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Valence quark distribution of light ρ and heavy J/ψ vector mesons in a light-cone quark model

Tanisha*, Satyajit Puhan†, Anurag Yadav‡, and Harleen Dahiya§

  • *Contact author: tanisha220902@gmail.com
  • †Contact author: puhansatyajit@gmail.com
  • ‡Contact author: anuragyadav1431905@gmail.com
  • §Contact author: dahiyah@nitj.ac.in
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Phys. Rev. D 112, 054035 – Published 22 September, 2025

DOI: https://doi.org/10.1103/cmbw-vcds

Abstract

In this work, we have investigated the valence quark structure through chiral-even vector quark generalized parton distributions (GPDs) of light ρ and heavy J/ψ vector mesons using the light-cone quark model. By solving the quark-quark correlator, we have represented the quark GPDs in the light-front wave function (LFWFs) form. The charge, magnetic, and quadrupole form factors of these particles have been derived from the vector quark GPDs and compared with available theoretical predictions and lattice simulation data. The structure functions corresponding to the Rosenbluth scattering cross section of these mesons have also been calculated and compared with available NJL model predictions. All the results of our calculations are found to follow a similar trend to other model results. We have also calculated the parton distribution functions (PDFs) of these particles in the forward limit of GPDs. The calculated PDFs have also been evolved to 5  GeV2 through next to next to leading order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolutions.

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References (101)

  1. M. K. Volkov and A. E. Radzhabov, The Nambu-Jona-Lasinio model and its development, Phys. Usp. 49, 551 (2006).
  2. B. A. Arbuzov, M. K. Volkov, and I. V. Zaitsev, NJL model derived from QCD, Int. J. Mod. Phys. A 21, 5721 (2006).
  3. Y. Ninomiya, W. Bentz, and I. C. Cloët, Dressed quark mass dependence of pion and kaon form factors, Phys. Rev. C 91, 025202 (2015).
  4. V. M. Belyaev and M. B. Johnson, Pion light cone wave functions and light front quark model, Phys. Lett. B 423, 379 (1998).
  5. H.-M. Choi, H.-Y. Ryu, and C.-R. Ji, Spacelike and timelike form factors for the (π0,η,η′)→γ*γ transitions in the light-front quark model, Phys. Rev. D 96, 056008 (2017).
  6. A. Yadav, S. Puhan, and H. Dahiya, Radiative transitions for the ground and excited charmonia states, arXiv:2504.14864.
  7. S. J. Brodsky, G. F. de Teramond, H. G. Dosch, and J. Erlich, Light-front holographic QCD and emerging confinement, Phys. Rep. 584, 1 (2015).
  8. G. F. de Teramond and S. J. Brodsky, Light-front holography: A first approximation to QCD, Phys. Rev. Lett. 102, 081601 (2009).
  9. A. Bacchetta, F. Conti, and M. Radici, Transverse-momentum distributions in a diquark spectator model, Phys. Rev. D 78, 074010 (2008).
  10. A. Bacchetta, F. G. Celiberto, M. Radici, and P. Taels, Transverse-momentum-dependent gluon distribution functions in a spectator model, Eur. Phys. J. C 80, 733 (2020).
  11. A. Bacchetta, F. G. Celiberto, and M. Radici, T-odd gluon distribution functions in a spectator model, Eur. Phys. J. C 84, 576 (2024).
  12. C. Lorcé, B. Pasquini, and P. Schweitzer, Transverse pion structure beyond leading twist in constituent models, Eur. Phys. J. C 76, 415 (2016).
  13. N. Strodthoff, B.-J. Schaefer, and L. von Smekal, Quark-meson-diquark model for two-color QCD, Phys. Rev. D 85, 074007 (2012).
  14. T. Maji and D. Chakrabarti, Light front quark-diquark model for the nucleons, Phys. Rev. D 94, 094020 (2016).
  15. A. I. Signal and F. G. Cao, Transverse momentum and transverse momentum distributions in the MIT bag model, Phys. Lett. B 826, 136898 (2022).
  16. K. Johnson, The M. I. T. bag model, Acta Phys. Pol. B 6, 865 (1975), https://inspirehep.net/literature/2861.
  17. J.-L. Zhang, Kaon GTMDs in the Dyson-Schwinger equations using contact interaction, arXiv:2409.04105.
  18. J.-L. Zhang, Z.-F. Cui, J. Ping, and C. D. Roberts, Contact interaction analysis of pion GTMDs, Eur. Phys. J. C 81, 6 (2021).
  19. H.-W. Lin et al., Parton distributions and lattice QCD calculations: A community white paper, Prog. Part. Nucl. Phys. 100, 107 (2018).
  20. M. J. Savage, Nuclear physics from lattice QCD, Prog. Part. Nucl. Phys. 67, 140 (2012).
  21. L. Y. Glozman, C. B. Lang, and M. Limmer, Angular momentum content of the rho-meson in lattice QCD, Phys. Rev. Lett. 103, 121601 (2009).
  22. S. Puhan, S. Sharma, N. Kumar, and H. Dahiya, Understanding the valence quark structure of the pion through GTMDs, arXiv:2504.14982.
  23. M. G. Echevarria, A. Idilbi, K. Kanazawa, C. Lorcé, A. Metz, B. Pasquini, and M. Schlegel, Proper definition and evolution of generalized transverse momentum dependent distributions, Phys. Lett. B 759, 336 (2016).
  24. S. Meissner, A. Metz, and M. Schlegel, Generalized parton correlation functions for a spin-1/2 hadron, J. High Energy Phys. 08 (2009) 056.
  25. S. Meissner, A. Metz, M. Schlegel, and K. Goeke, Generalized parton correlation functions for a spin-0 hadron, J. High Energy Phys. 08 (2008) 038.
  26. M. Diehl, Generalized parton distributions, Phys. Rep. 388, 41 (2003).
  27. J. M. M. Chavez, V. Bertone, F. De Soto Borrero, M. Defurne, C. Mezrag, H. Moutarde, J. Rodríguez-Quintero, and J. Segovia, Pion generalized parton distributions: A path toward phenomenology, Phys. Rev. D 105, 094012 (2022).
  28. W. Broniowski, V. Shastry, and E. Ruiz Arriola, Off-shell generalized parton distributions and form factors of the pion, Phys. Lett. B 840, 137872 (2023).
  29. M. Guidal, M. V. Polyakov, A. V. Radyushkin, and M. Vanderhaeghen, Nucleon form-factors from generalized parton distributions, Phys. Rev. D 72, 054013 (2005).
  30. M. Diehl, Introduction to GPDs and TMDs, Eur. Phys. J. A 52, 149 (2016).
  31. R. Angeles-Martinez et al., Transverse momentum dependent (TMD) parton distribution functions: status and prospects, Acta Phys. Pol. B 46, 2501 (2015).
  32. B. Pasquini, S. Cazzaniga, and S. Boffi, Transverse momentum dependent parton distributions in a light-cone quark model, Phys. Rev. D 78, 034025 (2008).
  33. S. Puhan and H. Dahiya, Leading twist T-even TMDs for the spin-1 heavy vector mesons, Phys. Rev. D 109, 034005 (2024).
  34. J. C. Collins and D. E. Soper, Parton distribution and decay functions, Nucl. Phys. B194, 445 (1982).
  35. A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thorne, Parton distributions: A new global analysis, Eur. Phys. J. C 4, 463 (1998).
  36. M. Gluck, E. Reya, and A. Vogt, Dynamical parton distributions of the proton and small x physics, Z. Phys. C 67, 433 (1995).
  37. A. Freese and I. C. Cloët, Quark spin and orbital angular momentum from proton generalized parton distributions, Phys. Rev. C 103, 045204 (2021).
  38. M. Guidal, H. Moutarde, and M. Vanderhaeghen, Generalized parton distributions in the valence region from deeply virtual Compton scattering, Rep. Prog. Phys. 76, 066202 (2013).
  39. X.-D. Ji, Deeply virtual Compton scattering, Phys. Rev. D 55, 7114 (1997).
  40. G. Xie, W. Kou, Q. Fu, Z. Ye, and X. Chen, Deeply virtual Compton scattering at future electron-ion colliders, Eur. Phys. J. C 83, 900 (2023).
  41. L. Favart, M. Guidal, T. Horn, and P. Kroll, Deeply virtual meson production on the nucleon, Eur. Phys. J. A 52, 158 (2016).
  42. S. Alekhin, Parton distributions from deep inelastic scattering data, Phys. Rev. D 68, 014002 (2003).
  43. S. Puhan, S. Sharma, N. Kaur, N. Kumar, and H. Dahiya, T-even TMDs for the spin-0 pseudo-scalar mesons upto twist-4 using light-front formalism, J. High Energy Phys. 02 (2024) 075.
  44. W. Qian and B.-Q. Ma, Vector meson omega-phi mixing and their form factors in light-cone quark model, Phys. Rev. D 78, 074002 (2008).
  45. S. J. Brodsky, M. Diehl, and D. S. Hwang, Light cone wave function representation of deeply virtual Compton scattering, Nucl. Phys. B596, 99 (2001).
  46. W. Cosyn and B. Pire, Transversity generalized parton distributions for the deuteron, Phys. Rev. D 98, 074020 (2018).
  47. W. Cosyn, A. Freese, and B. Pire, Polynomiality sum rules for generalized parton distributions of spin-1 targets, Phys. Rev. D 99, 094035 (2019).
  48. F. Cano and B. Pire, Deep electroproduction of photons and mesons on the deuteron, Eur. Phys. J. A 19, 423 (2004).
  49. J.-L. Zhang, G.-Z. Kang, and J.-L. Ping, ρ meson generalized parton distributions in the Nambu–Jona-Lasinio model, Phys. Rev. D 105, 094015 (2022).
  50. B.-D. Sun and Y.-B. Dong, Polarized generalized parton distributions and structure functions of the ρ meson, Phys. Rev. D 99, 016023 (2019).
  51. R. M. Davidson and E. Ruiz Arriola, Structure functions of pseudoscalar mesons in the SU(3) NJL model, Phys. Lett. B 348, 163 (1995).
  52. N. Kumar, Transverse densities and generalized parton distributions of the ρ meson in the light front quark model, Phys. Rev. D 99, 014039 (2019).
  53. L. Adhikari, Y. Li, M. Li, and J. P. Vary, Form factors and generalized parton distributions of heavy quarkonia in basis light front quantization, Phys. Rev. C 99, 035208 (2019).
  54. C. Shi, J. Li, P.-L. Yin, and W. Jia, Unpolarized generalized parton distributions of light and heavy vector mesons, Phys. Rev. D 107, 074009 (2023).
  55. B.-D. Sun and Y.-B. Dong, ρ meson unpolarized generalized parton distributions with a light-front constituent quark model, Phys. Rev. D 96, 036019 (2017).
  56. S. Puhan, N. Kumar, and H. Dahiya, Spin-1 unpolarized GPDs in light front formalism. DAE Symp. Nucl. Phys. 68, 825 (2025).
  57. H.-M. Choi and C.-R. Ji, Electromagnetic structure of the rho meson in the light front quark model, Phys. Rev. D 70, 053015 (2004).
  58. R. Hofstadter, Nuclear and nucleon scattering of high-energy electrons, Annu. Rev. Nucl. Part. Sci. 7, 231 (1957).
  59. V. A. Karmanov, On ambiguities of the spin-1 electromagnetic form-factors in light front dynamics, Nucl. Phys. A608, 316 (1996).
  60. P. L. Chung, F. Coester, and W. N. Polyzou, Charge form-factors of quark model pions, Phys. Lett. B 205, 545 (1988).
  61. S. J. Brodsky and J. R. Hiller, Universal properties of the electromagnetic interactions of spin one systems, Phys. Rev. D 46, 2141 (1992).
  62. L. L. Frankfurt, M. Strikman, and T. Frederico, Deuteron form-factors in the light cone quantum mechanics “good” component approach, Phys. Rev. C 48, 2182 (1993).
  63. J. P. B. C. De Melo, Unambiguous extraction of the electromagnetic form factors for spin-1 particles on the light-front, Phys. Lett. B 788, 152 (2019).
  64. M. Allahverdiyeva and S. Mamedov, Vector meson gravitational form factors and generalized parton distributions at finite temperature within the soft-wall AdS/QCD model, Eur. Phys. J. C 83, 447 (2023).
  65. M. Gurtler et al. (QCDSF Collaboration), Vector meson electromagnetic form factors, Proc. Sci. LATTICE2008 (2008) 051.
  66. C. J. Shultz, J. J. Dudek, and R. G. Edwards, Excited meson radiative transitions from lattice QCD using variationally optimized operators, Phys. Rev. D 91, 114501 (2015).
  67. A. Bacchetta and P. J. Mulders, Deep inelastic leptoproduction of spin-one hadrons, Phys. Rev. D 62, 114004 (2000).
  68. G. P. Lepage and S. J. Brodsky, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev. D 22, 2157 (1980).
  69. H. M. Choi and C.-R. Ji, Light cone quark model predictions for radiative meson decays, Nucl. Phys. A618, 291 (1997).
  70. A. Airapetian et al. (HERMES Collaboration), Ratios of helicity amplitudes for exclusive ρ0 electroproduction on transversely polarized protons, Eur. Phys. J. C 77, 378 (2017).
  71. L. Mankiewicz, G. Piller, and T. Weigl, Hard exclusive meson production and nonforward parton distributions, Eur. Phys. J. C 5, 119 (1998).
  72. S. A. Morrow et al. (CLAS Collaboration), Exclusive rho0 electroproduction on the proton at CLAS, Eur. Phys. J. A 39, 5 (2009).
  73. I. V. Anikin, B. Pire, and O. V. Teryaev, On gamma gamma* production of two ρ0 mesons, Phys. Rev. D 69, 014018 (2004).
  74. D. Boer et al., Gluons and the quark sea at high energies: Distributions, polarization, tomography, arXiv:1108.1713.
  75. R. Abdul Khalek et al., Science requirements and detector concepts for the electron-ion collider: EIC yellow report, Nucl. Phys. A1026, 122447 (2022).
  76. S. J. Brodsky, H.-C. Pauli, and S. S. Pinsky, Quantum chromodynamics and other field theories on the light cone, Phys. Rep. 301, 299 (1998).
  77. B. Pasquini, S. Rodini, and S. Venturini (MAP (Multi-dimensional Analyses of Partonic distributions) Collaboration), Valence quark, sea, and gluon content of the pion from the parton distribution functions and the electromagnetic form factor, Phys. Rev. D 107, 114023 (2023).
  78. C. Shi, J. Li, M. Li, X. Chen, and W. Jia, Transverse momentum distributions of valence quarks in light and heavy vector mesons, Phys. Rev. D 106, 014026 (2022).
  79. B.-W. Xiao, X. Qian, and B.-Q. Ma, The kaon form-factor in the light cone quark model, Eur. Phys. J. A 15, 523 (2002).
  80. S. Kaur, C. Mondal, and H. Dahiya, Light-front holographic ρ-meson distributions in the momentum space, J. High Energy Phys. 01 (2021) 136.
  81. S. Kaur, N. Kumar, J. Lan, C. Mondal, and H. Dahiya, Tomography of light mesons in the light-cone quark model, Phys. Rev. D 102, 014021 (2020).
  82. E. R. Berger, F. Cano, M. Diehl, and B. Pire, Generalized parton distributions in the deuteron, Phys. Rev. Lett. 87, 142302 (2001).
  83. B. G. Lasscock, J. Hedditch, D. B. Leinweber, and A. G. Williams, Vector meson electromagnetic form factors, Proc. Sci. LAT2006 (2006) 114 [arXiv:hep-lat/0611029].
  84. J.-L. Zhang, ρ meson form factors and parton distribution functions in impact parameter space*, Chin. Phys. C 49, 043104 (2025).
  85. R. J. Hernández-Pinto, L. X. Gutiérrez-Guerrero, M. A. Bedolla, and A. Bashir, Electric, magnetic, and quadrupole form factors and charge radii of vector mesons: From light to heavy sectors in a contact interaction, Phys. Rev. D 110, 114015 (2024).
  86. M. S. Bhagwat and P. Maris, Vector meson form factors and their quark-mass dependence, Phys. Rev. C 77, 025203 (2008).
  87. J. J. Dudek, R. G. Edwards, and D. G. Richards, Radiative transitions in charmonium from lattice QCD, Phys. Rev. D 73, 074507 (2006).
  88. Y.-L. Luan, X.-L. Chen, and W.-Z. Deng, Meson electro-magnetic form factors in an extended Nambu–Jona-Lasinio model including heavy quark flavors, Chin. Phys. C 39, 113103 (2015).
  89. B. Owen, W. Kamleh, D. Leinweber, B. Menadue, and S. Mahbub, Light meson form factors at near physical masses, Phys. Rev. D 91, 074503 (2015).
  90. M. I. Haftel, L. Mathelitsch, and H. F. K. Zingl, Electron-deuteron tensor polarization and the two-nucleon force, Phys. Rev. C 22, 1285 (1980).
  91. S. Kumano and Q.-T. Song, Twist-2 relation and sum rule for tensor-polarized parton distribution functions of spin-1 hadrons, J. High Energy Phys. 09 (2021) 141.
  92. S. Hino and S. Kumano, Structure functions in the polarized Drell-Yan processes with spin 1/2 and spin 1 hadrons. 2. Parton model, Phys. Rev. D 60, 054018 (1999).
  93. W. Cosyn, Y.-B. Dong, S. Kumano, and M. Sargsian, Tensor-polarized structure function b1 in standard convolution description of deuteron, Phys. Rev. D 95, 074036 (2017).
  94. M. Miyama and S. Kumano, Numerical solution of Q2 evolution equations in a brute force method, Comput. Phys. Commun. 94, 185 (1996).
  95. M. Hirai, S. Kumano, and M. Miyama, Numerical solution of Q2 evolution equations for polarized structure functions, Comput. Phys. Commun. 108, 38 (1998).
  96. M. Hirai, S. Kumano, and M. Miyama, Numerical solution of Q2 evolution equation for the transversity distribution Delta(T)q, Comput. Phys. Commun. 111, 150 (1998).
  97. Y. Ninomiya, W. Bentz, and I. C. Cloët, Transverse-momentum-dependent quark distribution functions of spin-one targets: Formalism and covariant calculations, Phys. Rev. C 96, 045206 (2017).
  98. J.-L. Zhang and J. Wu, ρ meson transverse momentum-dependent parton distributions, Eur. Phys. J. C 85, 13 (2025).
  99. J. Lan, C. Mondal, M. Li, Y. Li, S. Tang, X. Zhao, and J. P. Vary, Parton distribution functions of heavy mesons on the light front, Phys. Rev. D 102, 014020 (2020).
  100. M. Li, Y. Li, G. Chen, T. Lappi, and J. P. Vary, Light-front wavefunctions of mesons by design, Eur. Phys. J. C 82, 1045 (2022).
  101. W.-Y. Liu and I. Zahed, Tomography of the rho meson in the QCD instanton vacuum: Transverse momentum dependent parton distribution functions, Phys. Rev. D 112, 034028 (2025).

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Phys. Rev. D 112, 054035– Published 22 September, 2025
  • Received 15 May 2025
  • Accepted 8 September 2025
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