Exclusive photoproduction of a $\gamma \rho$ pair with a large invariant mass

Exclusive photoproduction of a $\gamma \rho$ pair in the kinematics where the pair has a large invariant mass and the final nucleon has a small transverse momentum is described in the collinear factorization framework. The scattering amplitude is calculated at leading order in ${\alpha }_s$ and the differential cross sections for the process where the $\rho -$meson is either longitudinally or transversely polarized are estimated in the kinematics of the JLab 12-GeV experiments.