for the cross section of charmonium photoproduction is found in a wide range of s and Q^2. The inclusion of the Melosh spin rotation increases the psi' photoproduction rate by a factor 2-3 and removes previously observed discrepancies in the psi' to J/psi ratio in photoproduction. We also calculate the charmonium-proton cross sections whose absolute values and energy dependences are found to correlate strongly with the sizes of the states.

Figures (12)

• Figure 1: Schematic representation of the amplitudes for the reactions $\gamma^*p \to \psi p$ (left) and $\psi\,p$ elastic scattering (right) in the rest frame of the proton. The $c\bar{c}$ fluctuation of the photon and the $\psi$ with transverse separation $r_T$ and c.m. energy $\sqrt{s}$ interact with the target proton via the cross section $\sigma(r_T,s)$ and produce a $J\!/\!\psi$ or $\psi'$.
• Figure 2: The dipole cross section as function of $r_T^2$ at energies $\sqrt{s}=10,\ 30,\ 100$ and $300\ \,\hbox{GeV}$ for GBW (left) and KST (right) parameterizations.
• Figure 3: Shapes of the potentials $V(r)$ for the four parameterizations employed in this paper. The curves for COR, LOG and POW are normalized at $r=1\,\hbox{fm}$ to the value of BT potential.
• Figure 4: The radial part of the wave function $\Psi_{nl}(r)$ for the $1S$ and $2S$ states calculated with four different potentials (see text).
• Figure 5: Three-dimensional plot for the light-cone wave functions for $J/\psi(1S)$ and $\psi'(2S)$ in the mixed $\alpha-{\vec{r}\,}_T$ representation for the BT potential BT.