  We calculate the cross-sections of diffractive single hadron photo- or
electroproduction with large $p_T$, on a nucleon or a nucleus in the shockwave
formalism. We use the hybrid formalism mixing collinear factorization with high
energy small-$x$ factorization with the impact factors computed at
next-to-leading order accuracy. We prove the cancellation of divergence and we
determine the finite parts of the differential cross-sections. We work in
general kinematics such that both photoproduction and leptoproduction are
considered. The results can be used to detect saturation effects, at both the
future EIC or already at LHC, using Ultra-Peripheral Collisions.
