Absorption of 1$P$-wave heavy charmonium $χ_{c1}(1P)$ in nuclei

We study the inclusive heavy charmonium $χ_{c1}(1P)$ photoproduction from nuclei near the kinematic threshold within the collision model, based on the nuclear spectral function, for incoherent direct photon–nucleon charmonium creation processes. The model accounts for the final $χ_{c1}(1P)$ absorption in nuclear medium, target nucleon binding and Fermi motion. We calculate the absolute and relative excitation functions on $^{12}$C and $^{184}$W target nuclei at near-threshold photon beam energies of 8.25–16.0 GeV, the absolute momentum differential cross sections and ratios of them for its production off these target nuclei at laboratory polar angles of 0$^{\circ}$–10$^{\circ}$ and for photon energy of 13 GeV as well as the A-dependences of the transparency ratios for the $χ_{c1}(1P)$ at photon energy of 13 GeV within the different scenarios for its absorption cross section in nuclei. We demonstrate that the absolute and relative observables considered reveal distinct sensitivity to these scenarios. Therefore, they might be useful for the determination of this cross section from the comparison of them with the experimental data from the future experiments at the upgraded up to 22 GeV CEBAF facility, which is of crucial importance in understanding of charmonium production and suppression in high-energy heavy–ion collisions in a search for the quark-gluon plasma.

💡 Research Summary

The paper presents a comprehensive theoretical study of the near‑threshold photoproduction of the P‑wave charmonium state χc1(1P) on nuclear targets, focusing on its subsequent absorption in the nuclear medium. Using a collision model based on the nuclear spectral function, the authors incorporate realistic nuclear effects such as nucleon binding energy, Fermi motion, and the final‑state interaction (absorption) of the produced χc1(1P) meson. The model treats the production as an incoherent, direct photon–nucleon process and assumes that the fully formed χc1(1P) propagates through the nucleus, interacting with nucleons with an effective absorption cross section σχcN. Four representative values for σχcN—3.5 mb, 7 mb, 14 mb, and 20 mb—are adopted, covering the spread of existing theoretical estimates for the χc–nucleon interaction at low energies.

Calculations are performed for two target nuclei, carbon‑12 and tungsten‑184, over photon energies from 8.25 GeV up to 16 GeV, which span the kinematic threshold for χc1(1P) production on a free nucleon. The authors compute (i) absolute excitation functions (total cross sections versus photon energy), (ii) relative excitation functions (ratios of tungsten to carbon cross sections), (iii) momentum‑differential cross sections at laboratory polar angles between 0° and 10°, and (iv) the A‑dependence of the transparency ratio TA (the ratio of the nuclear cross section to A times the elementary γ N → χc1 N cross section) at a fixed photon energy of 13 GeV.

Key findings include: the absolute excitation function rises sharply near the threshold and flattens above ~13 GeV; the magnitude of the cross section is strongly reduced as σχcN increases, reflecting stronger absorption. The relative excitation function exhibits a clear A‑dependence: for small σχcN the tungsten‑to‑carbon ratio follows roughly the mass‑number scaling, whereas for large σχcN the ratio is significantly suppressed, indicating that heavy nuclei are more opaque to χc1(1P). Momentum‑differential results show that low‑momentum χc1(1P) mesons (pLab < 1 GeV/c) are most sensitive to absorption, because they spend a longer time inside the nucleus; this effect is most pronounced at forward angles (0°–10°). The transparency ratio at 13 GeV varies from about 0.8 (carbon) and 0.6 (tungsten) for σχcN = 3.5 mb down to below 0.3 for σχcN = 20 mb, demonstrating that TA is an excellent observable for discriminating among the different absorption scenarios.

The authors discuss the broader context: χcJ states contribute substantially to J/ψ yields via radiative decays, so understanding their production and absorption is essential for interpreting J/ψ suppression patterns in heavy‑ion collisions, a classic signature of quark‑gluon plasma formation. Existing experimental data on χc1(1P) are limited to high‑energy proton–proton collisions; near‑threshold photoproduction offers a cleaner environment with negligible initial‑state interactions and well‑controlled kinematics. Recent observations of χc1(1P) and χc2(1P) by the GlueX collaboration at JLab, together with the planned upgrade of CEBAF to 22 GeV and higher photon intensities, provide a realistic opportunity to measure the observables proposed in this work.

In conclusion, the paper supplies detailed predictions for absolute and relative cross sections, momentum spectra, and transparency ratios for χc1(1P) photoproduction on light and heavy nuclei. By comparing these predictions with forthcoming data, it will be possible to extract the effective χc1–nucleon absorption cross section in nuclear matter, thereby refining our understanding of charmonium interaction mechanisms in cold nuclear media and improving the baseline needed for interpreting charmonium suppression in hot, deconfined quark‑gluon plasma created in high‑energy heavy‑ion collisions.