Gluon splitting at small $x$: a unified derivation for the JIMWLK, DGLAP and CSS equations
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| Format: | Preprint |
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2025
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| _version_ | 1866915542499065856 |
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| author | Caucal, Paul Iancu, Edmond Salazar, Farid Yuan, Feng |
| author_facet | Caucal, Paul Iancu, Edmond Salazar, Farid Yuan, Feng |
| contents | We revisit the calculation of the next-to-leading order (NLO) corrections to dijet production in electron-ion collisions at small $x$. We focus on the back-to-back configuration where the relative transverse momentum $P_\perp$ of the measured jets is much larger than both their momentum imbalance $K_\perp$ and the target saturation momentum $Q_s(x,A)$. In this regime, we present for the first time a complete calculation of the real NLO corrections at leading power in $1/P_\perp$. Our result exhibits TMD factorisation, with the same hard factor as at tree-level and a NLO correction to the Weiszäcker-Williams (WW) gluon transverse momentum dependent (TMD) distribution which involves four Wilson-line operators. By studying different kinematical regimes for $K_\perp$ and for the radiated gluon, we recover all the quantum evolutions that were previously identified for this process at NLO: the B-JIMWLK high-energy evolution and the CSS evolution of the gluon WW TMD, and the DGLAP evolution of the gluon PDF. When both $K_\perp$ and the transverse momentum transferred by the target are large compared to $Q_s$, all the Wilson-line operators boil down to the unintegrated gluon distribution and our NLO result for the gluon TMD can be used to isolate the transverse-momentum dependent gluon splitting function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_08454 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gluon splitting at small $x$: a unified derivation for the JIMWLK, DGLAP and CSS equations Caucal, Paul Iancu, Edmond Salazar, Farid Yuan, Feng High Energy Physics - Phenomenology Nuclear Theory We revisit the calculation of the next-to-leading order (NLO) corrections to dijet production in electron-ion collisions at small $x$. We focus on the back-to-back configuration where the relative transverse momentum $P_\perp$ of the measured jets is much larger than both their momentum imbalance $K_\perp$ and the target saturation momentum $Q_s(x,A)$. In this regime, we present for the first time a complete calculation of the real NLO corrections at leading power in $1/P_\perp$. Our result exhibits TMD factorisation, with the same hard factor as at tree-level and a NLO correction to the Weiszäcker-Williams (WW) gluon transverse momentum dependent (TMD) distribution which involves four Wilson-line operators. By studying different kinematical regimes for $K_\perp$ and for the radiated gluon, we recover all the quantum evolutions that were previously identified for this process at NLO: the B-JIMWLK high-energy evolution and the CSS evolution of the gluon WW TMD, and the DGLAP evolution of the gluon PDF. When both $K_\perp$ and the transverse momentum transferred by the target are large compared to $Q_s$, all the Wilson-line operators boil down to the unintegrated gluon distribution and our NLO result for the gluon TMD can be used to isolate the transverse-momentum dependent gluon splitting function. |
| title | Gluon splitting at small $x$: a unified derivation for the JIMWLK, DGLAP and CSS equations |
| topic | High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2510.08454 |