Order-$v^4$ corrections to heavy quark fragmentation to S-wave heavy quarkonium
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917166846050304 |
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| author | Cui, Sai Li, Yi-Jie Xu, Guang-Zhi Liu, Kui-Yong |
| author_facet | Cui, Sai Li, Yi-Jie Xu, Guang-Zhi Liu, Kui-Yong |
| contents | Within the framework of nonrelativistic quantum chromodynamics (NRQCD) factorization, we compute the $\mathcal{O}(v^{4})$ relativistic corrections to the fragmentation of a heavy quark into the color-singlet $^{1}S_{0}^{[1]}$ and $^{3}S_{1}^{[1]}$ quarkonium states. Using the Collins--Soper definition of the fragmentation function, we reproduce the known $\mathcal{O}(v^{2})$ results. We find that the $\mathcal{O}(v^{4})$ correction gives a positive contribution relative to the leading order result over a wide range of the light-cone momentum fraction $z$, while its magnitude remains much smaller than that of the $\mathcal{O}(v^{2})$ correction. This behavior indicates a good convergence of the NRQCD relativistic expansion in this process. We further extend the calculation to the fragmentation functions in the unequal-mass case at $\mathcal{O}(v^{4})$ and obtain the corresponding analytical expressions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20539 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Order-$v^4$ corrections to heavy quark fragmentation to S-wave heavy quarkonium Cui, Sai Li, Yi-Jie Xu, Guang-Zhi Liu, Kui-Yong High Energy Physics - Phenomenology Within the framework of nonrelativistic quantum chromodynamics (NRQCD) factorization, we compute the $\mathcal{O}(v^{4})$ relativistic corrections to the fragmentation of a heavy quark into the color-singlet $^{1}S_{0}^{[1]}$ and $^{3}S_{1}^{[1]}$ quarkonium states. Using the Collins--Soper definition of the fragmentation function, we reproduce the known $\mathcal{O}(v^{2})$ results. We find that the $\mathcal{O}(v^{4})$ correction gives a positive contribution relative to the leading order result over a wide range of the light-cone momentum fraction $z$, while its magnitude remains much smaller than that of the $\mathcal{O}(v^{2})$ correction. This behavior indicates a good convergence of the NRQCD relativistic expansion in this process. We further extend the calculation to the fragmentation functions in the unequal-mass case at $\mathcal{O}(v^{4})$ and obtain the corresponding analytical expressions. |
| title | Order-$v^4$ corrections to heavy quark fragmentation to S-wave heavy quarkonium |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2512.20539 |