On running coupling in the JIMWLK evolution and its Langevin formulation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911799000956928 |
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| author | Altinoluk, Tolga Beuf, Guillaume Lublinsky, Michael Skokov, Vladimir V. |
| author_facet | Altinoluk, Tolga Beuf, Guillaume Lublinsky, Michael Skokov, Vladimir V. |
| contents | 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 the ``daughter dipole'' prescription, which leads to a manifestly positive semidefinite Hamiltonian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10738 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On running coupling in the JIMWLK evolution and its Langevin formulation Altinoluk, Tolga Beuf, Guillaume Lublinsky, Michael Skokov, Vladimir V. High Energy Physics - Phenomenology 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 the ``daughter dipole'' prescription, which leads to a manifestly positive semidefinite Hamiltonian. |
| title | On running coupling in the JIMWLK evolution and its Langevin formulation |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2310.10738 |