Exclusive photoproduction of ${\eta }_c\gamma$ pairs with large invariant mass

In this manuscript, we analyze the exclusive photoproduction of ${\eta }_c\gamma$ pairs in the collinear factorization framework and evaluate its cross section in leading order in the strong coupling ${\alpha }_s$. We found that this channel is mostly sensitive to the behavior of the unpolarized gluon generalized parton distributions $H_g$ in the Efremov-Radyushkin-Brodsky-Lepage kinematics. We estimated numerically the cross section and the expected counting rates in the kinematics of middle-energy photoproduction experiments, which can be realized at the future Electron-Ion Collider or in the ultraperipheral collisions at LHC. We found that the cross section is sufficiently large for dedicated experimental study. We also estimated the role of this process as a potential background to ${\eta }_c$ photoproduction, which is considered as one of the possible gateways for studies of $t$-channel odderons. We found that the contribution of ${\eta }_c\gamma$ (with undetected photon) is on par with expected contributions of odderons in the kinematics of small momentum transfer $\left|t\right|\lesssim 0.5{\mathrm{GeV}}^2$, though decreases rapidly at larger $\left|t\right|$.