Unintegrated gluon distribution from the Ciafaloni-Catani-Fiorani-Marchesini equation

Abstract

The gluon distribution ${f(x,k}_{t}^{2},{\ensuremath{\mu}}^{2}),$ unintegrated over the transverse momentum ${k}_{t}$ of the gluon, satisfies the angular-ordered CCFM equation which interlocks the dependence on the scale ${k}_{t}$ with the scale $\ensuremath{\mu}$ of the probe. We show how, to leading logarithmic accuracy, the equation can be simplified to a single-scale problem. In particular we demonstrate how to determine the two-scale unintegrated distribution ${f(x,k}_{t}^{2},{\ensuremath{\mu}}^{2})$ from knowledge of the integrated gluon obtained from a unified scheme embodying both BFKL $[\mathrm{log}(1/x)]$ and DGLAP $(\mathrm{log}{\ensuremath{\mu}}^{2})$ evolution.