Small-$x$ Asymptotics of the Leading-Twist Flavor Singlet Quark TMDs

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Santiago, M. Gabriel, Adamiak, Daniel, Tawabutr, Yossathorn
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915728648568832
author Santiago, M. Gabriel
Adamiak, Daniel
Tawabutr, Yossathorn
author_facet Santiago, M. Gabriel
Adamiak, Daniel
Tawabutr, Yossathorn
contents In this paper, we investigate the small-$x$ behavior of the flavor-singlet, leading-twist quark Transverse Momentum Dependent parton distribution functions (TMDs) using the Light-Cone Operator Treatment. This formalism allows us to express TMD operators at small $x$ in terms of polarized dipole amplitudes, enabling a systematic approach to their small-$x$ evolution. We derive the evolution equations for these TMDs and solve them within the large-$N_c$ approximation under the linearized, Double-Logarithmic Approximation (DLA), where $N_c$ represents the number of quark colors. Expanding on previous work on unpolarized and helicity TMDs, we present the small-$x$ asymptotics for a comprehensive set of TMDs, including the Sivers function, helicity worm-gear, transversity, pretzelosity, Boer-Mulders, and transversity worm-gear distributions. Our results provide a complete picture of the small-$x$ asymptotic behavior for all leading-twist flavor-singlet quark TMDs. We also discuss the implications of our findings for phenomenological applications and outline potential avenues for further research, particularly in understanding non-linear effects and extending beyond the DLA and large-$N_c$ approximations.
format Preprint
id arxiv_https___arxiv_org_abs_2412_14154
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Small-$x$ Asymptotics of the Leading-Twist Flavor Singlet Quark TMDs
Santiago, M. Gabriel
Adamiak, Daniel
Tawabutr, Yossathorn
High Energy Physics - Phenomenology
Nuclear Theory
In this paper, we investigate the small-$x$ behavior of the flavor-singlet, leading-twist quark Transverse Momentum Dependent parton distribution functions (TMDs) using the Light-Cone Operator Treatment. This formalism allows us to express TMD operators at small $x$ in terms of polarized dipole amplitudes, enabling a systematic approach to their small-$x$ evolution. We derive the evolution equations for these TMDs and solve them within the large-$N_c$ approximation under the linearized, Double-Logarithmic Approximation (DLA), where $N_c$ represents the number of quark colors. Expanding on previous work on unpolarized and helicity TMDs, we present the small-$x$ asymptotics for a comprehensive set of TMDs, including the Sivers function, helicity worm-gear, transversity, pretzelosity, Boer-Mulders, and transversity worm-gear distributions. Our results provide a complete picture of the small-$x$ asymptotic behavior for all leading-twist flavor-singlet quark TMDs. We also discuss the implications of our findings for phenomenological applications and outline potential avenues for further research, particularly in understanding non-linear effects and extending beyond the DLA and large-$N_c$ approximations.
title Small-$x$ Asymptotics of the Leading-Twist Flavor Singlet Quark TMDs
topic High Energy Physics - Phenomenology
Nuclear Theory
url https://arxiv.org/abs/2412.14154