# Interplay of the CGC and TMD frameworks to all orders in kinematic twist

## TL;DR

This paper explores the relationship between the Color Glass Condensate (CGC) and improved TMD (iTMD) frameworks at small x, demonstrating how iTMD amplitudes can be derived from CGC amplitudes by removing genuine twist contributions, thus unifying different approaches in high-energy QCD.

## Contribution

It establishes a direct connection between CGC and iTMD amplitudes through a kinematic twist expansion, enhancing understanding of their interplay at all orders.

## Key findings

- iTMD amplitudes are obtained by removing genuine twist contributions from CGC amplitudes.
- The dipole-size expansion of CGC resembles the twist expansion of TMD amplitudes.
- The relation between iTMD and dilute low x frameworks is clarified.

## Abstract

A framework for an improved TMD (iTMD) factorization scheme at small $x$, involving off-shell perturbative subamplitudes, was recently developed as an interpolation between the TMD $k_t \ll Q$ regime and the BFKL $k_t \sim Q$ regime. In this article, we study the relation between CGC and iTMD amplitudes. We first show how the dipole-size expansion of CGC amplitudes resembles the twist expansion of a TMD amplitude. Then, by isolating kinematic twists, we prove that iTMD amplitudes are obtained with infinite kinematic twist accuracy by simply getting rid of all genuine twist contributions in a CGC amplitude. Finally we compare the amplitudes obtained via a proper kinematic twist expansion to those obtained via a more standard dilute expansion to show the relation between the iTMD framework and the dilute low $x$ framework.