Unintegrated dipole gluon distribution at small transverse momentum

TL;DR

This paper derives analytical expressions for the unintegrated dipole gluon distribution at small transverse momentum, revealing a series expansion related to Bell polynomials and a connection to the Sudakov form factor.

Contribution

It introduces a novel analytical approach to compute the unintegrated gluon distribution at small transverse momentum using Fourier transforms and series resummation.

Findings

Series expansion in Bell polynomials for the distribution.

Resummation reveals similarity to the Sudakov form factor.

Constant from saddle point condition influences the coupling role.

Abstract

We derive analytical results for unintegrated color dipole gluon distribution function at small transverse momentum. By Fourier transforming the $S$-matrix for large dipoles we derive the results in the form of a series of Bells polynomials. Interestingly, when resumming the series in leading log accuracy, the results showing up striking similarity with the Sudakov form factor with role play of coupling is being done by a constant that stems from the saddle point condition along the saturation line.