Small-$x$ evolution of dipole amplitude in momentum space: forward--off-forward correspondence
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912399747973120 |
|---|---|
| author | Agrawal, Sanskriti Abir, Raktim |
| author_facet | Agrawal, Sanskriti Abir, Raktim |
| contents | We have shown that the small-$x$ evolution of the off-forward leading-log dipole scattering amplitudes, both pomeron and odderon, in the momentum space can be completely determined by the evolution of the respective forward amplitudes, with rescaled momenta. In position space, if there is translation symmetry (assumption of a large nucleus), the dipole cross section depends on the positions of quarks and anti-quarks only through their separation. The present study is an equivalent proposition in the momentum space -- where translation symmetry in momentum bifurcates the amplitudes into two translationally symmetric functions along the ${\bf k}$ line in the ${\bf k}-{\bf Δ}$ plane. It also shows that high energy evolutions of dipole GTMDs can be achieved only by studying the evolution of dipole TMDs at small-$x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12497 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Small-$x$ evolution of dipole amplitude in momentum space: forward--off-forward correspondence Agrawal, Sanskriti Abir, Raktim High Energy Physics - Phenomenology High Energy Physics - Lattice Nuclear Theory We have shown that the small-$x$ evolution of the off-forward leading-log dipole scattering amplitudes, both pomeron and odderon, in the momentum space can be completely determined by the evolution of the respective forward amplitudes, with rescaled momenta. In position space, if there is translation symmetry (assumption of a large nucleus), the dipole cross section depends on the positions of quarks and anti-quarks only through their separation. The present study is an equivalent proposition in the momentum space -- where translation symmetry in momentum bifurcates the amplitudes into two translationally symmetric functions along the ${\bf k}$ line in the ${\bf k}-{\bf Δ}$ plane. It also shows that high energy evolutions of dipole GTMDs can be achieved only by studying the evolution of dipole TMDs at small-$x$. |
| title | Small-$x$ evolution of dipole amplitude in momentum space: forward--off-forward correspondence |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice Nuclear Theory |
| url | https://arxiv.org/abs/2411.12497 |