Unintegrated gluon distributions from the transverse coordinate representation of the CCFM equation in the single loop approximation

TL;DR

This paper derives an analytic solution for unintegrated gluon distributions using the Fourier-Bessel transform of the CCFM equation in the single loop approximation, enabling a comparison with exact solutions.

Contribution

It provides a novel analytic approach to express unintegrated gluon distributions in terms of integrated ones within the CCFM framework.

Findings

Analytic solution for gluon distribution moments $f_{ ext{omega}}(b,Q)$

Approximate expressions relate unintegrated to integrated gluon distributions

Comparison shows the effectiveness of the approximate method

Abstract

We utilise the fact that the CCFM equation in the single loop approximation can be diagonalised by the Fourier-Bessel transform. The analytic solution of the CCFM equation for the moments $f_{\omega}(b,Q)$ of the scale dependent gluon distribution is obtained, where $b$ is the transverse coordinate conjugate to the transverse momentum of the gluon. The unintegrated gluon distributions obtained from this solution are analysed. It is shown how the approximate treatment of the exact solution makes it possible to express the unintegrated gluon distributions in terms of the integrated ones. The corresponding approximate expressions for the unintegrated gluon distribution are compared with exact solution of the CCFM equation in the single loop approximation.