Hard exclusive photoproduction of photon-meson pairs: pseudoscalar channels $π$, $η$ and $η'$

TL;DR

The paper develops a leading-twist, leading-order QCD framework for hard exclusive photoproduction of photon–meson pairs γN → γM N′ with pseudoscalar mesons, deriving compact analytical expressions for quark GPD contributions and including two-gluon DA components for η and η′. It employs the GK GPD model, collinear factorization, and a pion-pole treatment to produce CMFFs that drive fully differential, single-differential, and integrated cross sections in the moderate-ξ region. Key findings include a strong pion-pole impact in γπ channels, notable gluon contributions in γη′ production, and a pronounced sensitivity to the pion DA shape, all of which come with sizable LO-scale uncertainties that necessitate NLO corrections. The results offer a transparent analytical baseline and numerical predictions to support future experimental tests and refinements of GPDs and meson DAs.

Abstract

We investigate the hard exclusive photoproduction of photon-meson pairs at leading-twist and leading-order in perturbative QCD, and focus on pseudoscalar mesons $\text{M} \in \{π^\pm, π^0, η, η'\}$. Compact analytical expressions are obtained for the amplitudes involving quark generalized parton distributions, with the two-gluon components of the $η$ and $η'$ distribution amplitudes included. The numerical analysis is performed in the moderate-$ξ$ region, where valence-quark GPDs are expected to be important. In this region, we find a strong impact of the pion-pole term in $γπ^\pm$ production, and a non-negligible effect for neutral mesons. We also observe a marked dependence of $γη'$ photoproduction on two-gluon contributions. This process offers enhanced sensitivity to the shape of the GPDs already at leading-order, while the tested dependence on the meson distribution amplitude and the renormalization scale introduces further theoretical uncertainties, the latter emphasizing the need for next-to-leading-order corrections. Our results provide a concise analytical framework and a numerical baseline for future studies.

Figures (22)

• Figure 1: Left: Factorization of $\gamma {\rm N} \to \gamma {\rm M} \, {\rm N}'$ process. Right: Brodsky--Lepage factorization for $\gamma {\rm M}' \to \gamma {\rm M}$ process.
• Figure 2: Left: Pion DAs. Shown are the asymptotic DA ($a_2 = 0$), the lattice-motivated DA with $a_2^\pi(\mu_0 = 2~\text{GeV}) = 0.116$RQCD:2019osh in the Gegenbauer representation (\ref{['eq:phiGegen-Q']}), and the beta-function ansatz (\ref{['eq:phi_expal']}) for $\eta = 0.5$, $0.4$, and $0.3$. Right: $\eta_8$ and $\eta_1$ DAs obtained from the Gegenbauer expansions (\ref{['eq:phiGegen-Q']}) and (\ref{['eq:phiGegen-G']}), with coefficients evaluated at $\mu_0 = 2~\text{GeV}$: $a_2^8 = -0.039$, $a_2^1 = -0.057$, and $a_2^g = 0.38$Kroll:2021zss.
• Figure 3: Representative Feynman diagrams contributing to $\gamma ( q_1 \bar{q}_2 ) \to \gamma ( q_1 \bar{q}_2 )$ (\ref{['eq:sub-qqqq']}).
• Figure 4: Representative Feynman diagrams contributing to $\gamma ( q \bar{q} ) \to \gamma ( g g )$ (\ref{['eq:sub-qqgg']}).
• Figure 5: Fully differential cross-section for $\gamma {\rm N} \to \gamma {\rm M} \, {\rm N}'$, with $M=\pi^+, \pi^-, \pi^0, \eta, \eta'$. Dashed and dash-dotted lines correspond to the vector and axial-vector GPD contributions, respectively, while solid lines show their sum, i.e., the total result. Thin lines represent axial and total results without the $\pi$-pole contribution. The kinematics are specified by $S_{\gamma {\rm N}}=20$ GeV$^2$, $s'=4$ GeV$^2$, yielding $\xi=0.117$, while $(-t)=(-t_0)$ (\ref{['eq:t0']}).