QCD Corrections to Inelastic $J/ψ$ Photoproduction

TL;DR

This paper delivers a complete NLO QCD analysis of inelastic J/ψ photoproduction, addressing γ + p → J/ψ + X across fixed-target and HERA kinematics. By computing virtual and real corrections, including the photon-quark channel and mass factorization in an extended MS-bar scheme, it provides finite, renormalized parton- and hadron-level cross sections expressed through scaling functions. The results show substantial NLO enhancements and reduced scale dependence at fixed-target energies, while exposing the limitations of fixed-order predictions near the soft-gluon/low-pT region at HERA, where resummation is needed. Overall, the work supports a gluon-distribution-driven description of inelastic J/ψ production, highlights sensitivity to small-x PDFs, and underscores the importance of higher-twist and relativistic corrections for precision phenomenology.

Abstract

We present a complete calculation of the higher-order perturbative QCD corrections to inelastic photoproduction of $J/ψ$ particles. A comprehensive analysis of total cross sections and differential distributions for the energy range of the fixed-target experiments and for inelastic $J/ψ$ photoproduction at HERA is performed. The cross section and the $J/ψ$ energy spectrum are compared with the available photoproduction data including first results from HERA. This analysis will not only provide information on the gluon distribution of the proton but appears to be a clean test for the underlying picture of quarkonium production as developed so far in the perturbative QCD sector.

Figures (20)

• Figure 1: The leading-order Feynman diagrams contributing to inelastic $J/\psi$ photoproduction. Additional graphs are obtained by reversing the arrows on the heavy quark lines.
• Figure 2: Generic Feynman diagrams contributing to the virtual amplitude (part 1): self-energy corrections (a,b) [36 diagrams], abelian vertex corrections ($\gamma c\overline{c}$- and $g c\overline{c}$-vertices) (c) [18 diagrams], and non-abelian vertex corrections (d) [12 diagrams].
• Figure 3: Generic Feynman diagrams contributing to the virtual amplitude (part 2): abelian four-point box graphs (a) [12 diagrams], abelian five-point box graphs (b) [6 diagrams], non-abelian four-point box graphs (c) [8 diagrams] and (d) [4 diagrams], non-abelian five-point box graphs (e) [4 diagrams] and (f) [2 diagrams], and diagrams involving four-gluon couplings (g) [2 diagrams] and (h) [1 diagram].
• Figure 4: Generic Feynman diagrams contributing to the gluon bremsstrahlung process (a-c) and the quark-antiquark splitting reaction (d).
• Figure 5: Feynman diagrams contributing to the photon-(anti-)quark subprocess $\gamma q(\overline{q})\to J/\psi\, gq(\overline{q})$. Additional graphs are obtained by reversing the arrows on the heavy quark lines.