An analysis of the fragmentation function of gluon at next-to-leading order approximation
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| Format: | Preprint |
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2025
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| _version_ | 1866916966468419584 |
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| author | Nakhaei, H. S. Boroun, G. R. |
| author_facet | Nakhaei, H. S. Boroun, G. R. |
| contents | We are investigating the behavior of the fragmentation function of a gluon, denoted as $ D_{g}(x,μ^2)$, where $μ$ represents the observable scale. This function is derived from the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. Our objective is to evolve the fragmentation function of a gluon for heavy-quark-antiquark bound states with large transverse momentum using a Laplace transform technique. This method enables us to calculate numerical solutions for two and four quarkonium states based on the known initial fragmentation function of gluons. We examine both leading-order (LO) and higher-order approximations for the fragmentation function of a gluon, $[g{\rightarrow}T_{nQ}]$, by integrating the evolved fragmentation function of the gluon at the initial scale. In our computations, we utilize the initial scales for $T^{2c}_{g}$ from Braaten-Yuan [E.Braaten and T.C.Yuan, Phys. Rev. Lett. {\bf71}, 1673 (1993)] and for $T^{4c}_{g}$ and $T^{4b}_{g}$ from Celiberto-Gatto-papa [ F. G. Celiberto, G. Gatto and A. Papa, Eur. Phys. J. C {\bf84}, 1071 (2024)] and Celiberto-Gatto [ F. G. Celiberto and G. Gatto, Phys. Rev. D {\bf111}, 034037 (2025)] respectively. Through comparing our predictions with existing literature results, we can accurately determine the evolution of the fragmentation function of a gluon at scale $μ$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_05256 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An analysis of the fragmentation function of gluon at next-to-leading order approximation Nakhaei, H. S. Boroun, G. R. High Energy Physics - Phenomenology We are investigating the behavior of the fragmentation function of a gluon, denoted as $ D_{g}(x,μ^2)$, where $μ$ represents the observable scale. This function is derived from the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. Our objective is to evolve the fragmentation function of a gluon for heavy-quark-antiquark bound states with large transverse momentum using a Laplace transform technique. This method enables us to calculate numerical solutions for two and four quarkonium states based on the known initial fragmentation function of gluons. We examine both leading-order (LO) and higher-order approximations for the fragmentation function of a gluon, $[g{\rightarrow}T_{nQ}]$, by integrating the evolved fragmentation function of the gluon at the initial scale. In our computations, we utilize the initial scales for $T^{2c}_{g}$ from Braaten-Yuan [E.Braaten and T.C.Yuan, Phys. Rev. Lett. {\bf71}, 1673 (1993)] and for $T^{4c}_{g}$ and $T^{4b}_{g}$ from Celiberto-Gatto-papa [ F. G. Celiberto, G. Gatto and A. Papa, Eur. Phys. J. C {\bf84}, 1071 (2024)] and Celiberto-Gatto [ F. G. Celiberto and G. Gatto, Phys. Rev. D {\bf111}, 034037 (2025)] respectively. Through comparing our predictions with existing literature results, we can accurately determine the evolution of the fragmentation function of a gluon at scale $μ$. |
| title | An analysis of the fragmentation function of gluon at next-to-leading order approximation |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2508.05256 |