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.
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Altinoluk et al. (2024) studied this question.
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