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Analysis of the fragmentation function of gluon at next-to-leading order approximation

H. S. Nakhaei* and G. R. Boroun†

  • *Contact author: SaghaeNakhaei.Hossein@razi.ac.ir
  • †Contact author: boroun@razi.ac.ir
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Phys. Rev. D 112, 054039 – Published 23 September, 2025

DOI: https://doi.org/10.1103/x9vl-d6pm

Abstract

We are investigating the behavior of the fragmentation function of a gluon, denoted as Dg(x,μ2), where μ represents the observable scale. This function is derived from the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi 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 and higher-order approximations for the fragmentation function of a gluon, [g→TnQ], by integrating the evolved fragmentation function of the gluon at the initial scale. In our computations, we utilize the initial scales for Tg2c from Braaten and Yuan [Phys. Rev. Lett. 71, 1673 (1993)] and for Tg4c and Tg4b from Celiberto et al. [Eur. Phys. J. C 84, 1071 (2024)] and Celiberto and Gatto [Phys. Rev. D 111, 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.

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Outline

Information

Phys. Rev. D 112, 054039– Published 23 September, 2025
  • Received 31 May 2025
  • Accepted 2 September 2025
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