Exclusive photoproduction of light and heavy vector mesons: thresholds to very high energies

A reaction model for $γ+ p \to V + p$, $V=ρ^0, ϕ, J/ψ, Υ$, which exposes the quark-antiquark content of the photon in making the transition $γ\to {q} \bar{q} + \mathbb P \to V$, where ${q}$ depends on $V$, and couples the intermediate ${q} \bar{q}$ system to the proton’s valence quarks via Pomeron ($\mathbb P$) exchange, is used to deliver a unified description of available data – both differential and total cross sections – from near threshold to very high energies, $W$, for all the $V$-mesons. For the $Υ$, this means $10\lesssim W/{\rm GeV} \lesssim 2,000$. Also provided are predictions for the power-law exponents that are empirically used to characterise the large-$W$ behaviour of the total cross sections and slope parameters characterising the near-threshold differential cross sections. Appealing to notions of vector meson dominance, the latter have been interpreted as vector-meson–proton scattering lengths. The body of results indicate that it is premature to link any $γ+ p \to V + p$ data with, for instance, in-proton gluon distributions, the quantum chromodynamics trace anomaly, or pentaquark production. Further developments in reaction theory and higher precision data are required before the validity of any such links can be assessed.

💡 Research Summary

The paper presents a comprehensive reaction model—referred to as “P‑dyn”—for exclusive photoproduction of vector mesons in the process γ + p → V + p, where V denotes any of the four ground‑state vector mesons ρ⁰, ϕ, J/ψ, or Υ. The central idea is to expose the quark‑antiquark (q q̄) component of the photon, let this q q̄ pair interact with the proton’s valence quarks through the exchange of a color‑singlet Pomeron (𝔓), and then convert the q q̄ system into an on‑shell vector meson. This mechanism is illustrated in Fig. 1 and mathematically encoded in Eq. (4), which is a four‑point loop integral containing (i) dressed quark propagators S_q(k), (ii) a photon‑quark vertex Γ_γ^μ taken in the Ball‑Chiu form, (iii) a Pomeron‑quark vertex Γ_𝔓^α = β_q γ^α (with a test using the full BC vertex), and (iv) the Bethe‑Salpeter amplitude of the vector meson Γ_V^ν.

All non‑perturbative ingredients—propagators and vertices—are obtained from Continuum/Lattice Schwinger Functions (CSMs), i.e. from QCD‑based calculations that do not rely on phenomenological parametrisations. The only phenomenological inputs are the Pomeron trajectory α_𝔓(t)=α₀+α₁ t, the proton isoscalar form factor F₀(t) (Eq. 12), and the strength β_q of the Pomeron‑quark coupling. These parameters are fixed by fitting a limited set of high‑energy data and then kept unchanged across the entire energy range.

The model yields analytic expressions for the differential cross section dσ/dΩ (Eq. 8) and its t‑dependence dσ/dt (Eq. 10). At high centre‑of‑mass energies W, the total cross section follows the Regge‑type power law σ_tot ∝ W^{4(α₀−1)}. Near threshold, the t‑distribution is characterised by a slope parameter b_V, which the authors reinterpret, via vector‑meson dominance (VMD), as a vector‑meson–proton scattering length a_{Vp}. This provides a phenomenological bridge between low‑energy data and an effective interaction radius.

Sensitivity studies show that replacing the simple γ^α Pomeron‑quark vertex with the full Ball‑Chiu vertex changes the predicted cross sections by less than 2.5 % in an L₁ norm, confirming that the results are robust against reasonable variations of the vertex structure. The model also reproduces the observed difference between light‑meson (ρ⁰, ϕ) and heavy‑meson (J/ψ, Υ) photoproduction, which is accommodated by using distinct Pomeron trajectory parameters for the two groups.

Extensive comparisons with experimental data are presented. For ρ⁰ and ϕ, the model accurately describes the near‑threshold differential cross sections and the extracted slope parameters. For J/ψ and Υ, it reproduces the total cross sections over a vast energy span (10 GeV ≲ W ≲ 2000 GeV), including the steep rise with energy that contradicts naïve perturbative QCD expectations. The agreement is achieved without any adjustable parameters beyond those fixed once from a subset of data, demonstrating the predictive power of the approach.

Despite this success, the authors caution against over‑interpreting photoproduction data as direct probes of the proton’s gluon parton distribution, the QCD trace anomaly, or exotic pentaquark states. The reaction mechanism is dominated by non‑perturbative Pomeron exchange and the detailed dynamics of the q q̄ conversion, which obscure any simple connection to those quantities. They argue that more refined reaction theory—particularly a better understanding of the mass dependence of β_q and α_𝔓(t)—and higher‑precision measurements are required before such links can be credibly established.

In summary, the paper delivers a unified, QCD‑grounded description of exclusive vector‑meson photoproduction from threshold to multi‑TeV energies. By combining non‑perturbative Schwinger‑function inputs with a Regge‑type Pomeron exchange, it resolves a long‑standing challenge of describing both light and heavy meson production within a single framework, and sets a clear agenda for future theoretical and experimental work.