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  • Letter
  • Open Access

Shedding light on the intrinsic transversal momentum distributions of pions and kaons

Jian Chai1,2 and Shan Cheng1,3,4,*

  • 1School of Physics and Electronics, Hunan University, 410082 Changsha, China
  • 2Institute of Theoretical Physics, School of Sciences, Henan University of Technology, Zhengzhou, Henan 450001, China
  • 3School for Theoretical Physics, Hunan University, 410082, Changsha, China
  • 4Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications, 410082 Changsha, China

  • *Contact author: scheng@hnu.edu.cn
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Phys. Rev. D 111, L071902 – Published 8 April, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.L071902

Abstract

We propose to introduce the intrinsic transversal momentum distribution functions (iTMDs), in conjunction with the light-cone distribution amplitudes, to elucidate the probability amplitude of encountering a meson state wherein the partons swiftly traverse along the longitudinal axis while gently oscillating in the transversal plane. The primary motivation stems from the oversight of soft transverse dynamics within the kT factorization formalism of an exclusive QCD process, which confines perturbative QCD (pQCD) predictions to scenarios involving large-momentum transfers. We meticulously investigate the π and K electromagnetic form factors using the iTMD-improved pQCD calculation at next-to-leading order. By analyzing data in the timelike physical regions, we obtain the transversal size parameters βπ2=0.51±0.04  GeV−2 and βK2=0.30±0.05  GeV2. We then extract the chiral mass of pions to be m0π(1  GeV)=1.84±0.07  GeV and explain the precise measurements of kaon form factors in the perturbative timelike region. As a remarkable byproduct, we found that the incorporation of iTMDs improves the pQCD predictions for electromagnetic form factors, extending the applicable range to a few GeV2. This improvement allows for direct comparison with existing measurements and lattice QCD evaluations.

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References (37)

  1. A. H. Mueller, Phys. Rep. 73, 237 (1981).
  2. S. J. Brodsky and G. P. Lepage, in Perturbative Quantum Chromodynamics, edited by A. H. Mueller (World Scientific, Singapore, 1989).
  3. A. V. Efremov and A. V. Radyushkin, Phys. Lett. 94B, 245 (1980).
  4. G. P. Lepage and S. J. Brodsky, Phys. Rev. D 22, 2157 (1980).
  5. S. Cheng, Phys. Rev. D 100, 013007 (2019).
  6. V. M. Braun, G. P. Korchemsky, and D. Müller, Prog. Part. Nucl. Phys. 51, 311 (2003).
  7. V. M. Braun and I. E. Filyanov, Z. Phys. C 48, 239 (1990).
  8. P. Ball, V. M. Braun, and A. Lenz, J. High Energy Phys. 05 (2006) 004.
  9. J. Chai, S. Cheng, and J. Hua, Eur. Phys. J. C 83, 556 (2023).
  10. H. Leutwyler, Phys. Lett. B 378, 313 (1996).
  11. S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
  12. H. n. Li, Y. L. Shen, Y. M. Wang, and H. Zou, Phys. Rev. D 83, 054029 (2011).
  13. S. Cheng, Y. Y. Fan, and Z. J. Xiao, Phys. Rev. D 89, 054015 (2014).
  14. S. Cheng, A. Khodjamirian, and A. V. Rusov, Phys. Rev. D 102, 074022 (2020).
  15. G. P. Lepage, S. J. Brodsky, T. Huang, and P. B. Mackenzie, in Particles and Fields 2: Proceedings of the Banff Summer Institute, edited by A. Z. Capri and A. N. Kamal (Plenum Press, New York, 1983), p. 83.
  16. R. Jakob and P. Kroll, Phys. Lett. B 315, 463 (1993); 319, 545(E) (1993).
  17. P. Kroll, Eur. Phys. J. C 71, 1623 (2011).
  18. V. M. Braun, A. Khodjamirian, and M. Maul, Phys. Rev. D 61, 073004 (2000).
  19. J. Bijnens and A. Khodjamirian, Eur. Phys. J. C 26, 67 (2002).
  20. L. Chang, I. C. Cloët, C. D. Roberts, S. M. Schmidt, and P. C. Tandy, Phys. Rev. Lett. 111, 141802 (2013).
  21. C. D. Roberts, D. G. Richards, T. Horn, and L. Chang, Prog. Part. Nucl. Phys. 120, 103883 (2021).
  22. G. Wang, J. Liang, T. Draper, K.-F. Liu, and Y.-B. Yang (χQCD Collaboration), Phys. Rev. D 104, 074502 (2021).
  23. H. T. Ding, X. Gao, A. D. Hanlon, S. Mukherjee, P. Petreczky, Q. Shi, S. Syritsyn, R. Zhang, and Y. Zhao, Phys. Rev. Lett. 133, 181902 (2024).
  24. L. B. Chen, W. Chen, F. Feng, and Y. Jia, Phys. Rev. Lett. 132, 201901 (2024).
  25. Y. Ji, B. X. Shi, J. Wang, Y. F. Wang, Y. M. Wang, and H. X. Yu, arXiv:2411.03658.
  26. J. P. Lees et al. (BABAR Collaboration), Phys. Rev. D 86, 032013 (2012).
  27. M. Fujikawa et al. (Belle Collaboration), Phys. Rev. D 78, 072006 (2008).
  28. M. Ablikim et al. (BESIII Collaboration), Phys. Lett. B 753, 629 (2016); 812, 135982(E) (2021).
  29. S. R. Amendolia et al. (NA7 Collaboration), Nucl. Phys. B277, 168 (1986).
  30. T. Horn et al. (Jefferson Lab F(pi)-2 Collaboration), Phys. Rev. Lett. 97, 192001 (2006).
  31. G. M. Huber et al. (Jefferson Lab Collaboration), Phys. Rev. C 78, 045203 (2008).
  32. H. n. Li and S. Mishima, Phys. Rev. D 80, 074024 (2009).
  33. J. P. Lees et al. (BABAR Collaboration), Phys. Rev. D 88, 032013 (2013).
  34. J. P. Lees et al. (BABAR Collaboration), Phys. Rev. D 92, 072008 (2015).
  35. M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 99, 032001 (2019).
  36. Z. Q. Yao, D. Binosi, and C. D. Roberts, Phys. Lett. B 855, 138823 (2024).
  37. L. B. Chen, W. Chen, F. Feng, and Y. Jia, arXiv:2407.21120.

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Phys. Rev. D 111, L071902– Published 8 April, 2025
  • Received 24 December 2024
  • Accepted 12 March 2025
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