Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.15243 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908889340968960 |
|---|---|
| author | Cougoulic, Florian Korcyl, Piotr Stebel, Tomasz |
| author_facet | Cougoulic, Florian Korcyl, Piotr Stebel, Tomasz |
| contents | We systematically derive expressions for ten small-$x$ Transverse Momentum Dependent (TMD) distributions in the Gaussian approximation, three in the quark-gluon sector and seven in the gluon-gluon sector; for the general $SU(N_c)$ gauge group. The derived formulae depend on the logarithm of the dipole amplitude. Using the McLerran-Venugopalan model for the initial condition, we simulate the dipole amplitude as well as estimate all ten TMD distributions for $N_c \in \{2,3,4,5\}$. We compare these explicit numerical results with the derived expressions and find very good agreement for all studied values of $N_c$. Consequently, we study the scaling with $N_c$ of the TMD distributions. Thanks to that, we are able to derive the large-$N_c$ limit of the Gaussian approximation results and show that they agree with expressions obtained in the mean-field approximation. By comparing with our numerical results, we are able to demonstrate the size, origin, and significance of subleading-$N_c$ corrections. This work sets the stage for a systematic study of subleading corrections induced by the JIMWLK evolution in the rapidity evolution of the TMD distributions. Interestingly, we find an exact sum rule that relates all seven gluon-gluon TMD operators at $N_c = 3$ and arbitrary $x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15243 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Small-x TMD distributions initial condition: Nc-dependence and Gaussian approximations Cougoulic, Florian Korcyl, Piotr Stebel, Tomasz High Energy Physics - Phenomenology Nuclear Theory We systematically derive expressions for ten small-$x$ Transverse Momentum Dependent (TMD) distributions in the Gaussian approximation, three in the quark-gluon sector and seven in the gluon-gluon sector; for the general $SU(N_c)$ gauge group. The derived formulae depend on the logarithm of the dipole amplitude. Using the McLerran-Venugopalan model for the initial condition, we simulate the dipole amplitude as well as estimate all ten TMD distributions for $N_c \in \{2,3,4,5\}$. We compare these explicit numerical results with the derived expressions and find very good agreement for all studied values of $N_c$. Consequently, we study the scaling with $N_c$ of the TMD distributions. Thanks to that, we are able to derive the large-$N_c$ limit of the Gaussian approximation results and show that they agree with expressions obtained in the mean-field approximation. By comparing with our numerical results, we are able to demonstrate the size, origin, and significance of subleading-$N_c$ corrections. This work sets the stage for a systematic study of subleading corrections induced by the JIMWLK evolution in the rapidity evolution of the TMD distributions. Interestingly, we find an exact sum rule that relates all seven gluon-gluon TMD operators at $N_c = 3$ and arbitrary $x$. |
| title | Small-x TMD distributions initial condition: Nc-dependence and Gaussian approximations |
| topic | High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2603.15243 |