Investigating the 4-point truncation of the JIMWLK evolution equation

Alam, Mohammad

Investigating the 4-point truncation of the JIMWLK evolution equation

Thesis / Dissertation

2025

Publisher

University of Cape Town

Department

Department of Physics

Faculty

Faculty of Science

Abstract

The Colour Glass Condensate (CGC) is a dense gluonic state that dominates in-state hadrons in deep inelastic scattering (DIS). The JIMWLK equation describes the rapidity evolution of Wilson line correlators in the CGC framework, which are crucial for computing cross-sections in DIS. However, JIMWLK generates an infinite hierarchy of coupled integro-differential equations (the Balitsky hierarchy), for which no analytical or numerical solutions exist. To address this, R. Moerman and H. Weigert introduced a parameterisation scheme that reparameterises the rapidity dependence of Wilson line correlators into n-point colour structure functions while preserving JIMWLK symmetry, gauge invari-ance, and finiteness for Nc. Since this involves an infinite sum, truncation at some order p is necessary. While 2- and 3-point truncations have been studied extensively, this thesis extends the framework to 4-point truncations to capture the physics of 4-point Wilson line correlators. We first refine the parameteri-sation scheme, identifying an additional term required at the 4-point level. We then construct a suitable basis for adjoint singlet states, which may help isolate iterated 2-point contributions, and leverage Hermitian Young Projection Operators and transition operators—key tools in the 4-point truncation studied by J. Alcock-Zeilinger and H. Weigert. Applying the 4-point truncation to Wilson line correlators, we aimed to derive an update equation for the 4-point colour structure functions, facilitating numerical implementation. Although significant progress has been made, the unresolved complexities suggest the need for new techniques and frameworks. This thesis provides an outlook on potential approaches to overcoming these challenges and advancing our understanding of high-energy QCD.

Keywords

Colour Glass Condensate

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