Order-$v^4$ corrections to heavy quark fragmentation to S-wave heavy quarkonium

Sai Cui; Yi-Jie Li; Guang-Zhi Xu; Kui-Yong Liu

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arXiv · 2512.20539

Order-$v^4$ corrections to heavy quark fragmentation to S-wave heavy quarkonium

Sai Cui·Yi-Jie Li·Guang-Zhi Xu·Kui-Yong Liu

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Abstract

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.

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Sai Cui, Yi-Jie Li, Guang-Zhi Xu, Kui-Yong Liu. 2025-12-23. Order-$v^4$ corrections to heavy quark fragmentation to S-wave heavy quarkonium. https://arxiv.org/abs/2512.20539

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