The evolution of the small x gluon TMD

TL;DR

This paper investigates the evolution of the small x gluon TMD in the dilute limit, demonstrating its compliance with both CS and BFKL equations, and emphasizing the joint use of HEF and TMD factorization for resummation.

Contribution

It provides a combined analysis of small x gluon TMD evolution satisfying both CS and BFKL equations using a simple quark target model.

Findings

Small x gluon TMD satisfies both CS and BFKL evolution equations.

Confirms the necessity of joint HEF and TMD factorization for resummation.

Supports earlier findings on high energy and TMD factorization compatibility.

Abstract

We study the evolution of the small $x$ gluon transverse momentum dependent(TMD) distribution in the dilute limit. The calculation has been carried out in the Ji-Ma-Yuan scheme using a simple quark target model. As expected, we find that the resulting small $x$ gluon TMD simultaneously satisfies both the Collins-Soper(CS) evolution equation and the Balitsky-Fadin-Kuraev-Lipatov(BFKL) evolution equation. We thus confirmed the earlier finding that the high energy factorization(HEF) and the TMD factorization should be jointly employed to resum the different type large logarithms in a process where three relevant scales are well separated.