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arXiv · 2310.10738

On running coupling in the JIMWLK evolution and its Langevin formulation

Tolga Altinoluk·Guillaume Beuf·Michael Lublinsky·Vladimir V. Skokov
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Abstract

Various conventional running coupling prescriptions reproducing $\beta_ 0$-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 $\beta_0$-dependent terms to the DGLAP evolution of the projectile. The remaining $\beta_0$-dependent contributions sum up into so-called the ``daughter dipole'' prescription, which leads to a manifestly positive semidefinite Hamiltonian.

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Tolga Altinoluk, Guillaume Beuf, Michael Lublinsky, Vladimir V. Skokov. 2023-10-16. On running coupling in the JIMWLK evolution and its Langevin formulation. https://arxiv.org/abs/2310.10738

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