We solve a unified integral equation to obtain the x, ${\mathit{Q}}_{\mathit{T}}$, and Q dependence of the gluon distribution of a proton in the small x regime, where x and ${\mathit{Q}}_{\mathit{T}}$ are the longitudinal momentum fraction and the transverse momentum of the gluon probed at a scale Q. The equation generates a gluon with a steep ${\mathit{x}}^{\mathrm{-}\lambda }$ behavior, with λ∼0.5, and a ${\mathit{Q}}_{\mathit{T}}$ distribution which broadens as x decreases. We compare our solutions with, on the one hand, those that we obtain using the double-leading-logarithm approximation to Altarelli-Parisi evolution and, on the other hand, to those that we determine from the BFKL equation.

• Received 7 March 1995

DOI:https://doi.org/10.1103/PhysRevD.52.1445