A Linear Evolution for Non-Linear Dynamics and Correlations in Realistic Nuclei

TL;DR

Problem: high density QCD evolution in realistic nuclei requires accounting for target correlations beyond the BK framework. Approach: a linear generating functional equation is developed to sum fan diagrams, then extended to include nucleus correlations via a constant-parameter mapping to BK, and finally generalized to Glauber-Mueller multiple rescatterings using an effective dipole-splitting vertex. Key contributions: (i) a linear evolution for the generating functional, (ii) a correlation-generalized nonlinear BK-type equation with K_A and κ_A, (iii) a Glauber-Mueller–based nonlinear equation that sums semi-enhanced diagrams, and (iv) numerical demonstrations showing saturation at $N_A=1/K_A$ and sizable shadowing corrections. Significance: provides a systematic framework for incorporating target correlations in realistic nuclei and refines predictions for ion-ion and heavy-ion collisions, with implications for RHIC phenomenology.

Abstract

A new approach to high energy evolution based on a linear equation for QCD generating functional is developed. This approach opens a possibility for systematic study of correlations inside targets, and, in particular, inside realistic nuclei. Our results are presented as three new equations. The first one is a linear equation for QCD generating functional (and for scattering amplitude) that sums the 'fan' diagrams. For the amplitude this equation is equivalent to the non-linear Balitsky-Kovchegov equation. The second equation is a generalization of the Balitsky-Kovchegov non-linear equation to interactions with realistic nuclei. It includes a new correlation parameter which incorporates, in a model dependent way, correlations inside the nuclei. The third equation is a non - linear equation for QCD generating functional (and for scattering amplitude) that in addition to the 'fan' diagrams sums the Glauber-Mueller multiple rescatterings.

Figures (6)

• Figure 1: The equation for the probability to find $n$-dipoles in one fast dipole. The wave line shows a single dipole.
• Figure 2: The exchange of the single BFKL Pomeron for dipole-nucleus scattering.
• Figure 3: A single dipole and two dipole nucleus amplitudes.
• Figure 4: The solution of Eq. (\ref{['NLEQGFAA']}) as a function of $r$ for $b_t\,=\,0$.
• Figure 5: The 'fan' diagrams (Fig. \ref{['endi']}-1 and Fig. \ref{['endi']}-2) for dipole-nucleus interaction. First enhanced diagram (Fig. \ref{['endi']}-3). Fig. \ref{['endi']}-4 shows a model for the interaction of the BFKL Pomeron with nucleus target.