On running coupling in the JIMWLK evolution and its Langevin formulation

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

doi:10.1007/JHEP03(2024)131

On running coupling in the JIMWLK evolution and its Langevin formulation

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

Department of Physics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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 language	English
Article number	131
Journal	Journal of High Energy Physics
Volume	2024
Issue number	3
DOIs	https://doi.org/10.1007/JHEP03(2024)131
State	Published - 1 Mar 2024

Keywords

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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10.1007/JHEP03(2024)131

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title = "On running coupling in the JIMWLK evolution and its Langevin formulation",

abstract = "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.",

keywords = "Deep Inelastic Scattering or Small-x Physics, Effective Field Theories of QCD, Resummation",

author = "Tolga Altinoluk and Guillaume Beuf and Michael Lublinsky and Skokov, {Vladimir V.}",

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AU - Altinoluk, Tolga

AU - Beuf, Guillaume

AU - Lublinsky, Michael

AU - Skokov, Vladimir V.

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/3/1

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N2 - 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.

AB - 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.

KW - Deep Inelastic Scattering or Small-x Physics

KW - Effective Field Theories of QCD

KW - Resummation

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ER -

On running coupling in the JIMWLK evolution and its Langevin formulation

Abstract

Keywords

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