On running coupling in the JIMWLK evolution and its Langevin formulation

• Published in: The journal of high energy physics Vol. 2024; no. 3; pp. 131 - 28
• Main Authors: Altinoluk, Tolga, Beuf, Guillaume, Lublinsky, Michael, Skokov, Vladimir V.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 21.03.2024; Springer Nature B.V; SpringerOpen
• Subjects: Accuracy; Classical and Quantum Gravitation; Coupling; Deep Inelastic Scattering or Small-x Physics; Dipoles; Effective Field Theories of QCD; Elementary Particles; Evolution; Phenomenology; Physics; Physics and Astronomy; Prescriptions; Projectiles; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Resummation; String Theory; Effective Field Theories of QCD; Resummation; Deep Inelastic Scattering or Small-x Physics
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP03(2024)131

A bstract Various conventional running coupling prescriptions reproducing β 0 -dependent terms of NLO JIMWLK are reviewed and found to be theoretically inconsistent: the JIMWLK evolution Hamiltonian with running coupling violates the requirement of positive semidefiniteness. This requirement appears to be tightly related to the possibility of having a Langevin formulation for the evolution. We also review the scheme that attributes a part of β 0 -dependent terms to the DGLAP evolution of the projectile. The remaining β 0 -dependent contributions sum up into so-called “daughter dipole” prescription, which leads to a manifestly positive semidefinite Hamiltonian.