On running coupling in the JIMWLK evolution and its Langevin formulation

2023/10/16 by Altinoluk, Tolga, Beuf, Guillaume, Lublinsky, Michael +1
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph)

paper · doi:10.48550/arxiv.2310.10738

Abstract

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 β₀-dependent terms to the DGLAP evolution of the projectile. The remaining β₀-dependent contributions sum up into so-called the ``daughter dipole'' prescription, which leads to a manifestly positive semidefinite Hamiltonian.

Related

• Not all that is β₀ is β-function: the DGLAP resummation and the running coupling in NLO JIMWLK
• Progress in implementing the kinematical constraint into the small-x JIMWLK evolution equation
• Reconciling the kinematical constraint with the JIMWLK evolution equation: correlation functions non-local in rapidity
• The CSS Hamiltonian: high energy evolution of rapidity dependent observables
• Calculation of the running coupling in non-Abelian gauge theories from Jarzynski's equality