On running coupling in the JIMWLK evolution and its Langevin formulation

Tolga Altinoluk, Guillaume Beuf, Michael Lublinsky, Vladimir V. Skokov

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Various conventional running coupling prescriptions reproducing β0-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 “daughter dipole” prescription, which leads to a manifestly positive semidefinite Hamiltonian.

Original languageEnglish
Article number131
JournalJournal of High Energy Physics
Issue number3
StatePublished - 1 Mar 2024


  • Deep Inelastic Scattering or Small-x Physics
  • Effective Field Theories of QCD
  • Resummation

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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