Diffractive dissociation and saturation scale from non-linear evolution in high energy DIS

Abstract

This paper presents the first numerical solution to the non-linear evolution equation for diffractive dissociation processes in deep inelastic scattering. It is shown that the solution depends on one scaling variable $\ddot{I}„=Q^2/Q_s^{D2}(x,x_0)$, where $Q_s^D(x,x_0)$ is the saturation scale for the diffraction processes. The dependence of the saturation scale $Q_s^D(x,x_0)$ on both $x$ and $x_0$ is investigated, ($Y_0=\ln (1/x_0)$ is a minimal rapidity gap for the diffraction process). The $x$ - dependence of $Q_s^D$ turns out to be the same as of the saturation scale in the total inclusive DIS cross section. In our calculations $Q_s^D(x,x_0)$ reveals only mild dependence on $x_0$. The scaling is shown to hold for $x\ll x_0$ but is violated at $x\sim x_0$.

13 pages, 9 figures