In the single-term splitting function model, complex maps turn DGLAP contour integrals into Laplace transforms whose inverse yields Barnes integrals for the Bessel solution.
On the $k_{\perp}$ dependent gluon density of the proton
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abstract
The $k_{\perp}$ dependent gluon distribution is calculated accounting for the resummation of small~$x$ effects due to the Lipatov equation. It is represented by a convolution of a gluon density in the collinear limit and a universal function ${\cal G}(x,k^2,\mu)$ for which an analytic expression is derived.
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Analytical solution to DGLAP integro-differential equation via complex maps in domains of contour integrals
In the single-term splitting function model, complex maps turn DGLAP contour integrals into Laplace transforms whose inverse yields Barnes integrals for the Bessel solution.