Low x physics as an infinite twist (G)TMD framework: unravelling the origins of saturation

We show how the formulations of low x physics involving Wilson line operators can be fully rewritten into an infinite twist TMD or GTMD framework, respectively for inclusive and exclusive observables. This leads to a perfect match between low x physics and moderate x formulations of QCD in terms of GTMDs, TMDs, GPDs or PDFs. We derive the BFKL limit as a kinematic limit and argue that beyond the Wandzura-Wilczek approximation, 3-body and 4-body unintegrated PFDs should be taken into account even in this regime. Finally we analyse how saturation should be understood as 3 distinct effects: saturation through non-linearities in the evolution equations at small x, saturation through multiple interactions with slow gluons as TMD gauge links, and saturation as the enhancement of genuine twist corrections.