2019/01/23 by Nestor Armesto, Néstor Armesto, Fabio Domínguez +5 · 61 citations
Physics and Astronomy · #Charge density #Color-glass condensate #Density matrix #Entropy (arrow of time) #High-Energy Particle Collisions Research #Master equation #Matrix (chemical analysis) #Probability density function #Pulsars and Gravitational Waves Research #Quantum Chromodynamics and Particle Interactions #Quantum entanglement #Random matrix #Time evolution #hep-ph
paper · pdf · doi:10.1007/jhep05(2019)025
published in Journal of High Energy Physics 2019(5) (Springer Nature) · 22 pages, 1 figure
arxiv created 2019/01/23 · openalex created_date 2019/02/21 · openalex publication_date 2019/05/01 · arxiv updated 2019/05/22 · openalex updated_date 2026/08/05
A bstract We introduce the notion of the Color Glass Condensate (CGC) density matrix \widehatρ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>ρ</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:math> . This generalizes the concept of probability density for the distribution of the color charges in the hadronic wave function and is consistent with understanding the CGC as an effective theory after integration of part of the hadronic degrees of freedom. We derive the evolution equations for the density matrix and show that the JIMWLK evolution equation arises here as the evolution of diagonal matrix elements of ρ in the color charge density basis. We analyze the behavior of this density matrix under high energy evolution and show that its purity decreases with energy. We show that the evolution equation for the density matrix has the celebrated Kossakowsky-Lindblad form describing the non-unitary evolution of the density matrix of an open system. Additionally, we consider the dilute limit and demonstrate that, at large rapidity, the entanglement entropy of the density matrix grows linearly with rapidity according to (d)/(dy)Se=γ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mi>d</mml:mi><mml:mi>dy</mml:mi></mml:mfrac><mml:msub><mml:mi>S</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>γ</mml:mi></mml:math> , where γ is the leading BFKL eigenvalue. We also discuss the evolution of \widehatρ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>ρ</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:math> in the saturated regime and relate it to the Levin-Tuchin law and find that the entropy again grows linearly with rapidity, but at a slower rate. By analyzing the dense and dilute regimes of the full density matrix we are able to establish a duality between the regimes. Finally we introduce the Wigner functional derived from this density matrix and discuss how it can be used to determine the distribution of color currents, which may be instrumental in understanding dynamical features of QCD at high energy.