Boundary conditions in the QCD nucleus-nucleus scattering problem

TL;DR

This paper investigates boundary conditions in QCD nucleus-nucleus scattering within an effective field theory framework, revealing that more accurate, non-local boundary conditions significantly alter classical field solutions and their symmetry properties.

Contribution

It introduces non-local, exponential boundary conditions for interacting BFKL pomerons in nucleus-nucleus scattering, showing their impact on classical solutions and symmetry breaking.

Findings

Correct boundary conditions lead to different classical solutions.

Symmetry breaking occurs at lower rapidities than previously thought.

The minimal action value saturates around rapidity 10.

Abstract

In the framework of the effective field theory for interacting BFKL pomerons, applied to nucleus-nucleus scattering, boundary conditions for the classical field equations are discussed. Correspondence with the QCD diagrams at the boundary rapidities requires pomeron interaction with the participating nuclei to be exponential and non-local. Commonly used 'eikonal' boundary conditions, local and linear in fields, follow in the limit of small QCD pomeron-nucleon coupling. Numerical solution of the classical field equations, which sum all tree diagrams for central gold-gold scattering, demonstrates that corrected boundary conditions lead to substantially different results, as compared to the eikonal conditions studied in earlier publications. A breakdown of projectile-target symmetry for particular solutions discovered earlier in \cite{bom} is found to occur at roughly twice lower rapidity. Most important, due to a high non-linearity of the problem, the found asymmetric solutions are not unique but form a family growing in number with rapidity. The minimal value for the action turns out to be much lower than with the eikonal boundary conditions and saturates at rapidities around 10.