Hard exclusive photoproduction of photon-meson pairs: pseudoscalar channels $\pi$, $\eta$ and ${\eta }^{\prime }$

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 $\text{M}\in \{{\pi }^{\pm },{\pi }^0,\eta ,{\eta }^{\prime }\}$. Compact analytical expressions are obtained for the amplitudes involving quark generalized parton distributions, with the two-gluon components of the $\eta$ and ${\eta }^{\prime }$ 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 $\gamma {\eta }^{\prime }$ 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.

48 pages, 22 figures