Understanding the relation between QCD evolution in the Bjorken limit and the Regge limit is crucial to achieve a complete and smooth picture of proton and nuclear structure for arbitrary Bjorken x values. The hope, in the small x regime where gluon density is expected to reach saturation and the naif partonic breaks down, was that by computing higher order corrections to small x evolution (BK equation) one would capture more and more of the physics at moderate x. However, this research program has encountered some challenges. At NLO large collinear logarithms are present and needs to be resummed spoiling the renormalization group structure established at LO.
In order to overcome these formal difficulties we revisit the shock wave approach for high energy scattering by proposing a new gauge invariant operator definition for hadronic operators at small x that accounts systematically for the collinear limit of the unintegrated gluon distribution. I will discuss in particular inclusive DIS as a first application.