Towards a New Global QCD Analysis: Solution to the Non-Linear Equation at Arbitrary Impact Parameter

Abstract

A numerical solution is presented for the non-linear evolution equation that governs the dynamics of high parton density QCD. It is shown that thesolution falls off as $e^{-b/R}$ at large values of the impact parameter $b$. The power-like tail of the amplitude appears in impact parameter distributions only after the inclusion of dipoles of size larger than the target, a configuration for which the non-linear equation is not valid. The value, energy and impact parameterof the saturation scale $Q_s(y=\ln(1/x),b)$) are calculated both for fixed and running QCD coupling cases. It is shown that the solution exhibits geometrical scaling behaviour. The radius of interaction increases as the rapidity in accordance with the Froissart theorem. The solution we obtain differs from previous attempts, where an anzatz for $b$ behaviour was made. The solutions for running and fixed $\as$ differ. For running $\as$ we obtain a larger radius of interaction (approximately twice as large), a steeper rapidity dependence, and a larger value of the saturation scale.