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  • Access by Xinjiang University

Analysis on the parton distribution functions of heavy mesons

Satyajit Puhan*

  • *Contact author: puhansatyajit@gmail.com

Phys. Rev. D 114, 034056 – Published 26 August, 2026

DOI: https://doi.org/10.1103/6gjf-24ll

Abstract

In this work, we investigate the constituent parton distribution functions (PDFs) of the kaon and heavy pseudoscalar mesons within the light-cone quark model. Starting from the initial-scale quark and antiquark PDFs, obtained by evaluating the quark-quark correlation functions for individual mesons, we perform QCD evolution to determine their partonic structure at higher energy scales. The QCD evolution is carried out using the next-to-leading-order (NLO) Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations. We further compute the average longitudinal momentum fractions carried by the individual constituents at both the model and evolved scales. In addition, we predict the NLO structure functions of the kaon at energy scales relevant to the upcoming Electron-Ion Collider (EIC). For the COMPASS++/AMBER experiment, we also present detailed predictions for the NLO Drell-Yan cross sections induced by both K+ and K beams, using carbon, tungsten, and aluminum as nuclear targets. Finally, we demonstrate the dominance of the heavier constituents over the lighter constituents in heavy mesons in terms of the momentum fractions they carry.

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References (112)

  1. S. J. Brodsky, H.-C. Pauli, and S. S. Pinsky, Phys. Rep. 301, 299 (1998).
  2. H. Mineo, W. Bentz, N. Ishii, A. W. Thomas, and K. Yazaki, Nucl. Phys. A735, 482 (2004).
  3. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961).
  4. S. P. Klevansky, Rev. Mod. Phys. 64, 649 (1992).
  5. F. Schlumpf, Phys. Rev. D 50, 6895 (1994).
  6. S. J. Brodsky and G. F. de Teramond, Phys. Rev. Lett. 96, 201601 (2006).
  7. C. D. Roberts and S. M. Schmidt, Prog. Part. Nucl. Phys. 45, S1 (2000).
  8. X. Ji, G. A. Miller, and C. Yang, Research 9, 1369 (2026).
  9. S. Meissner, A. Metz, and M. Schlegel, J. High Energy Phys. 08 (2009) 056.
  10. K. Goeke, A. Metz, and M. Schlegel, Phys. Lett. B 618, 90 (2005).
  11. S. Puhan, S. Sharma, N. Kumar, and H. Dahiya, Prog. Theor. Exp. Phys. 2025, 083B02 (2025).
  12. M. Diehl, Phys. Rep. 388, 41 (2003).
  13. J. M. M. Chavez, V. Bertone, F. De Soto Borrero, M. Defurne, C. Mezrag, H. Moutarde, J. Rodríguez-Quintero, and J. Segovia, Phys. Rev. D 105, 094012 (2022).
  14. J.-L. Zhang and J.-L. Ping, Eur. Phys. J. C 81, 814 (2021).
  15. W. Broniowski, V. Shastry, and E. Ruiz Arriola, Phys. Lett. B 840, 137872 (2023).
  16. M. Guidal, M. V. Polyakov, A. V. Radyushkin, and M. Vanderhaeghen, Phys. Rev. D 72, 054013 (2005).
  17. S. Puhan, S. Sharma, N. Kumar, and H. Dahiya, arXiv:2604.11116.
  18. M. Diehl, Eur. Phys. J. A 52, 149 (2016).
  19. R. Angeles-Martinez et al., Acta Phys. Pol. B 46, 2501 (2015).
  20. B. Pasquini, S. Cazzaniga, and S. Boffi, Phys. Rev. D 78, 034025 (2008).
  21. S. Puhan, S. Sharma, N. Kaur, N. Kumar, and H. Dahiya, J. High Energy Phys. 02 (2024) 075.
  22. S. Puhan and H. Dahiya, Phys. Rev. D 109, 034005 (2024).
  23. S. Puhan, S. Sharma, N. Kumar, and H. Dahiya, Phys. Rev. D 113, 036030 (2026).
  24. J. C. Collins and D. E. Soper, Nucl. Phys. B194, 445 (1982).
  25. A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thorne, Eur. Phys. J. C 4, 463 (1998).
  26. M. Gluck, E. Reya, and A. Vogt, Z. Phys. C 67, 433 (1995).
  27. S. Puhan and H. Dahiya, Phys. Rev. D 111, 114039 (2025).
  28. J. Arrington, C. D. Roberts, and J. M. Zanotti, J. Phys. G 34, S23 (2007).
  29. P. C. e. a. Barry, Phys. Rev. Lett. 121, 152001 (2018).
  30. E. D. Bloom et al., Phys. Rev. Lett. 23, 930 (1969).
  31. G. Altarelli and G. Parisi, Nucl. Phys. B126, 298 (1977).
  32. F. D. Aaron et al. (H1 Collaboration), Eur. Phys. J. C 68, 381 (2010).
  33. S. Chekanov et al. (ZEUS Collaboration), Nucl. Phys. B637, 3 (2002).
  34. M. Bonesini et al. (WA70 Collaboration), Z. Phys. C 37, 535 (1988).
  35. W.-C. Chang, J.-C. Peng, S. Platchkov, and T. Sawada, Phys. Rev. D 107, 056008 (2023).
  36. S. D. Drell and T.-M. Yan, Phys. Rev. Lett. 25, 316 (1970); 25, 902(E) (1970).
  37. C. Lorcé, A. Metz, B. Pasquini, and P. Schweitzer, Encycl. Part. Phys. 2, 167 (2026).
  38. G. Aad et al. (ATLAS Collaboration), J. High Energy Phys. 07 (2021) 223.
  39. Hari Govind P, Satyajit Puhan, Abhishek K. P, Reetanshu Pandey, Harleen Dahiya, Arvind Kumar, and Suneel Dutt, Phys. Rev. D 114, 016010 (2026).
  40. J. Lan, C. Mondal, S. Jia, X. Zhao, and J. P. Vary, Phys. Rev. D 101, 034024 (2020).
  41. T. Gutsche, V. E. Lyubovitskij, I. Schmidt, and A. Vega, J. Phys. G 42, 095005 (2015).
  42. C. Shi, L. Lu, and W. Jia, arXiv:2602.24187.
  43. J. S. Conway et al. (E615 Collaboration), Phys. Rev. D 39, 92 (1989).
  44. C. Bourrely, W.-C. Chang, and J.-C. Peng, Phys. Rev. D 105, 076018 (2022).
  45. P. C. Barry, C.-R. Ji, N. Sato, and W. Melnitchouk (Jefferson Lab Angular Momentum (JAM) Collaboration), Phys. Rev. Lett. 127, 232001 (2021).
  46. W.-C. Chang, J.-C. Peng, S. Platchkov, and T. Sawada, Phys. Rev. D 102, 054024 (2020).
  47. I. Novikov et al., Phys. Rev. D 102, 014040 (2020).
  48. M. Gluck, E. Reya, and I. Schienbein, Eur. Phys. J. C 10, 313 (1999).
  49. J. Miller, J. Torsiello, I. Anderson, K. Cichy, M. Constantinou, J. Delmar, and S. Lampreich, Phys. Rev. D 113, 114506 (2026).
  50. C. Alexandrou et al. (Extended Twisted Mass Collaboration), Phys. Rev. Lett. 134, 131902 (2025).
  51. Y. Choi, A. J. Arifi, H.-M. Choi, and C.-R. Ji, arXiv:2512.21642.
  52. G. F. de Teramond and S. J. Brodsky, Phys. Rev. Lett. 102, 081601 (2009).
  53. M. Ding, K. Raya, D. Binosi, L. Chang, C. D. Roberts, and S. M. Schmidt, Phys. Rev. D 101, 054014 (2020).
  54. S.-i. Nam, Phys. Rev. D 86, 074005 (2012).
  55. P. C. Barry, C.-R. Ji, W. Melnitchouk, N. Sato, and F. Steffens (JAM Collaboration), arXiv:2510.11979.
  56. W.-C. Chang, J.-C. Peng, S. Platchkov, and T. Sawada, Phys. Lett. B 855, 138820 (2024).
  57. C. Bourrely, F. Buccella, W.-C. Chang, and J.-C. Peng, Phys. Lett. B 848, 138395 (2024).
  58. J. Badier et al. (Saclay-CERN-College de France-Ecole Poly-Orsay Collaboration), Phys. Lett. B 93, 354 (1980).
  59. M. J. Corden et al., Phys. Lett. 96B, 411 (1980).
  60. B. Adams et al., arXiv:1808.00848.
  61. Z. Lu, Z. Yu, T. Lin, Y.-T. Liang, R. Wang, W. Chang, and W. Xiong, Phys. Rev. D 113, 114002 (2026).
  62. A. C. Aguilar et al., Eur. Phys. J. A 55, 190 (2019).
  63. Q. Wu, Z.-F. Cui, and J. Segovia, Phys. Rev. D 111, 116023 (2025).
  64. L. Albino, I. M. Higuera-Angulo, K. Raya, and A. Bashir, Phys. Rev. D 106, 034003 (2022).
  65. J. Lan, C. Mondal, M. Li, Y. Li, S. Tang, X. Zhao, and J. P. Vary, Phys. Rev. D 102, 014020 (2020).
  66. S. Tang, Y. Li, P. Maris, and J. P. Vary, Eur. Phys. J. C 80, 522 (2020).
  67. C. Shi, P. Liu, Y.-L. Du, and W. Jia, Phys. Rev. D 110, 094010 (2024).
  68. S. Puhan and H. Dahiya, Proc. Sci. HQL2023 (2024) 089 [arXiv:2408.07717].
  69. C. Shi, J. Li, M. Li, X. Chen, and W. Jia, Phys. Rev. D 106, 014026 (2022).
  70. A. Karlberg, P. Nason, G. Salam, G. Zanderighi, and F. Dreyer, Eur. Phys. J. C 86, 157 (2026).
  71. A. Buckley, J. Ferrando, S. Lloyd, K. Nordström, B. Page, M. Rüfenacht, M. Schönherr, and G. Watt, Eur. Phys. J. C 75, 132 (2015).
  72. M. B. Hecht, C. D. Roberts, and S. M. Schmidt, Phys. Rev. C 63, 025213 (2001).
  73. G. P. Lepage and S. J. Brodsky, Phys. Rev. D 22, 2157 (1980).
  74. X.-d. Ji, J.-P. Ma, and F. Yuan, Eur. Phys. J. C 33, 75 (2004).
  75. S. J. Brodsky, M. Diehl, and D. S. Hwang, Nucl. Phys. B596, 99 (2001).
  76. S. J. Brodsky, Tech. Rep., SLAC National Accelerator Laboratory (2000), invited talk, https://inspirehep.net/literature/538476.
  77. B. Pasquini, S. Rodini, and S. Venturini (MAP (Multi-dimensional Analyses of Partonic distributions) Collaboration), Phys. Rev. D 107, 114023 (2023).
  78. X. Luan and Z. Lu, Phys. Rev. D 110, 074022 (2024).
  79. W. Qian and B.-Q. Ma, Phys. Rev. D 78, 074002 (2008).
  80. Tanisha, S. Puhan, A. Yadav, and H. Dahiya, Phys. Rev. D 112, 054035 (2025).
  81. S. Puhan, N. Kaur, and H. Dahiya, Phys. Rev. D 111, 014008 (2025).
  82. R. Acharyya, S. Puhan, and H. Dahiya, Phys. Rev. D 110, 034020 (2024).
  83. G. P. Lepage and S. J. Brodsky, Phys. Rev. D 22, 2157 (1980).
  84. S. J. Brodsky, Y. Frishman, G. P. Lepage, and C. T. Sachrajda, Phys. Lett. 91B, 239 (1980).
  85. B.-W. Xiao, X. Qian, and B.-Q. Ma, Eur. Phys. J. A 15, 523 (2002).
  86. S. Puhan, N. Kaur, A. Kumar, S. Dutt, and H. Dahiya, Nucl. Phys. B1017, 116940 (2025).
  87. A. J. Arifi, H.-M. Choi, C.-R. ji, and Y. Oh, Phys. Rev. D 106, 014009 (2022).
  88. H. M. Choi and C.-R. Ji, Nucl. Phys. A618, 291 (1997).
  89. A. Dwibedi, S. Puhan, S. Ghosh, and H. Dahiya, Prog. Theor. Exp. Phys. 2026, 063B04 (2026).
  90. A. Harindranath, in International School on Light-Front Quantization and Non-Perturbative QCD (To be followed by the Workshop 3-14 Jun 1996) (1996), https://inspirehep.net/literature/426903.
  91. T. Maji and D. Chakrabarti, Phys. Rev. D 94, 094020 (2016).
  92. A. Bacchetta, F. G. Celiberto, M. Radici, and P. Taels, Eur. Phys. J. C 80, 733 (2020).
  93. C. Shi, M. Li, X. Chen, and W. Jia, Phys. Rev. D 104, 094016 (2021).
  94. R. Acharyya, S. Puhan, H. Dahiya, and N. Kumar, Chin. Phys. C 49, 023104 (2025).
  95. Y. Li, P. Maris, X. Zhao, and J. P. Vary, Phys. Lett. B 758, 118 (2016).
  96. Y. Li, P. Maris, and J. P. Vary, Phys. Rev. D 96, 016022 (2017).
  97. S. Tang, Y. Li, P. Maris, and J. P. Vary, Phys. Rev. D 98, 114038 (2018).
  98. B. Almeida-Zamora, L. Albino, A. Bashir, J. J. Cobos-Martínez, and J. Segovia, arXiv:2602.10775.
  99. G. P. Salam and J. Rojo, Comput. Phys. Commun. 180, 120 (2009).
  100. V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972).
  101. L. N. Lipatov, Sov. J. Nucl. Phys. 20, 94 (1975).
  102. Y. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977).
  103. C. Chen, L. Chang, C. D. Roberts, S. Wan, and H.-S. Zong, Phys. Rev. D 93, 074021 (2016).
  104. A. Watanabe, T. Sawada, and C. W. Kao, Nucl. Part. Phys. Proc. 300–302, 121 (2018).
  105. C. Alexandrou, S. Bacchio, I. Cloët, M. Constantinou, K. Hadjiyiannakou, G. Koutsou, and C. Lauer (ETM Collaboration), Phys. Rev. D 104, 054504 (2021).
  106. T. Horn and K. e. a. Park, Tech. Rep. C12-15-006A, Jefferson Lab (2015), (accessed: 2021-09-16), URL https://www.jlab.org/exp_prog/proposals/17/C12-15-006A.pdf.
  107. K. Kovarik et al., Phys. Rev. D 93, 085037 (2016).
  108. C. Anastasiou, L. J. Dixon, K. Melnikov, and F. Petriello, Phys. Rev. Lett. 91, 182002 (2003).
  109. J. Lan, J. Chen, Z. Zhu, C. Mondal, X. Zhao, and J. P. Vary (BLFQ Collaboration), Phys. Lett. B 868, 139654 (2025).
  110. X. Chen, Proc. Sci. DIS2018 (2018) 170 [arXiv:1809.00448].
  111. E. C. Aschenauer et al., arXiv:1409.1633.
  112. J. L. Abelleira Fernandez et al. (LHeC Study Group), J. Phys. G 39, 075001 (2012).

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