Solution of the Fan Diagram Equation in 2+1 Dimensional QCD

Details Solution of the Fan Diagram Equation in 2+1 Dimensional QCD Solution of the Fan Diagram Equation in 2+1 Dimensional QCD

2004-06-17

arxiv.org/abs/hep-ph/0406193v1

Nucl.Phys. B698 (2004) 255-276

Physics

High Energy Physics

High Energy Physics - Phenomenology

23 pages

Scientific paper

10.1016/j.nuclphysb.2004.07.035

We investigate the Balitsky-Kovchegov (BK) equation for D=3 space-time dimensions, corresponding to one transverse coordinate, and we show that it can be solved analytically. The explicit solutions are found in the linear approximation and for the paricular cases when they do not depend on the impact parameter of the dipole or on its rapidity. It is shown, that in a general case different solutions are related by an infinite parameter group of transformations. The key observation is that the equation has the Kowalewskaya-Painlev\'{e} property, which gives the possibility of reducing the non-linear problem to the solution of a linear integral equation.

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