- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Gravitational form factors of pion from top-down holographic QCD

Daisuke Fujii1,2,*, Akihiro Iwanaka2,†, and Mitsuru Tanaka3,‡

  • *Contact author: daisuke@rcnp.osaka-u.ac.jp
  • †Contact author: iwanaka@rcnp.osaka-u.ac.jp
  • ‡Contact author: tanaka@hken.phys.nagoya-u.ac.jp
PDF

Phys. Rev. D 110, L091501 – Published 8 November, 2024

DOI: https://doi.org/10.1103/PhysRevD.110.L091501

Abstract

The gravitational form factors (GFFs) of pions are calculated from a top-down holographic quantum chromodynamics (QCD) approach with momentum transfer dependence for the first time. It is important because the GFFs of hadrons have information on the internal stress distribution that may provide insight into the mechanism of how QCD forms hadrons. The forward limit value of this GFFs, i.e., the D-term, was also obtained. Furthermore, in this approach, we observe the so-called glueball dominance, in which pions have gravitational interactions via infinite glueball spectra.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (116)

  1. Maxim V. Polyakov and Peter Schweitzer, Forces inside hadrons: Pressure, surface tension, mechanical radius, and all that, Int. J. Mod. Phys. A 33, 1830025 (2018).
  2. V. D. Burkert, L. Elouadrhiri, F. X. Girod, C. Lorcé, P. Schweitzer, and P. E. Shanahan, Colloquium: Gravitational form factors of the proton, Rev. Mod. Phys. 95, 041002 (2023).
  3. M. Diehl, Generalized parton distributions, Phys. Rep. 388, 41 (2003).
  4. A. V. Belitsky and A. V. Radyushkin, Unraveling hadron structure with generalized parton distributions, Phys. Rep. 418, 1 (2005).
  5. Cédric Mezrag, An introductory lecture on generalised parton distributions, Few-Body Syst. 63, 62 (2022).
  6. V. D. Burkert, L. Elouadrhiri, and F. X. Girod, The pressure distribution inside the proton, Nature (London) 557, 396 (2018).
  7. B. Duran et al., Determining the gluonic gravitational form factors of the proton, Nature (London) 615, 813 (2023).
  8. S. Uehara et al. (Belle Collaboration), Measurement of γγ*→π0 transition form factor at Belle, Phys. Rev. D 86, 092007 (2012).
  9. M. Masuda et al. (Belle Collaboration), Study of π0 pair production in single-tag two-photon collisions, Phys. Rev. D 93, 032003 (2016).
  10. S. Kumano, Qin-Tao Song, and O. V. Teryaev, Hadron tomography by generalized distribution amplitudes in pion-pair production process γ*γ→π0π0 and gravitational form factors for pion, Phys. Rev. D 97, 014020 (2018).
  11. Ph. Hagler et al. (LHPC Collaboration), Nucleon generalized parton distributions from full lattice QCD, Phys. Rev. D 77, 094502 (2008).
  12. Gunnar Bali, Sara Collins, Meinulf Göckeler, Rudolf Rödl, Andreas Schäfer, and Andre Sternbeck, Nucleon generalized form factors from lattice QCD with nearly physical quark masses, Proc. Sci. LATTICE2015 (2016) 118 [arXiv:1601.04818].
  13. P. E. Shanahan and W. Detmold, Gluon gravitational form factors of the nucleon and the pion from lattice QCD, Phys. Rev. D 99, 014511 (2019).
  14. Constantia Alexandrou, Martha Constantinou, Kyriakos Hadjiyiannakou, Karl Jansen, Christos Kallidonis, Giannis Koutsou, and Alejandro Vaquero Avilés-Casco, Nucleon spin structure from lattice QCD, Proc. Sci. DIS2018 (2018) 148 [arXiv:1807.11214].
  15. C. Alexandrou et al., Moments of nucleon generalized parton distributions from lattice QCD simulations at physical pion mass, Phys. Rev. D 101, 034519 (2020).
  16. C. Alexandrou, S. Bacchio, M. Constantinou, J. Finkenrath, K. Hadjiyiannakou, K. Jansen, G. Koutsou, H. Panagopoulos, and G. Spanoudes, Complete flavor decomposition of the spin and momentum fraction of the proton using lattice QCD simulations at physical pion mass, Phys. Rev. D 101, 094513 (2020).
  17. Dimitra A. Pefkou, Daniel C. Hackett, and Phiala E. Shanahan, Gluon gravitational structure of hadrons of different spin, Phys. Rev. D 105, 054509 (2022).
  18. Daniel C. Hackett, Dimitra A. Pefkou, and Phiala E. Shanahan, Gravitational form factors of the proton from lattice QCD, Phys. Rev. Lett. 132, 251904 (2024).
  19. Hervé Dutrieux, Robert G. Edwards, Colin Egerer, Joseph Karpie, Christopher Monahan, Kostas Orginos, Anatoly Radyushkin, David Richards, Eloy Romero, and Savvas Zafeiropoulos (HadStruc Collaboration), Towards unpolarized GPDs from pseudo-distributions, J. High Energy Phys. 08 (2024) 162.
  20. D. Brommel, M. Diehl, M. Gockeler, Ph. Hagler, R. Horsley, D. Pleiter, Paul E. L. Rakow, A. Schafer, G. Schierholz, and J. M. Zanotti, Structure of the pion from full lattice QCD, Proc. Sci. LAT2005 (2006) 360 [arXiv:hep-lat/0509133].
  21. Dirk Brommel, Pion structure from the lattice, Ph.D. thesis, Regensburg University, 2007.
  22. Yi-Bo Yang, Ying Chen, Terrence Draper, Ming Gong, Keh-Fei Liu, Zhaofeng Liu, and Jian-Ping Ma, Meson mass decomposition from lattice QCD, Phys. Rev. D 91, 074516 (2015).
  23. Marius Löffler, Philipp Wein, Thomas Wurm, Simon Weishäupl, Daniel Jenkins, Rudolf Rödl, Andreas Schäfer, and Lisa Walter (RQCD Collaboration), Mellin moments of spin dependent and independent PDFs of the pion and rho meson, Phys. Rev. D 105, 014505 (2022).
  24. Daniel C. Hackett, Patrick R. Oare, Dimitra A. Pefkou, and Phiala E. Shanahan, Gravitational form factors of the pion from lattice QCD, Phys. Rev. D 108, 114504 (2023).
  25. Tadakatsu Sakai and Shigeki Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113, 843 (2005).
  26. Tadakatsu Sakai and Shigeki Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys. 114, 1083 (2005).
  27. Neil R. Constable and Robert C. Myers, Spin two glueballs, positive energy theorems and the AdS/CFT correspondence, J. High Energy Phys. 10 (1999) 037.
  28. Richard C. Brower, Samir D. Mathur, and Chung-I Tan, Glueball spectrum for QCD from AdS supergravity duality, Nucl. Phys. B587, 249 (2000).
  29. Hiroyuki Hata, Tadakatsu Sakai, Shigeki Sugimoto, and Shinichiro Yamato, Baryons from instantons in holographic QCD, Prog. Theor. Phys. 117, 1157 (2007).
  30. Koji Hashimoto, Takayuki Hirayama, and Deog Ki Hong, Quark mass dependence of hadron spectrum in holographic QCD, Phys. Rev. D 81, 045016 (2010).
  31. Koji Hashimoto, Norihiro Iizuka, Takaaki Ishii, and Daisuke Kadoh, Three-flavor quark mass dependence of baryon spectra in holographic QCD, Phys. Lett. B 691, 65 (2010).
  32. Toshiya Imoto, Tadakatsu Sakai, and Shigeki Sugimoto, Mesons as open strings in a holographic dual of QCD, Prog. Theor. Phys. 124, 263 (2010).
  33. Takaaki Ishii, Toward bound-state approach to strangeness in holographic QCD, Phys. Lett. B 695, 392 (2011).
  34. Yizhuang Liu and Ismail Zahed, Heavy baryons and their exotics from instantons in holographic QCD, Phys. Rev. D 95, 116012 (2017).
  35. Yizhuang Liu and Ismail Zahed, Heavy and strange holographic baryons, Phys. Rev. D 96, 056027 (2017).
  36. Koji Hashimoto, Yoshinori Matsuo, and Takeshi Morita, Nuclear states and spectra in holographic QCD, J. High Energy Phys. 12 (2019) 001.
  37. Yizhuang Liu, Maciej A. Nowak, and Ismail Zahed, Holographic tetraquarks and the newly observed Tcc+ at LHCb, Phys. Rev. D 105, 054021 (2022).
  38. Theodoros Nakas and Konstantinos S. Rigatos, Fermions and baryons as open-string states from brane junctions, J. High Energy Phys. 12 (2020) 157.
  39. Yasuhiro Hayashi, Takahiro Ogino, Tadakatsu Sakai, and Shigeki Sugimoto, Stringy excited baryons in holographic quantum chromodynamics, Prog. Theor. Exp. Phys. 2020, 053B04 (2020).
  40. Daisuke Fujii and Atsushi Hosaka, Heavy baryons in holographic QCD with higher dimensional degrees of freedom, Phys. Rev. D 101, 126008 (2020).
  41. Hideo Suganuma and Keiichiro Hori, Topological objects in holographic QCD, Phys. Scr. 95, 074014 (2020).
  42. Yizhuang Liu, Maciej A. Nowak, and Ismail Zahed, Holographic charm and bottom pentaquarks. I. Mass spectra with spin effects, Phys. Rev. D 104, 114021 (2021).
  43. Yizhuang Liu, Maciej A. Nowak, and Ismail Zahed, Hyperons and Θs+ in holographic QCD, Phys. Rev. D 105, 114021 (2022).
  44. Koji Hashimoto, Chung-I Tan, and Seiji Terashima, Glueball decay in holographic QCD, Phys. Rev. D 77, 086001 (2008).
  45. Koji Hashimoto, Tadakatsu Sakai, and Shigeki Sugimoto, Holographic baryons: Static properties and form factors from gauge/string duality, Prog. Theor. Phys. 120, 1093 (2008).
  46. Hiroyuki Hata, Masaki Murata, and Shinichiro Yamato, Chiral currents and static properties of nucleons in holographic QCD, Phys. Rev. D 78, 086006 (2008).
  47. Keun-Young Kim and Ismail Zahed, Electromagnetic baryon form factors from holographic QCD, J. High Energy Phys. 09 (2008) 007.
  48. Hovhannes R. Grigoryan, T. S. H. Lee, and Ho-Ung Yee, Electromagnetic nucleon-to-delta transition in holographic QCD, Phys. Rev. D 80, 055006 (2009).
  49. C. A. Ballon Bayona, Henrique Boschi-Filho, Nelson R. F. Braga, and Marcus A. C. Torres, Form factors of vector and axial-vector mesons in holographic D4-D8 model, J. High Energy Phys. 01 (2010) 052.
  50. C. A. Ballon Bayona, Henrique Boschi-Filho, Nelson R. F. Braga, and Marcus A. C. Torres, Scattering vector mesons in D4 / D8 model, Nucl. Phys. B, Proc. Suppl. 199, 119 (2010).
  51. C. A. Ballon Bayona, Henrique Boschi-Filho, Nelson R. F. Braga, and Marcus A. C. Torres, Deep inelastic scattering for vector mesons in holographic D4-D8 model, J. High Energy Phys. 10 (2010) 055.
  52. Aleksey Cherman and Takaaki Ishii, Long-distance properties of baryons in the Sakai-Sugimoto model, Phys. Rev. D 86, 045011 (2012).
  53. C. A. Ballon Bayona, Henrique Boschi-Filho, Nelson R. F. Braga, Matthias Ihl, and Marcus A. C. Torres, Generalized baryon form factors and proton structure functions in the Sakai-Sugimoto model, Nucl. Phys. B866, 124 (2013).
  54. Masayasu Harada and Mannque Rho, Integrating holographic vector dominance to hidden local symmetry for the nucleon form factor, Phys. Rev. D 83, 114040 (2011).
  55. Frederic Brünner, Denis Parganlija, and Anton Rebhan, Glueball decay rates in the Witten-Sakai-Sugimoto model, Phys. Rev. D 91, 106002 (2015); 93, 109903(E) (2016).
  56. Si-wen Li, Glueball–baryon interactions in holographic QCD, Phys. Lett. B 773, 142 (2017).
  57. Ori C. Druks, Pang H. C. Lau, and Ismail Zahed, Electromagnetic and axial current form factors and spectroscopy of three-flavor holographic baryons, Phys. Rev. D 99, 054022 (2019).
  58. Daisuke Fujii and Atsushi Hosaka, Decay properties of Roper resonance in the holographic QCD, Phys. Rev. D 104, 014022 (2021).
  59. Yizhuang Liu, Maciej A. Nowak, and Ismail Zahed, Holographic charm and bottom pentaquarks. II. Open and hidden decay widths, Phys. Rev. D 104, 114022 (2021).
  60. Yizhuang Liu, Kiminad A. Mamo, Maciej A. Nowak, and Ismail Zahed, Holographic charm and bottom pentaquarks. III. Excitations through photoproduction of heavy mesons, Phys. Rev. D 104, 114023 (2021).
  61. Akihiro Iwanaka, Daisuke Fujii, and Atsushi Hosaka, Decay properties of N(1535) in the holographic QCD, Phys. Rev. D 105, 114057 (2022).
  62. Daisuke Fujii, Akihiro Iwanaka, and Atsushi Hosaka, Electromagnetic transition amplitude for Roper resonance from holographic QCD, Phys. Rev. D 106, 014010 (2022).
  63. Daisuke Fujii, Dynamical properties of baryon resonances in the holographic QCD, Ph.D. thesis, Osaka University, 2023.
  64. Francesco Bigazzi and Federico Castellani, Resonance contributions to nucleon spin structure in holographic QCD, J. High Energy Phys. 04 (2024) 037.
  65. Florian Hechenberger, Josef Leutgeb, and Anton Rebhan, Radiative meson and glueball decays in the Witten-Sakai-Sugimoto model, Phys. Rev. D 107, 114020 (2023).
  66. G. Ramalho and M. T. Peña, Electromagnetic transition form factors of baryon resonances, Prog. Part. Nucl. Phys. 136, 104097 (2024).
  67. Federico Castellani, Nucleon electric and magnetic polarizabilities in Holographic QCD, Phys. Rev. D 110, 066001 (2024).
  68. Florian Hechenberger, Josef Leutgeb, and Anton Rebhan, Spin-1 glueballs in the Witten-Sakai-Sugimoto model, Phys. Rev. D 109, 074014 (2024).
  69. Mitsutoshi Fujita, Yoshitaka Hatta, Shigeki Sugimoto, and Takahiro Ueda, Nucleon D-term in holographic quantum chromodynamics, Prog. Theor. Exp. Phys. 2022, 093B06 (2022).
  70. Zainul Abidin and Carl E. Carlson, Gravitational form factors in the axial sector from an AdS/QCD model, Phys. Rev. D 77, 115021 (2008).
  71. Zainul Abidin and Carl E. Carlson, Gravitational form factors of vector mesons in an AdS/QCD model, Phys. Rev. D 77, 095007 (2008).
  72. Zainul Abidin and Carl E. Carlson, Nucleon electromagnetic and gravitational form factors from holography, Phys. Rev. D 79, 115003 (2009).
  73. Kiminad A. Mamo and Ismail Zahed, Diffractive photoproduction of J/ψ and ϒ using holographic QCD: Gravitational form factors and GPD of gluons in the proton, Phys. Rev. D 101, 086003 (2020).
  74. Dipankar Chakrabarti, Chandan Mondal, Asmita Mukherjee, Sreeraj Nair, and Xingbo Zhao, Gravitational form factors and mechanical properties of proton in a light-front quark-diquark model, Phys. Rev. D 102, 113011 (2020).
  75. Kiminad A. Mamo and Ismail Zahed, Nucleon mass radii and distribution: Holographic QCD, lattice QCD and GlueX data, Phys. Rev. D 103, 094010 (2021).
  76. Kiminad A. Mamo and Ismail Zahed, J/ψ near threshold in holographic QCD: A and D gravitational form factors, Phys. Rev. D 106, 086004 (2022).
  77. Minaya Allahverdiyeva and Shahin 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).
  78. Maxim V. Polyakov and C. Weiss, Skewed and double distributions in pion and nucleon, Phys. Rev. D 60, 114017 (1999).
  79. Wojciech Broniowski and Enrique Ruiz Arriola, Gravitational and higher-order form factors of the pion in chiral quark models, Phys. Rev. D 78, 094011 (2008).
  80. T. Frederico, E. Pace, B. Pasquini, and G. Salme, Pion generalized parton distributions with covariant and light-front constituent quark models, Phys. Rev. D 80, 054021 (2009).
  81. Pere Masjuan, Enrique Ruiz Arriola, and Wojciech Broniowski, Meson dominance of hadron form factors and large-Nc phenomenology, Phys. Rev. D 87, 014005 (2013).
  82. Hyeon-Dong Son and Hyun-Chul Kim, Stability of the pion and the pattern of chiral symmetry breaking, Phys. Rev. D 90, 111901 (2014).
  83. Cristiano Fanelli, Emanuele Pace, Giovanni Romanelli, Giovanni Salme, and Marco Salmistraro, Pion generalized parton distributions within a fully covariant constituent quark model, Eur. Phys. J. C 76, 253 (2016).
  84. Jonathan Hudson and Peter Schweitzer, D term and the structure of pointlike and composed spin-0 particles, Phys. Rev. D 96, 114013 (2017).
  85. Adam Freese, Adam Freese, Ian C. Cloët, and Ian C. Cloët, Gravitational form factors of light mesons, Phys. Rev. C 100, 015201 (2019); 105, 059901(E) (2022).
  86. A. F. Krutov and V. E. Troitsky, Pion gravitational form factors in a relativistic theory of composite particles, Phys. Rev. D 103, 014029 (2021).
  87. Edward Shuryak and Ismail Zahed, Nonperturbative quark-antiquark interactions in mesonic form factors, Phys. Rev. D 103, 054028 (2021).
  88. Guy F. de Téramond, H. G. Dosch, Tianbo Liu, Raza Sabbir Sufian, Stanley J. Brodsky, and Alexandre Deur (HLFHS Collaboration), Gluon matter distribution in the proton and pion from extended holographic light-front QCD, Phys. Rev. D 104, 114005 (2021).
  89. Khepani Raya, Zhu-Fang Cui, Lei Chang, Jose-Manuel Morgado, Craig D. Roberts, and Jose Rodriguez-Quintero, Revealing pion and kaon structure via generalised parton distributions*, Chin. Phys. C 46, 013105 (2022).
  90. Xuan-Bo Tong, Jian-Ping Ma, and Feng Yuan, Gluon gravitational form factors at large momentum transfer, Phys. Lett. B 823, 136751 (2021).
  91. A. F. Krutov and V. E. Troitsky, Relativistic composite-particle theory of the gravitational form factors of the pion: Quantitative results, Phys. Rev. D 106, 054013 (2022).
  92. Yin-Zhen Xu, Minghui Ding, Khépani Raya, Craig D. Roberts, José Rodríguez-Quintero, and Sebastian M. Schmidt, Pion and kaon electromagnetic and gravitational form factors, Eur. Phys. J. C 84, 191 (2024).
  93. Yang Li and James P. Vary, Stress inside the pion in holographic light-front QCD, Phys. Rev. D 109, L051501 (2024).
  94. Wojciech Broniowski and Enrique Ruiz Arriola, Gravitational form factors of the pion and meson dominance, arXiv:2405.07815.
  95. Wei-Yang Liu, Edward Shuryak, Christian Weiss, and Ismail Zahed, Pion gravitational form factors in the QCD instanton vacuum I, Phys. Rev. D 110, 054021 (2024).
  96. Wei-Yang Liu, Edward Shuryak, and Ismail Zahed, Pion gravitational form factors in the QCD instanton vacuum II, Phys. Rev. D 110, 054022 (2024).
  97. John F. Donoghue and H. Leutwyler, Energy and momentum in chiral theories, Z. Phys. C 52, 343 (1991).
  98. Volker D. Burkert, Jefferson Lab at 12 GeV: The science program, Annu. Rev. Nucl. Part. Sci. 68, 405 (2018).
  99. R. Abdul Khalek et al., Science requirements and detector concepts for the electron-ion collider: EIC yellow report, Nucl. Phys. A1026, 122447 (2022).
  100. Daniele P. Anderle et al., Electron-ion collider in China, Front. Phys. (Beijing) 16, 64701 (2021).
  101. F. Georges et al. (Jefferson Lab Hall A Collaboration), Deeply virtual Compton scattering cross section at high Bjorken xB, Phys. Rev. Lett. 128, 252002 (2022).
  102. G. Christiaens et al. (CLAS Collaboration), First CLAS12 measurement of deeply virtual Compton scattering beam-spin asymmetries in the extended valence region, Phys. Rev. Lett. 130, 211902 (2023).
  103. I. Yu. Kobzarev and L. B. Okun, Gravitational interaction of fermions, Zh. Eksp. Teor. Fiz. 43, 1904 (1962).
  104. Heinz Pagels, Energy-momentum structure form factors of particles, Phys. Rev. 144, 1250 (1966).
  105. Edward Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2, 505 (1998).
  106. Sebastian de Haro, Sergey N. Solodukhin, and Kostas Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217, 595 (2001).
  107. Ingmar Kanitscheider, Kostas Skenderis, and Marika Taylor, Precision holography for non-conformal branes, J. High Energy Phys. 09 (2008) 094.
  108. S. S. Gubser, Igor R. Klebanov, and Alexander M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428, 105 (1998).
  109. Edward Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2, 253 (1998).
  110. Roberto Casero, Elias Kiritsis, and Angel Paredes, Chiral symmetry breaking as open string tachyon condensation, Nucl. Phys. B787, 98 (2007).
  111. Koji Hashimoto, Takayuki Hirayama, and Akitsugu Miwa, Holographic QCD and pion mass, J. High Energy Phys. 06 (2007) 020.
  112. Oren Bergman, Shigenori Seki, and Jacob Sonnenschein, Quark mass and condensate in HQCD, J. High Energy Phys. 12 (2007) 037.
  113. Avinash Dhar and Partha Nag, Sakai-Sugimoto model, Tachyon condensation and chiral symmetry breaking, J. High Energy Phys. 01 (2008) 055.
  114. Koji Hashimoto, Takayuki Hirayama, Feng-Li Lin, and Ho-Ung Yee, Quark mass deformation of holographic massless QCD, J. High Energy Phys. 07 (2008) 089.
  115. Avinash Dhar and Partha Nag, Tachyon condensation and quark mass in modified Sakai-Sugimoto model, Phys. Rev. D 78, 066021 (2008).
  116. Robert McNees, Robert C. Myers, and Aninda Sinha, On quark masses in holographic QCD, J. High Energy Phys. 11 (2008) 056.

Outline

Information

Phys. Rev. D 110, L091501– Published 8 November, 2024
  • Received 11 August 2024
  • Accepted 7 October 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation