Hard exclusive photoproduction of photon-meson pairs: pseudoscalar channels $\pi$, $\eta$ and $\eta'$

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 $\text{M} \in \{\pi^\pm, \pi^0, \eta, \eta'\}$. Compact analytical expressions are obtained for the amplitudes involving quark generalized parton distributions, with the two-gluon components of the $\eta$ and $\eta'$ distribution amplitudes included. The numerical analysis is performed in the moderate-$\xi$ region, where valence-quark GPDs are expected to be important. In this region, we find a strong impact of the pion-pole term in $\gamma\pi^\pm$ production, and a non-negligible effect for neutral mesons. We also observe a marked dependence of $\gamma\eta'$ 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.