NLO computation of diffractive di-hadron production in a saturation framework

The cross-sections of diffractive double hadron photo- or electroproduction with large $p_T$, on a nucleon or a nucleus, are calculated to NLO accuracy. A hybrid formalism mixing collinear factorization and high energy small-$x$ factorization, more precisely the shockwave formalism for the latter, is used to derive the results. The cancellation of divergences is explicitly shown, and the finite parts of the NLO differential cross-sections are found. We work in arbitrary kinematics such that both photoproduction and leptoproduction are considered. The results are therefore usable, to detect saturation effects, at both the future EIC or already at LHC, using Ultra Peripheral Collisions.