Skip to main content
SpringerLink
Log in

Proton mass decomposition: Naturalness and interpretations

  • View & Perspective
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

I discuss the scope and naturalness of the proton mass decomposition (or sum rule) published in Phys. Rev. Lett. 74, 1071 (1995) and answer a few criticisms that appeared recently in the literature, focusing particularly on its interpretation and the quantum anomalous energy contribution. I comment on the so-called frame-independent or invariant-mass decomposition from the trace of the energy-momentum tensor. I stress the importance of measuring the quantum anomalous energy through experiments. Finally, I point out a large discrepancy in the scalar radius of the nucleon extracted from vector-meson productions and lattice QCD calculations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References and notes

  1. X.-D. Ji, A QCD analysis of the mass structure of the nucleon, Phys. Rev. Lett. 74, 1071 (1995), arXiv: hep-ph/9410274

    Article  ADS  Google Scholar 

  2. E. Hecht, How Einstein confirmed E0 = mc2, Am. J. Phys. 79, 591 (2011)

    Article  ADS  Google Scholar 

  3. J. Dudek, et al., Physics opportunities with the 12 GeV upgrade at Jefferson Lab, Eur. Phys. J. A 48, 187 (2012), arXiv: 1208.1244 [hep-ex]

    Article  ADS  Google Scholar 

  4. A. Accardi, et al., Electron Ion Collider: The next QCD frontier: Understanding the glue that binds us all, Eur. Phys. J. A 52, 268 (2016), arXiv: 1212.1701 [nucl-ex]

    Article  ADS  Google Scholar 

  5. Third Workshop on Proton Mass: Origin and Perspective, https://indico.phy.anl.gov/event/2 (2021)

  6. D. E. Kharzeev, The mass radius of the proton, arXiv: 2102.00110 [hep-ph] (2021)

  7. L. B. Okun, The concept of mass, Phys. Today 42, 31 (1989)

    Article  Google Scholar 

  8. G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68, 1125 (1996), arXiv: hep-ph/9512380

    Article  ADS  Google Scholar 

  9. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory, Addison-Wesley, Reading, USA, 1995

    Google Scholar 

  10. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Remarks on Higgs-Boson interactions with nucleons, Phys. Lett. B 78, 443 (1978)

    Article  ADS  Google Scholar 

  11. J. C. Collins, A. Duncan, and S. D. Joglekar, Trace and dilatation anomalies in gauge theories, Phys. Rev. D 16, 438 (1977)

    Article  ADS  Google Scholar 

  12. N. K. Nielsen, The energy-momentum tensor in a non-Abelian quark gluon theory, Nucl. Phys. B 120, 212 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  13. Y. Chen, et al., Glueball spectrum and matrix elements on anisotropic lattices, Phys. Rev. D 73, 014516 (2006), arXiv: hep-lat/0510074

    Article  ADS  Google Scholar 

  14. A. Abdel-Rehim, C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, C. Kallidonis, G. Koutsou, and A. Vaquero Aviles-Casco (ETM), Direct evaluation of the quark content of nucleons from lattice QCD at the physical point, Phys. Rev. Lett. 116, 252001 (2016), arXiv: 1601.01624 [hep-lat]

    Article  ADS  Google Scholar 

  15. C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, C. Kallidonis, G. Koutsou, A. Vaquero Avilés-Casco, and C. Wiese, Nucleon spin and momentum decomposition using lattice QCD simulations, Phys. Rev. Lett. 119, 142002 (2017), arXiv: 1706.02973 [hep-lat]

    Article  ADS  Google Scholar 

  16. Y.-B. Yang, J. Liang, Y.-J. Bi, Y. Chen, T. Draper, K.-F. Liu, and Z. Liu, Proton mass decomposition from the QCD energy momentum tensor, Phys. Rev. Lett. 121, 212001 (2018), arXiv: 1808.08677 [hep-lat]

    Article  ADS  Google Scholar 

  17. F. He, P. Sun, and Y.-B. Yang, A demonstration of hadron mass origin from QCD trace anomaly, arXiv: 2101.04942 [hep-lat] (2021)

  18. I. Zahed, Mass sum rule of hadrons in the QCD instanton vacuum, arXiv: 2102.08191 [hep-ph] (2021)

  19. D. Kharzeev, H. Satz, A. Syamtomov, and G. Zinovjev, J/ψ photoproduction and the gluon structure of the nucleon, Eur. Phys. J. C 9, 459 (1999), arXiv: hep-ph/9901375

    Article  ADS  Google Scholar 

  20. Y. Hatta and D.-L. Yang, Holographic J/ψ production near threshold and the proton mass problem, Phys. Rev. D 98, 074003 (2018), arXiv: 1808.02163 [hep-ph]

    Article  ADS  Google Scholar 

  21. K. A. Mamo and I. 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), arXiv: 1910.04707 [hep-ph]

    Article  ADS  Google Scholar 

  22. R. Wang, J. Evslin, and X. Chen, The origin of proton mass from J/ψ photo-production data, Eur. Phys. J. C 80, 507 (2020), arXiv: 1912.12040 [hep-ph]

    Article  ADS  Google Scholar 

  23. R. Boussarie and Y. Hatta, QCD analysis of near-threshold quarkonium leptoproduction at large photon virtualities, Phys. Rev. D 101, 114004 (2020), arXiv: 2004.12715 [hep-ph]

    Article  ADS  Google Scholar 

  24. Z.-E. Meziani and S. Joosten, Origin of the Proton Mass? Heavy Quarkonium Production at Threshold from Jefferson Lab to an Electron-Ion Collider, in: Probing Nucleons and Nuclei in High Energy Collisions: Dedicated to the Physics of the Electron-Ion Collider, 2020, pp 234–237, doi:https://doi.org/10.1142/9789811214950_0048

  25. X. Ji and Y. Liu, Quantum anomalous energy effects on the nucleon mass, arXiv: 2101.04483 [hep-ph] (2021)

  26. P. Di Francesco, P. Mathieu, and D. Senechal, Conformal Field Theory, Graduate Texts in Contemporary Physics, Springer-Verlag, New York, 1997

    MATH  Google Scholar 

  27. F. Karsch, SU (N) gauge theory couplings on asymmetric lattices, Nucl. Phys. B 205, 285 (1982)

    Article  ADS  Google Scholar 

  28. H. J. Rothe, Lattice energy sum rule and the trace anomaly, Phys. Lett. B 364, 227 (1995), arXiv: hep-lat/9508005

    Article  ADS  Google Scholar 

  29. X.-D. Ji and W. Lu, A modern anatomy of electron mass, arXiv: hep-ph/9802437 (1998)

  30. B.-D. Sun, Z.-H. Sun, and J. Zhou, Trace anomaly contribution to hydrogen atom mass, arXiv: 2012.09443 [hep-ph] (2020)

  31. A. Metz, B. Pasquini, and S. Rodini, Revisiting the proton mass decomposition, arXiv: 2006.11171 [hep-ph] (2020)

  32. M. E. Luke, A. V. Manohar, and M. J. Savage, A QCD calculation of the interaction of quarkonium with nuclei, Phys. Lett. B 288, 355 (1992), arXiv: hep-ph/9204219

    Article  ADS  Google Scholar 

  33. D. Kharzeev, Quarkonium interactions in QCD, Proc. Int. Sch. Phys. Fermi 130, 105 (1996), arXiv: nucl-th/9601029

    Google Scholar 

  34. E. V. Shuryak, Probing the boundary of the non-perturbative QCD by small size instantons, arXiv: hep-ph/9909458 (1999)

  35. A. Chodos, R. Jaffe, K. Johnson, C. B. Thorn, and V. Weisskopf, A new extended model of hadrons, Phys. Rev. D 9, 3471 (1974)

    Article  ADS  MathSciNet  Google Scholar 

  36. C. D. Roberts and C. Mezrag, Emergent phenomena and partonic structure in hadrons, EPJ Web Conf. 137, 01017 (2017), arXiv: 1611.09863 [nucl-th]

    Article  Google Scholar 

  37. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. II, Ch. 28, 1963

  38. X. Ji, Fundamental properties of the proton in lightfront zero modes, Nucl. Phys. B, 115181 (2020), arXiv: 2003.04478 [hep-ph]

  39. Y. Hatta and Y. Zhao, Parton distribution function for the gluon condensate, Phys. Rev. D 102, 034004 (2020), arXiv: 2006.02798 [hep-ph]

    Article  ADS  Google Scholar 

  40. Y. Guo, X. Ji, and K. Shiells, Novel twist-three transversespin sum rule for the proton and related generalized parton distributions, arXiv: 2101.05243 [hep-ph] (2021)

  41. Y. Hatta, A. Rajan, and K. Tanaka, Quark and gluon contributions to the QCD trace anomaly, JHEP 12, 008 (2018), arXiv: 1810.05116 [hep-ph]

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. K. Tanaka, Three-loop formula for quark and gluon contributions to the QCD trace anomaly, JHEP 01, 120 (2019), arXiv: 1811.07879 [hep-ph]

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. C. Lorcé, On the hadron mass decomposition, Eur. Phys. J. C 78, 120 (2018), arXiv: 1706.05853 [hep-ph]

    Article  ADS  Google Scholar 

  44. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Pergamon Press, 1984

  45. E. Shuryak, Strongly coupled quark-gluon plasma in heavy ion collisions, Rev. Mod. Phys. 89, 035001 (2017), arXiv: 1412.8393 [hep-ph]

    Article  ADS  MathSciNet  Google Scholar 

  46. X.-D. Ji, Gauge-invariant decomposition of nucleon spin, Phys. Rev. Lett. 78, 610 (1997), arXiv: hep-ph/9603249

    Article  ADS  Google Scholar 

  47. J. Gasser and H. Leutwyler, Chiral perturbation theory: Expansions in the mass of the strange quark, Nucl. Phys. B 250, 465 (1985)

    Article  ADS  Google Scholar 

  48. C. Alexandrou, S. Bacchio, M. Constantinou, J. Finkenrath, K. Hadjiyiannakou, K. Jansen, G. Koutsou, and A. Vaquero Aviles-Casco, Nucleon axial, tensor, and scalar charges and σ-terms in lattice QCD, Phys. Rev. D 102, 054517 (2020), arXiv: 1909.00485 [hep-lat]

    Article  ADS  Google Scholar 

  49. M. Gong, et al. (XQCD), Strangeness and charmness content of the nucleon from overlap fermions on 2+1-flavor domain-wall fermion configurations, Phys. Rev. D 88, 014503 (2013), arXiv: 1304.1194 [hep-ph]

    Article  ADS  Google Scholar 

  50. X.-D. Ji, Breakup of hadron masses and energy-momentum tensor of QCD, Phys. Rev. D 52, 271 (1995), arXiv: hep-ph/9502213

    Article  ADS  Google Scholar 

  51. H. Pagels, Energy-momentum structure form factors of particles, Phys. Rev. 144, 1250 (1966)

    Article  ADS  Google Scholar 

  52. X.-D. Ji, W. Melnitchouk, and X. Song, Study of off-forward parton distributions, Phys. Rev. D 56, 5511 (1997), arXiv: hep-ph/9702379

    Article  ADS  Google Scholar 

  53. R. Wang, W. Kou, and X. Chen, Extraction of the proton mass radius from the vector-meson photoproductions near thresholds, arXiv: 2102.01610 [hep-ph], 2021

  54. K. A. Mamo and I. Zahed, Nucleon mass radii and distribution: Holographic QCD, lattice QCD and GlueX data, arXiv: 2103.03186 [hep-ph] (2021)

  55. P. Hagler, et al. (LHPC), Nucleon generalized parton distributions from full lattice QCD, Phys. Rev. D 77, 094502 (2008), arXiv: 0705.4295 [hep-lat]

    Article  ADS  Google Scholar 

  56. P. Hagler, Hadron structure from lattice quantum chromodynamics, Phys. Rep. 490, 49 (2010), arXiv: 0912.5483 [hep-lat]

    Article  ADS  MathSciNet  Google Scholar 

  57. 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), arXiv: 1810.04626 [hep-lat]

    Article  ADS  Google Scholar 

  58. M. V. Polyakov and P. Schweitzer, Forces inside hadrons: Pressure, surface tension, mechanical radius, and all that, Int. J. Mod. Phys. A 33, 1830025 (2018), arXiv: 1805.06596 [hep-ph]

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank K. F. Liu, Y. Z. Liu, D. Kharzeev, A. Metz, Z.-E. Meziani, B. Pasquini, S. Rodini, A. Schaefer, F. Yuan, and I. Zahed for discussions and comments on the manuscript, and Y. Guo and Y. Su for help. I particularly thank Y. Z. Liu for helping with the gravitational form factors. This material was supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under contract number DE-SC0020682, and Southeastern Universities Research Association.

Author information

Authors and Affiliations

  1. Center for Nuclear Femtography, SURA, 1201 New York Ave., NW, 20005, Washington, DC, USA

    Xiangdong Ji

  2. Department of Physics, University of Maryland, College Park, MD, 20742, USA

    Xiangdong Ji

Authors
  1. Xiangdong Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiangdong Ji.

Additional information

arXiv: 2102.07830. This article can also be found at http://journal.hep.com.cn/fop/EN/10.1007/s11467-021-1065-x.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ji, X. Proton mass decomposition: Naturalness and interpretations. Front. Phys. 16, 64601 (2021). https://doi.org/10.1007/s11467-021-1065-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-021-1065-x

Search

Navigation