Evolution of the transverse-momentum dependent gluon distribution at small $x$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910925370425344 |
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| author | Caucal, Paul Iancu, Edmond |
| author_facet | Caucal, Paul Iancu, Edmond |
| contents | Using the colour dipole picture for photon-nucleus interactions at small $x$ together with the Color Glass Condensate (CGC) effective theory, we demonstrate that the next-to-leading (NLO) order corrections to the cross-section for the inclusive production of a pair of hard jets encode not only the JIMWLK evolution with decreasing $x$, but also the DGLAP evolution of the gluon distribution function and the CSS evolution of the gluon transverse momentum dependent (TMD) distribution. The emergent CSS equation takes the form of a rate equation describing the evolution of the dijet distribution in the transverse momentum imbalance $K_\perp$ when increasing the dijet relative momentum $P_\perp$. All three types of evolution become important when both $P_\perp$ and $K_\perp$ are much larger than the nuclear saturation momentum $Q_s(x)$ and we propose a framework which encompasses all of them. The solution to the JIMWLK equation provides the source term for the DGLAP evolution with increasing $K_\perp$, which in turn generates the initial condition for the CSS evolution with increasing $P_\perp$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04238 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Evolution of the transverse-momentum dependent gluon distribution at small $x$ Caucal, Paul Iancu, Edmond High Energy Physics - Phenomenology Nuclear Theory Using the colour dipole picture for photon-nucleus interactions at small $x$ together with the Color Glass Condensate (CGC) effective theory, we demonstrate that the next-to-leading (NLO) order corrections to the cross-section for the inclusive production of a pair of hard jets encode not only the JIMWLK evolution with decreasing $x$, but also the DGLAP evolution of the gluon distribution function and the CSS evolution of the gluon transverse momentum dependent (TMD) distribution. The emergent CSS equation takes the form of a rate equation describing the evolution of the dijet distribution in the transverse momentum imbalance $K_\perp$ when increasing the dijet relative momentum $P_\perp$. All three types of evolution become important when both $P_\perp$ and $K_\perp$ are much larger than the nuclear saturation momentum $Q_s(x)$ and we propose a framework which encompasses all of them. The solution to the JIMWLK equation provides the source term for the DGLAP evolution with increasing $K_\perp$, which in turn generates the initial condition for the CSS evolution with increasing $P_\perp$. |
| title | Evolution of the transverse-momentum dependent gluon distribution at small $x$ |
| topic | High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2406.04238 |