The JIMWLK evolution and the s-channel unitarity

TL;DR

This paper explores the constraints of unitarity on the Hamiltonian of QCD Reggeon Field Theory, analyzing the JIMWLK evolution and revealing unitarity violations in dense target states.

Contribution

It explicitly formulates unitarity constraints on RFT Hamiltonians and examines their realization in the JIMWLK framework, highlighting unitarity issues in dense states.

Findings

JIMWLK Hamiltonian is unitary on dilute projectile states.

JIMWLK Hamiltonian violates unitarity on dense target states.

Unitarity constraints shape the form of RFT Hamiltonians.

Abstract

Further developing ideas set forth in \cite{KLL}, we discuss QCD Reggeon Field Theory (RFT) and formulate restrictions imposed on its Hamiltonian by the unitarity of underlying QCD. We identify explicitly the QCD RFT Hilbert space, provide algebra of the basic degrees of freedom (Wilson lines and their duals) and the algorithm for calculating the scattering amplitudes. We formulate conditions imposed on the "Fock states" of RFT by unitary nature of QCD, and explain how these constraints appear as unitarity constraints on possible RFT hamiltonians that generate energy evolution of scattering amplitudes. We study the realization of these constraints in the dense-dilute limit of RFT where the appropriate Hamiltonian is the JIMWLK Hamiltonian $H_{JIMWLK}$. We find that the action $H_{JIMWLK}$ on the dilute projectile states is unitary, but acting on dense "target" states it violates unitarity and generates states with negative probabilities through energy evolution.