Pion Valence-Quark TMD from Continuum Schwinger Function Methods and Gaussian GTMD
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915634573475840 |
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| author | Ding, Minghui |
| author_facet | Ding, Minghui |
| contents | We employ the continuum Schwinger function method to investigate the unpolarized valence-quark transverse-momentum-dependent parton distribution function (TMD) of the pion at the hadron scale. The first seventeen generalized Mellin-transverse moments, constructed from lightlike and transverse vectors, are computed and found to be well described by a factorized ansatz, in which the longitudinal component coincides with the distribution function (DF) and the transverse momentum follows a Gaussian form. The Gaussianity relation between the mean and mean-squared transverse momenta is satisfied with approximately $99\%$ accuracy in our numerical results, with the mean-squared transverse momentum equal to $0.231\,\text{GeV}^2$. Using the extracted TMD, we test the hypothesis that the quark's transverse spatial distribution also follows a Gaussian form and find that the resulting electromagnetic form factor is in good agreement with existing data. These results indicate that the intrinsic transverse-momentum and transverse-spatial distributions of valence quarks in the pion can be accurately approximated by a Gaussian ansatz, supporting its use in phenomenological analyses and experimental fits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18349 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pion Valence-Quark TMD from Continuum Schwinger Function Methods and Gaussian GTMD Ding, Minghui High Energy Physics - Phenomenology Nuclear Theory We employ the continuum Schwinger function method to investigate the unpolarized valence-quark transverse-momentum-dependent parton distribution function (TMD) of the pion at the hadron scale. The first seventeen generalized Mellin-transverse moments, constructed from lightlike and transverse vectors, are computed and found to be well described by a factorized ansatz, in which the longitudinal component coincides with the distribution function (DF) and the transverse momentum follows a Gaussian form. The Gaussianity relation between the mean and mean-squared transverse momenta is satisfied with approximately $99\%$ accuracy in our numerical results, with the mean-squared transverse momentum equal to $0.231\,\text{GeV}^2$. Using the extracted TMD, we test the hypothesis that the quark's transverse spatial distribution also follows a Gaussian form and find that the resulting electromagnetic form factor is in good agreement with existing data. These results indicate that the intrinsic transverse-momentum and transverse-spatial distributions of valence quarks in the pion can be accurately approximated by a Gaussian ansatz, supporting its use in phenomenological analyses and experimental fits. |
| title | Pion Valence-Quark TMD from Continuum Schwinger Function Methods and Gaussian GTMD |
| topic | High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2511.18349 |