The CSS Hamiltonian: high energy evolution of rapidity dependent observables
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910538891526144 |
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| author | Duan, Haowu Kovner, Alex Lublinsky, Michael |
| author_facet | Duan, Haowu Kovner, Alex Lublinsky, Michael |
| contents | We consider evolution of observables which depend on a small but fixed value of longitudinal momentum fraction $x$, to high rapidity, such that $η>\ln 1/x$. We show that this evolution is not given by the JIMWLK (or BK) equation. We derive the evolution Hamiltonian - $H_{CSS-JIMWLK}$ which generates this evolution in the cases of dilute and dense projectile wave function. The two limits yield identical results for $H_{CSS-JIMWLK}$. We show that the resulting evolution for the gluon TMD is identical to the (double logarithmic) perturbative Collins-Soper-Sterman evolution equation in the longitudinal resolution parameter at a fixed and very large transverse resolution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15960 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The CSS Hamiltonian: high energy evolution of rapidity dependent observables Duan, Haowu Kovner, Alex Lublinsky, Michael High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory We consider evolution of observables which depend on a small but fixed value of longitudinal momentum fraction $x$, to high rapidity, such that $η>\ln 1/x$. We show that this evolution is not given by the JIMWLK (or BK) equation. We derive the evolution Hamiltonian - $H_{CSS-JIMWLK}$ which generates this evolution in the cases of dilute and dense projectile wave function. The two limits yield identical results for $H_{CSS-JIMWLK}$. We show that the resulting evolution for the gluon TMD is identical to the (double logarithmic) perturbative Collins-Soper-Sterman evolution equation in the longitudinal resolution parameter at a fixed and very large transverse resolution. |
| title | The CSS Hamiltonian: high energy evolution of rapidity dependent observables |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2407.15960 |