Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Searching for the rules that govern hadron construction

Nature volume 534, pages 487–493 (2016)Cite this article

Subjects

Abstract

Just as quantum electrodynamics describes how electrons are bound in atoms by the electromagnetic force, mediated by the exchange of photons, quantum chromodynamics (QCD) describes how quarks are bound inside hadrons by the strong force, mediated by the exchange of gluons. QCD seems to allow hadrons constructed from increasingly many quarks to exist, just as atoms with increasing numbers of electrons exist, yet such complex constructions seemed, until recently, not to be present in nature. Here we describe advances in the spectroscopy of mesons that are refining our understanding of the rules for predicting hadron structure from QCD.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: The charmonium spectrum.
Figure 2: Electron–positron annhiliation cross-sections.
Figure 3: Number of events collected as a function of invariant mass.
Figure 4: Lattice QCD computation of the meson spectrum.
Figure 5: Calculation of the ρ resonance.

Similar content being viewed by others

References

  1. Aubert, J. J. et al. Experimental observation of a heavy particle J. Phys. Rev. Lett. 33, 1404 (1974)

    Article  ADS  CAS  Google Scholar 

  2. Augustin, J. E. et al. Discovery of a narrow resonance in e+e− annihilation. Phys. Rev. Lett. 33, 1406 (1974)

    Article  ADS  CAS  Google Scholar 

  3. Eichten, E., Gottfried, K., Kinoshita, T., Lane, D. & Yan, T.-M. Charmonium: the model. Phys. Rev. D 17, 3090 (1978)

    Article  ADS  CAS  Google Scholar 

  4. Liu, Z. Q. et al. Study of e+e− → π+π−J/ψ and observation of a charged charmoniumlike state at Belle. Phys. Rev. Lett. 110, 252002 (2013)

    Article  ADS  CAS  PubMed  Google Scholar 

  5. Ablikim, M. et al. Observation of a charged charmoniumlike structure in e+e− → π+π−J/ψ at = 4.26 GeV. Phys. Rev. Lett. 110, 252001 (2013). This paper describes the observation of the Z (3900) at BESIII in decays to a charged pion and a J / ψ , simultaneously discovered at Belle4

    Article  ADS  CAS  PubMed  Google Scholar 

  6. Xiao, T., Dobbs, S., Tomaradze, A. & Seth, K. K. Observation of the charged hadron and evidence for the neutral in e+e− → ππJ/ψ at MeV. Phys. Lett. B 727, 366 (2013)

    Article  ADS  CAS  Google Scholar 

  7. Ablikim, M. et al. Observation of a charged charmoniumlike structure Z c (4020) and search for the Z c (3900) in e+e− → π+π−h c . Phys. Rev. Lett. 111, 242001 (2013)

    Article  ADS  CAS  PubMed  Google Scholar 

  8. Chilikin, K. et al. Observation of a new charged charmoniumlike state in decays. Phys. Rev. D 90, 112009 (2014)

    Article  ADS  CAS  Google Scholar 

  9. Aaij, R. et al. Observation of the resonant character of the Z(4430)− state. Phys. Rev. Lett. 112, 222002 (2014)

    Article  ADS  CAS  PubMed  Google Scholar 

  10. Chilikin, K. et al. Experimental constraints on the spin and parity of the Z(4430)+ . Phys. Rev. D 88, 074026 (2013)

    Article  ADS  CAS  Google Scholar 

  11. Mizuk, R. et al. Observation of two resonance-like structures in the π+χ c1 mass distribution in exclusive decays. Phys. Rev. D 78, 072004 (2008)

    Article  ADS  CAS  Google Scholar 

  12. Aaij, R. et al. Observation of J/ψp resonances consistent with pentaquark states in decays. Phys. Rev. Lett. 115, 072001 (2015)

    Article  ADS  CAS  PubMed  Google Scholar 

  13. Bondar, A. et al. Observation of two charged bottomonium-like resonances in ϒ(5S) decays. Phys. Rev. Lett. 108, 122001 (2012). This paper describes the discovery of two Z b peaks at Belle in decays to a charged pion and bottomonium.

    Article  ADS  CAS  PubMed  Google Scholar 

  14. Meyer, C. A. & Swanson, E. S. Hybrid mesons. Prog. Part. Nucl. Phys. 82, 21–58 (2015)

    Article  ADS  CAS  Google Scholar 

  15. Ivanov, E. I. et al. Observation of exotic meson production in the reaction π−p → η′π−p at 18 GeV/c . Phys. Rev. Lett. 86, 3977 (2001)

    Article  ADS  CAS  PubMed  Google Scholar 

  16. Alekseev, A. et al. Observation of a JPC = 1−+ exotic resonance in diffractive dissociation of 190 GeV/c π− into π−π−π+ . Phys. Rev. Lett. 104, 241803 (2010)

    Article  ADS  CAS  PubMed  Google Scholar 

  17. Kuhn, J. et al. Exotic meson production in the f 1(1285)π− system observed in the reaction π−p → ηπ+π−π−p at 18 GeV/c. Phys. Lett. B 595, 109–117 (2004)

    Article  ADS  CAS  Google Scholar 

  18. Adams, G. S. et al. Amplitude analyses of the decays χ c1 → ηπ+π− and χ c1 → η′π+π− . Phys. Rev. D 84, 112009 (2011)

    Article  ADS  CAS  Google Scholar 

  19. Kronfeld, A. S. Twenty-first century lattice gauge theory: results from the QCD Lagrangian. Annu. Rev. Nucl. Part. Sci. 62, 265–284 (2012)

    Article  ADS  CAS  Google Scholar 

  20. Kronfeld, A. S. in 100 Years of Subatomic Physics (eds Henley, E. M. & Ellis, S. D. ) 493–518 (World Scientific Publishing, 2013)

  21. Ding, H.-T., Karsch, F. & Mukherjee, S. Thermodynamics of strong-interaction matter from lattice QCD. Int. J. Mod. Phys. E 24, 1530007 (2015)

    Article  ADS  CAS  MATH  Google Scholar 

  22. Aoki, S. et al. Review of lattice results concerning low-energy particle physics. Eur. Phys. J. C 74, 2890 (2014)

    Article  ADS  CAS  PubMed  Google Scholar 

  23. Dudek, J. J., Edwards, R. G., Peardon, M. J., Richards, D. G. & Thomas, C. E. Highly excited and exotic meson spectrum from dynamical lattice QCD. Phys. Rev. Lett. 103, 262001 (2009)

    Article  ADS  PubMed  CAS  Google Scholar 

  24. Dudek, J. J., Edwards, R. G., Peardon, M. J., Richards, D. G. & Thomas, C. E. Toward the excited meson spectrum of dynamical QCD. Phys. Rev. D 82, 034508 (2010)

    Article  ADS  CAS  Google Scholar 

  25. Peardon, M. et al. A novel quark-field creation operator construction for hadronic physics in lattice QCD. Phys. Rev. D 80, 054506 (2009)

    Article  ADS  CAS  Google Scholar 

  26. Egri, G. I. et al. Lattice QCD as a video game. Comput. Phys. Commun. 177, 631–639 (2007)

    Article  ADS  CAS  Google Scholar 

  27. Clark, M., Babich, R., Barrows, K., Brower, R. & Rebbi, C. Solving lattice QCD systems of equations using mixed precision solvers on GPUs. Comput. Phys. Commun. 181, 1517 (2010)

    Article  ADS  CAS  MATH  Google Scholar 

  28. Horn, D. & Mandula, J. A model of mesons with constituent gluons. Phys. Rev. D 17, 898 (1978)

    Article  ADS  CAS  Google Scholar 

  29. Isgur, N. & Paton, J. E. A flux tube model for hadrons in QCD. Phys. Rev. D 31, 2910 (1985)

    Article  ADS  CAS  Google Scholar 

  30. Jaffe, R. L., Johnson, K. & Ryzak, Z. Qualitative features of the glueball spectrum. Ann. Phys. 168, 344–367 (1986)

    Article  ADS  CAS  Google Scholar 

  31. Barnes, T., Close, F. E., de Viron, F. & Weyers, J. Q anti-Q G hermaphrodite mesons in the MIT bag model. Nucl. Phys. B 224, 241–264 (1983)

    Article  ADS  Google Scholar 

  32. Chanowitz, M. S. & Sharpe, S. R. Hybrids: mixed states of quarks and gluons. Nucl. Phys. B 222, 211 (1983); erratum Nucl. Phys. B 228, 588 (1983)

    ADS  Google Scholar 

  33. General, I. J., Contanch, S. R. & Llanes-Estrada, F. J. QCD Coulomb gauge approach to hybrid mesons. Eur. Phys. J. C 51, 347–358 (2007)

    Article  ADS  CAS  Google Scholar 

  34. Guo, P., Szczepaniak, A. P., Galata, G., Vassallo, A. & Santopinto, E. Heavy quarkonium hybrids from Coulomb gauge QCD. Phys. Rev. D 78, 056003 (2008)

    Article  ADS  CAS  Google Scholar 

  35. Liu, L. et al. Excited and exotic charmonium spectroscopy from lattice QCD. J. High Energy Phys. 07, 126 (2012)

    Article  ADS  CAS  Google Scholar 

  36. Moir, G., Peardon, M., Ryan, S. M., Thomas, C. E. & Liu, L. Excited spectroscopy of charmed mesons from lattice QCD. J. High Energy Phys. 05, 021 (2013)

    Article  ADS  CAS  Google Scholar 

  37. Dudek, J. J. et al. Isoscalar meson spectroscopy from lattice QCD. Phys. Rev. D 83, 111502 (2011)

    Article  ADS  CAS  Google Scholar 

  38. Dudek, J. J. The lightest hybrid meson supermultiplet in QCD. Phys. Rev. D 84, 074023 (2011). This paper describes the interpretation of lattice QCD computed spectra, leading to a simple rule for the construction of hybrid mesons.

    Article  ADS  CAS  Google Scholar 

  39. Lüscher, M. Two particle states on a torus and their relation to the scattering matrix. Nucl. Phys. B 354, 531 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  40. Rummukainen, K. & Gottlieb, S. A. Resonance scattering phase shifts on a nonrest frame lattice. Nucl. Phys. B 450, 397 (1995)

    Article  ADS  Google Scholar 

  41. Kim, C. h., Sachrajda, C. T. & Sharpe, S. R. Finite-volume effects for two-hadron states in moving frames. Nucl. Phys. B 727, 218 (2005)

    Article  ADS  CAS  Google Scholar 

  42. Christ, N. H., Kim, C. & Yamazaki, T. Finite volume corrections to the two-particle decay of states with non-zero momentum. Phys. Rev. D 72, 114506 (2005)

    Article  ADS  CAS  Google Scholar 

  43. He, S., Feng, X. & Liu, C. Two particle states and the S-matrix elements in multi-channel scattering. J. High Energy Phys. 07, 011 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  44. Hansen, M. T. & Sharpe, S. R. Multiple-channel generalization of Lellouch-Luscher formula. Phys. Rev. D 86, 016007 (2012)

    Article  ADS  CAS  Google Scholar 

  45. Briceño, R. A. & Davoudi, Z. Moving multichannel systems in a finite volume with application to proton-proton fusion. Phys. Rev. D 88, 094507 (2013)

    Article  ADS  CAS  Google Scholar 

  46. Guo, P., Dudek, J., Edwards, R. & Szczepaniak, A. P. Coupled-channel scattering on a torus. Phys. Rev. D 88, 014501 (2013)

    Article  ADS  CAS  Google Scholar 

  47. Aoki, S. et al. Lattice QCD calculation of the rho meson decay width. Phys. Rev. D 76, 094506 (2007)

    Article  ADS  CAS  Google Scholar 

  48. Feng, X., Jansen, K. & Renner, D. B. Resonance Parameters of the rho-meson from lattice QCD. Phys. Rev. D 83, 094505 (2011)

    Article  ADS  CAS  Google Scholar 

  49. Lang, C. B., Mohler, D., Prelovsek, S. & Vidmar, M. Coupled channel analysis of the rho meson decay in lattice QCD. Phys. Rev. D 84, 054503 (2011); erratum Phys. Rev. D 89, 059903 (2014)

    Article  CAS  Google Scholar 

  50. Aoki, S. et al. ρ meson decay in 2+1 flavor lattice QCD. Phys. Rev. D 84, 094505 (2011)

    Article  ADS  CAS  Google Scholar 

  51. Pelissier, C. & Alexandru, A. Resonance parameters of the rho-meson from asymmetrical lattices. Phys. Rev. D 87, 014503 (2013)

    Article  ADS  CAS  Google Scholar 

  52. Fu, Z. Lattice study on πK scattering with moving wall source. Phys. Rev. D 85, 074501 (2012)

    Article  ADS  CAS  Google Scholar 

  53. Lang, C. B., Leskovec, L., Mohler, D. & Prevlosek, S. Kπ scattering for isospin 1/2 and 3/2 in lattice QCD. Phys. Rev. D 86, 054508 (2012)

    Article  ADS  CAS  Google Scholar 

  54. Dudek, J. J., Edwards, R. G. & Thomas, C. E. Energy dependence of the ρ resonance in ππ elastic scattering from lattice QCD. Phys. Rev. D 87, 034505 (2013); erratum Phys. Rev. D 90, 099902 (2014)

    Article  CAS  Google Scholar 

  55. Bugg, D. V. How resonances can synchronise with thresholds. J. Phys. G 35, 075005 (2008)

    Article  ADS  CAS  Google Scholar 

  56. Guo, F.-K., Meissner, U.-G., Wang, W. & Yang, Z. How to reveal the exotic nature of the P c (4450). Phys. Rev. D 92, 071502 (2015)

    Article  ADS  CAS  Google Scholar 

  57. Swanson, E. S. Z b and Z c exotic states as coupled channel cusps. Phys. Rev. D 91, 034009 (2015)

    Article  ADS  CAS  Google Scholar 

  58. Szczepaniak, A. P. Triangle singularities and XYZ quarkonium peaks. Phys. Lett. B 747, 410–416 (2015)

    Article  ADS  CAS  Google Scholar 

  59. Wang, Q., Hanhart, C. & Zhao, Q. Systematic study of the singularity mechanism in heavy quarkonium decays. Phys. Lett. B 725, 106–110 (2013)

    Article  ADS  CAS  Google Scholar 

  60. Godfrey, S. & Isgur, N. Mesons in a relativized quark model with chromodynamics. Phys. Rev. D 32, 189 (1985)

    Article  ADS  CAS  Google Scholar 

  61. Olive, K. A. et al. Review of particle physics. Chin. Phys. C 38, 090001 (2014)

    Article  ADS  CAS  Google Scholar 

  62. Bai, J. Z. et al. Measurements of the cross-section for e+e− → hadrons at center-of-mass energies from 2 GeV to 5 GeV. Phys. Rev. Lett. 88, 101802 (2002)

    Article  ADS  CAS  PubMed  Google Scholar 

  63. Osterheld, A. et al. Measurements of total hadronic and inclusive D* cross-sections in e+e− annihilations between 3.87 GeV and 4.5 GeV. Stanford Linear Accelerator Center Report No. SLAC-PUB-4160, http://slac.stanford.edu/pubs/slacpubs/4000/slac-pub-4160.pdf (1986)

  64. Lees, J. P. et al. (BaBar Collaboration) Study of the reaction e+e− → J/ψπ+π− via initial-state radiation at BaBar. Phys. Rev. D 86, 051102 (2012). This paper describes the discovery of the Y (4260) by the BaBar Collaboration in the process e+e−→ π+π−J / ψ

    Article  ADS  CAS  Google Scholar 

  65. Lees, J. P. et al. Study of the reaction e+e− → ψ(2S)π−π− via initial-state radiation at BaBar. Phys. Rev. D 89, 111103 (2014)

    Article  ADS  CAS  Google Scholar 

  66. Wang, X. L. et al. Observation of two resonant structures in e+e− → π+π−ψ(2S) via initial state radiation at Belle. Phys. Rev. Lett. 99, 142002 (2007)

    Article  ADS  CAS  PubMed  Google Scholar 

  67. Dudek, J. J., Edwards, R. G., Guo, P. & Thomas, C. E. Toward the excited isoscalar meson spectrum from lattice QCD. Phys. Rev. D 88, 094505 (2013). This paper describes the detailed excited state spectra of light-quark mesons computed in lattice QCD.

  68. Wilson, D. J., Briceno, R. A., Dudek, J. J., Edwards, R. G. & Thomas, C. E. Coupled scattering in P-wave and the ρ resonance from lattice QCD. Phys. Rev. D 92, 094502 (2015). This paper describes the mapping out of the ππ scattering amplitude and observation of the ρ resonance in lattice QCD.

Download references

Acknowledgements

J.J.D. acknowledges support provided by US Department of Energy contract DE-AC05-06OR23177, under which Jefferson Science Associates manages Jefferson Laboratory and the Early Career Award contract DE-SC0006765. M.R.S. and R.E.M. are supported by US Department of Energy contract DE-FG02-05ER41374. M.R.S. acknowledges the Jefferson Science Associates Sabbatical Leave Support Program. We thank L. Weinstein for comments on the initial draft of this manuscript.

Author information

Authors and Affiliations

  1. Department of Physics, Indiana University, Bloomington, 47405, Indiana, USA

    Matthew R. Shepherd & Ryan E. Mitchell

  2. Department of Physics, Old Dominion University, Norfolk, 23529, Virginia, USA

    Jozef J. Dudek

  3. Jefferson Lab, Newport News, Virginia, 23606, USA

    Jozef J. Dudek

Authors
  1. Matthew R. Shepherd
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jozef J. Dudek
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ryan E. Mitchell
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed equally to this manuscript.

Corresponding author

Correspondence to Matthew R. Shepherd.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Related audio

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shepherd, M., Dudek, J. & Mitchell, R. Searching for the rules that govern hadron construction. Nature 534, 487–493 (2016). https://doi.org/10.1038/nature18011

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature18011

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing