Small-$x$ Asymptotics of the Leading-Twist Flavor Singlet Quark TMDs
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| Format: | Preprint |
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2024
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| 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 |
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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 |