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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.28747 |
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| _version_ | 1866913168424435712 |
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| author | Wang, Lei |
| author_facet | Wang, Lei |
| contents | We calculate the Sudakov-limited maximum phase-space density associated with the linearly polarized gluon TMD coefficient $h_1^{\perp g}$ in the saturation region. Using Mueller's occupancy argument together with the small-$x$ Weizsäcker-Williams (WW) and dipole gluon distributions of Metz and Zhou, we find $n_{h,{\rm DP}}^{\rm max}=2n_g^{\rm max}\sim2α_s^{-3/2}$ for the dipole distribution in the same phase-space normalization. This dipole result is a process-dependent TMD proxy, not a literal gluon number density. For the WW distribution, the deep-saturation tensor coefficient lacks the logarithmic enhancement needed for the Mueller saddle, so the maximum is pushed toward the saturation boundary. We also perform a numerical Collins-Soper evolution study and find that the $J_2$ Bessel weight in the tensor TMD definition reduces the resolved peak, giving $c_h^{\rm num}\simeq6.6$--$7.1$ for representative EIC scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28747 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximum phase-space density of linearly polarized gluon TMDs in the saturation region Wang, Lei High Energy Physics - Phenomenology We calculate the Sudakov-limited maximum phase-space density associated with the linearly polarized gluon TMD coefficient $h_1^{\perp g}$ in the saturation region. Using Mueller's occupancy argument together with the small-$x$ Weizsäcker-Williams (WW) and dipole gluon distributions of Metz and Zhou, we find $n_{h,{\rm DP}}^{\rm max}=2n_g^{\rm max}\sim2α_s^{-3/2}$ for the dipole distribution in the same phase-space normalization. This dipole result is a process-dependent TMD proxy, not a literal gluon number density. For the WW distribution, the deep-saturation tensor coefficient lacks the logarithmic enhancement needed for the Mueller saddle, so the maximum is pushed toward the saturation boundary. We also perform a numerical Collins-Soper evolution study and find that the $J_2$ Bessel weight in the tensor TMD definition reduces the resolved peak, giving $c_h^{\rm num}\simeq6.6$--$7.1$ for representative EIC scales. |
| title | Maximum phase-space density of linearly polarized gluon TMDs in the saturation region |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2605.28747 |