Evolution of gluon TMDs from small to moderate x

TL;DR

This paper derives and analyzes a comprehensive evolution equation for gluon transverse momentum dependent distributions (TMDs), unifying different kinematic regimes and revealing both known and novel results across the full range of Bjorken x and transverse momentum.

Contribution

It introduces a new evolution equation for gluon TMDs that unifies small and moderate x regimes, providing insights into their behavior across all kinematic ranges.

Findings

Derivation of a unified evolution equation for gluon TMDs

Recovery of known results in specific limits

Identification of previously unknown behaviors in gluon TMD evolution

Abstract

Recently we obtained an evolution equation of gluon TMDs, which addresses a problem of unification of different kinematic regimes. It describes evolution in the whole range of Bjorken $x_B$ and the whole range of transverse momentum $k_\perp$. In this notes I study different limits of this evolution equation and show how it yields several well-known and some previously unknown results.