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

## TL;DR

This paper demonstrates how low x physics can be reformulated within an infinite twist TMD/GTMD framework, unifying it with moderate x QCD descriptions and providing new insights into the origins of saturation effects.

## Contribution

It introduces a comprehensive rewriting of low x physics using infinite twist TMD/GTMD frameworks, linking it with moderate x QCD and highlighting the role of higher-body PDFs in saturation.

## Key findings

- Reformulation of low x physics in TMD/GTMD frameworks
- Derivation of the BFKL limit as a kinematic boundary
- Identification of three distinct saturation effects

## Abstract

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 PDFs should be taken into account even in this regime. Finally, we analyze how saturation should be understood as three 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.