Diffractive vector meson photo-production in oxygen--oxygen and neon--neon ultraperipheral collisions at energies available at the CERN Large Hadron Collider

The energy-dependent hotspot model is used to predict cross sections for vector-meson diffractive photo-nuclear production off oxygen ($γ$O) and neon ($γ$Ne) that can be extracted from ultra-peripheral O–O and Ne–Ne collisions, recently recorded at the LHC. In both cases, two models are used to describe the nuclear shapes. Woods-Saxon prescriptions for O and Ne as well as an alpha-cluster description of O and a bowling-pin-like shape for Ne, according to the PGCM formalism. Predictions are presented for the dependence on the centre-of-mass energy of the photon–nucleus system, as well as on Mandelstam-$t$, of the cross sections for the coherent and the incoherent photo-nuclear production of $ρ^{0}$ and J/$ψ$ vector mesons. Furthermore, the rapidity dependence of the ultra-peripheral cross section is reported for all cases. It is found that the incoherent process provides a measurable signature for the approach to the gluon-saturation regime, and that the simultaneous determination of $ρ^{0}$ and J/$ψ$ coherent and incoherent production provides a strong constraint on nuclear models for both O and Ne.

💡 Research Summary

The paper presents a detailed phenomenological study of diffractive vector‑meson photoproduction in ultra‑peripheral collisions (UPCs) of the newly recorded oxygen–oxygen (O–O) and neon–neon (Ne–Ne) systems at the LHC, where the nucleon–nucleon centre‑of‑mass energy is √sNN = 5.36 TeV. Using the energy‑dependent hotspot model, the authors calculate both coherent (elastic) and incoherent (break‑up) cross sections for the light ρ⁰ and the heavy J/ψ mesons. Two distinct nuclear‑geometry descriptions are employed for each ion: a conventional three‑parameter Woods‑Saxon (WS) density and a more microscopic clustering picture – an α‑cluster tetrahedron for ¹⁶O and a Projected‑Generator‑Coordinate‑Method (PGCM) “bowling‑pin” shape for ²⁰Ne.

The theoretical framework combines the dipole picture of photon–hadron interactions with the Good‑Walker formalism. The photon fluctuates into a quark‑antiquark dipole, which scatters off the target via a two‑gluon exchange. The dipole–nucleus cross section is built from the GBW parametrisation of the dipole amplitude N(x,r) and a nuclear thickness function T_A(b) that is constructed as a superposition of nucleons, each containing a number of Gaussian hotspots whose width B_hs≈0.2 fm. Crucially, the number of hotspots grows with decreasing Bjorken‑x (or increasing energy), mimicking the rise of the gluon density and providing a built‑in mechanism for gluon saturation.

Coherent production is proportional to the square of the average scattering amplitude ⟨A⟩, reflecting the interaction with the whole colour field of the nucleus. Incoherent production is proportional to the variance ⟨|A|²⟩−|⟨A⟩|² and therefore probes event‑by‑event fluctuations of the colour field, i.e. the distribution of hotspots inside the nucleus.

Key findings:

1. Coherent spectra for both ρ⁰ and J/ψ are remarkably insensitive to the choice of nuclear geometry. Up to the first diffraction dip (|t|≈0.2 GeV²) the WS and clustering models give almost identical dσ/dt, indicating that the average gluon density is dominated by the overall nuclear radius rather than sub‑nucleonic clustering.

2. Incoherent spectra show a strong model dependence. The WS description, with nucleons and hotspots spread over a larger volume, yields a larger incoherent cross section in the experimentally accessible |t| range (0.1–2 GeV²). The α‑cluster (O) and PGCM (Ne) models confine hotspots within compact clusters, reducing the number of independent configurations and thus suppressing the variance. Consequently, the incoherent dσ/dt is significantly lower for the clustered nuclei.

3. Energy dependence of the incoherent component provides a clear saturation signature. For ρ⁰ at large |t| the incoherent cross section first rises with W, reaches a maximum, and then declines as W increases further – exactly the behaviour predicted when gluon saturation sets in. The J/ψ, being heavier, exhibits a milder turnover; its incoherent cross section flattens at high W rather than decreasing sharply. This mass‑dependent behaviour matches earlier observations in proton‑proton and proton‑lead UPCs.

4. t‑fixed energy scans reveal complementary information. At small |t| (probing large transverse areas) the incoherent cross section grows monotonically with energy for both mesons and both geometries. At larger |t| (probing small transverse spots) the WS model still shows a modest increase, whereas the clustered models display a clear decrease for ρ⁰ and a saturation‑like plateau for J/ψ. Multi‑differential measurements (d²σ/dW dt) could therefore disentangle nuclear shape effects from genuine saturation dynamics.

5. Rapidity distributions are provided for the full UPC cross sections. At mid‑rapidity (y≈0) the photon–nucleus centre‑of‑mass energies correspond to W≈75 GeV for ρ⁰ and W≈120 GeV for J/ψ. The predicted integrated cross sections are of order tens of μb, well within the reach of the ALICE and CMS detectors given the recorded O–O and Ne–Ne luminosities.

The authors compare their results with existing Pb–Pb and Xe–Xe UPC data, finding consistent normalisations and confirming that the energy‑dependent hotspot model, previously validated for heavy‑ion collisions, also describes light‑ion systems. They argue that the simultaneous measurement of coherent and incoherent ρ⁰ and J/ψ production in O–O and Ne–Ne collisions will place stringent constraints on nuclear geometry (WS vs clustering) and on the onset of gluon saturation in small nuclei.

In summary, the paper demonstrates that ultra‑peripheral O–O and Ne–Ne collisions at the LHC constitute a powerful laboratory for probing sub‑nucleonic fluctuations and saturation effects. The incoherent component, especially its energy and t‑dependence, emerges as a sensitive observable that can discriminate between traditional Woods‑Saxon densities and more refined cluster models, while also providing a direct experimental handle on the saturation regime of QCD. The study paves the way for future measurements at the LHC and for complementary investigations at the forthcoming Electron‑Ion Collider, where similar techniques can be applied to map the gluon landscape of nuclei with unprecedented precision.