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

TL;DR

The paper develops a parameter-free, covariant Pomeron-dyn model for γ+p→V+p (V∈{ρ^0, φ, J/ψ, Υ}) that explicitly exposes the qq̄ content of the photon via a dynamical γ→q$q̄$ transition coupled to the proton through Pomeron exchange. Using rainbow-ladder truncation in covariant Schwinger-function methods, the authors compute the γ→q$q̄$ transition, the vector-meson Bethe-Salpeter amplitudes, and the relevant propagators/vertices to predict differential and total cross sections from near threshold to very high energies, with predictions validated against extensive data and contrasted with a simplified Pomeron–vector-meson model. They extract power-law exponents for the high-$W$ behavior and near-threshold slope parameters (interpreted as VMD-based scattering lengths) and examine their consistency with empirical trends, finding good agreement for heavy mesons and notable near-threshold effects for light ones. The results argue that linking near-threshold γ+p→V+p data to in-proton gluon distributions, the QCD trace anomaly, or pentaquark production is premature, highlighting the need for improved reaction theory and higher-precision data to draw such connections.

Abstract

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.

Figures (19)

• Figure 1: Reaction model for $\gamma + p \to V + p$, referred to hereafter as $\mathbb P -$dyn. The quark-antiquark, ${\mathpzc q}\bar{\mathpzc q}$, component of the dressed-photon is probed by Pomeron exchange with the proton, producing an on-shell vector meson, $V$. Referring to Eq. \ref{['EqtqP']}: the green rectangle describes Pomeron exchange, $\Gamma^{\mathbb P}$, including its couplings to the proton and quark -- see Sect. \ref{['SecPomeron']}. Further, the solid black curve is $S_q$, the dressed $q$ quark propagator; the shaded lighter-blue circle is $\Gamma_\mu^\gamma$, the dressed-$\gamma q \bar{q}$ vertex; and the shaded red circle is $\Gamma_\nu$, the $V$-meson Bethe-Salpeter amplitude -- see Sect. \ref{['sec:3']}. Kinematics: $s=W^2 = -(p_2^2+ P^2)$; $t=-(p_2-p_1)^2$.
• Figure 2: $\mathbb{P}-$am reaction model for $\gamma + p \to V + p$. Compared with our dynamical model, $\mathbb{P}-$dyn, sketched in Fig. \ref{['FigPomMechanism']}, $\mathbb{P}-$am replaces the $\gamma\to {\mathpzc q} \bar{\mathpzc q} + \mathbb P \to V$ transition matrix element by a momentum-independent $\gamma\to V$ transition coupling (akin to vector meson dominance) along with a form factor, $F_V$, that expresses a Pomeron--vector-meson form factor.
• Figure 3: Pion and vector meson properties listed in Table \ref{['TabStatic']}, computed using CSMs with interaction parameters in Table \ref{['tab:1']}Qin:2018dqpXu:2019ilhYao:2021pyf: ( A) Masses and ( B) leptonic decay constants. Blue squares indicate CSM results; red triangles indicate experimental values at a sensible level of precision ParticleDataGroup:2024cfk.
• Figure 4: $W$-dependence of total cross section for $\rho^{0}$ photoproduction, $W_{\rm th}^{\rho} = 1.714\,$GeV. Solid purple curve -- $\mathbb{P}-$dyn; dashed black curve -- $\mathbb{P}-$am. Data sources: black circles -- Aachen-Hamburg-Heidelberg-Munich:1975jed; cyan diamonds (fixed target) -- Bonn-CERN-EcolePoly-Glasgow-Lancaster-Manchester-Orsay-Paris-Rutherford-Sheffield:1982qiv; green squares Park:1971tsBallam:1971wq; blue stars Egloff:1979mg; red left and right triangles H1:1996prvH1:2020lzc; and red open squares -- pseudodata inferred Strakovsky:2025ews from differential $\pi^+\pi^-p$ photoproduction cross sections measured with CLAS at JLab and analysed within the JM model Mokeev:2015lda (see text).
• Figure 5: Differential cross section for $\rho^{0}$ photoproduction compared with data ZEUS:1995bfs (blue squares) in the range $60<W<$$80$ GeV. Solid purple curve -- $\mathbb{P}-$dyn; dashed black curve: $\mathbb{P}-$am. Both are computed at the average energy $\text{W}=70$ GeV. Pomeron trajectory and quark–Pomeron couplings used are given in Table \ref{['tab:1']} -- Row 1.