Il Nuovo Cimento (1955-1965)

, Volume 25, Issue 2, pp 337–354 | Cite as

The 27-fold way and other ways: symmetries of mesons-baryon resonances

  • S. L. Glashow
  • J. J. Sakurai


Meson-baryon resonances are discussed within the framework of unitary symmetry based upon the Gell-Mann-Ne’eman baryon octet (the eightfold way). It is argued that the low-lyingJ=3/2+ isobars ({ie337-1}, Y*0, Y*1, Y*2, etc.) realize a twenty-seven-dimensional representation of SU(3). Purely group-theoretic considerations directly following from unitary symmetry are compared with dynamical considerations suggested by the coupling constant combinations required by unitary symmetry andR-symmetry. Higher resonances are briefly discussed.


Si discutono la risonanze mesone-barione entro lo schema della simmetria unitaria basata sull’ottetto barionico di Gell-Mann-Ne’eman (la via ottupla). Si deduce che le isobareJ=3/2+ basse ({ie354-1}, Y*0, Y*1, Y*2, ecc.) realizzano una rappresentazione a 27 dimensioni dell’SU(3). Si confrontano le considerazioni puramente basate sulla teoria dei gruppi derivanti dalla simmetria unitaria con le considerazioni suggerite dalle combinazioni della costante di accoppiamento richieste dalla simmetria unitaria e dalla simmetriaR. Si discutono brevemente le risonanze più elevate.


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  1. (1).
    M. Gell-Mann:California Institute of Technology Synchrotron Laboratory Report, CTSL-20 (1961) (unpublished).Google Scholar
  2. (2).
    Y. Ne’eman:Nucl. Phys.,26, 222 (1961).MathSciNetCrossRefGoogle Scholar
  3. (3).
    For the {ie338-1} parity, seeM. Block, E. B. Brucker, I. S. Hughes, T. Kikuchi, C. Meltzer, F. Anderson, A. Pevsner, E. M. Harth, J. Leitner andH. O. Cohn:Phys Rev. Lett.,3, 291 (1959); andE. F. Beall, B. Cork, D. Keefe, P. G. Murphy andW. A. Wenzel:Phys. Rev. Lett.,8, 57 (1962). For the {ie338-2} parity, seeR. D. Tripp, M. B. Watson andM. Ferro-Luzzi:Phys. Rev. Lett.,8, 175 (1962).ADSCrossRefGoogle Scholar
  4. (4).
    Seee.g.,G. F. Chew andF. E. Low:Phys. Rev.,101, 1570 (1956).MathSciNetADSCrossRefzbMATHGoogle Scholar
  5. (6).
    S. Coleman andS. L. Glashow:Phys. Rev. Lett.,6, 423 (1961).ADSCrossRefGoogle Scholar
  6. (7).
    R. P. Ely, S.-Y. Fung, G. Gidal, Y.-L. Pan, W. M. Powell andH. S. White:Phys. Rev. Lett.,7, 458 (1961).ADSCrossRefGoogle Scholar
  7. (8).
    J. J. Sakurai:Phys. Rev. Lett.,7, 426 (1961).ADSCrossRefGoogle Scholar
  8. (10).
    J. Dowell, B. Leontic, A. Lundby, R. Meunier, G. Petmezas, J. P. Stroot andM. Szeptyaka:Proceedings of the Aix-en Provence Conference on Elementary Particles (to be published).Google Scholar
  9. (11).
    S. E. Wolf, N. Schmitz, L. J. Lloyd, W. Lasker, F. S. Crawford, J. J. Button, J. A. Anderson andG. Alexander:Rev. Mod. Phys.,33, 439 (1961).ADSCrossRefGoogle Scholar
  10. (12).
    This result has been derived independently byS. Okubo: (to be published);R. P. Feynman: (private communication) suggests that (mass)2 should be used in mass formulae such as (9) for bosons.Google Scholar
  11. (13).
    P. L. Bastien, J. P. Berge, O. I. Dahl, M. Ferro-Luzzi, D. H. Miller, J. J. Murray, A. H. Rosenfeld andM. B. Watson:Phys. Rev. Lett.,8, 114 (1962) suggest that the η meson at 550 MeV may be identified with the χ meson. We note without comment the proximity of this mass to the predicted χ mass.ADSCrossRefGoogle Scholar
  12. (16).
    Seee.g. M. Gell-Mann:Phys. Rev.,106, 1296 (1957).MathSciNetADSCrossRefzbMATHGoogle Scholar
  13. (17).
    Seee.g. S. C. Frautschi andJ. D. Walecka:Phys. Rev.,120, 1486 (1960).MathSciNetADSCrossRefzbMATHGoogle Scholar
  14. (18).
    D. Amati, A. Stanghellini andB. Vitale:Nuovo Cimento,13, 1143 (1959);M. Nauenberg:Phys. Rev. Lett.,2, 351 (1959);R. H. Capps:Phys. Rev.,119, 1735 (1960);D. Amati, B. Vitale andA. Stanghellini:Phys. Rev. Lett.,5, 524 (1960);J. Franklin: (unpublished).CrossRefzbMATHGoogle Scholar
  15. (19).
    R, C. Hwa andD. Feldman:Nuovo Cimento,23, 914 (1962).CrossRefGoogle Scholar
  16. (21).
    The possible existence of a resonance in KΛ scattering has been discussed byA. Kanazawa [Phys. Rev.,123, 997 (1961)], from a somewhat different point of view.MathSciNetADSCrossRefGoogle Scholar
  17. (22).
    J. J. Sakurai:Ann. Phys.,11, 1 (1960).MathSciNetADSCrossRefGoogle Scholar
  18. (23).
    Seee.g. review paper ofR. Omnès andG. Valladas:Proceedings of the Aix-en-Provence Conference on Elementary Particles (to be published).Google Scholar
  19. (24).
    R. H. Dalitz:Phys. Rev. Lett.,6, 239 (1961). See alsoM. Ross andG. L. Shaw:Ann. Phys.,13, 147 (1961).ADSCrossRefGoogle Scholar
  20. (25).
    Historically this kind of model was first discussed byK. Itabashi, M. Kato, K. Nakagawa andG. Takeda [Progr. Theor. Phys.,24, 529 (1960)], in connection with {ie350-1} and {ie350-2}.MathSciNetADSCrossRefGoogle Scholar
  21. (27).
    G. F. Chew andS. C. Frautschi:Phys. Rev. Lett.,8, 41 (1961). See alsoR. Blankenbecler andM. L. Goldberger: (to be published) andS. C. Frautschi, M. Gell-Mann andF. Zachariasen: (to be published).ADSCrossRefGoogle Scholar
  22. (28).
    The so-called « Kerth bump » in theT=0 {ie351-1} cross section at a total center of mass of 1815 MeV may well correspond to anf 5/2 resonance.L. Kerth:Rev. Mod. Phys.,33, 389 (1961) based on work ofV. Cook, B. Cork, T. Hoang, D. Keefe, L. Kerth, W. Wenzel andT. Zipf.ADSCrossRefGoogle Scholar
  23. (29).
    R. Behrends, J. Dreitlein, C. Fronsdal andW. Lee [Rev. Mod. Phys.,34, 1 (1962)], have emphasized the possibility that {ie351-2} and Y1* are members of the unitary 10.MathSciNetADSCrossRefzbMATHGoogle Scholar
  24. (30).
    R. Cutkosky: (Private communication toM. Gell-Mann). based on work ofR. E. Cutkosky, J. Kalckar andP. Tarjanne.Google Scholar

Copyright information

© Società Italiana di Fisica 1962

Authors and Affiliations

  • S. L. Glashow
    • 1
  • J. J. Sakurai
    • 2
    • 3
  1. 1.Institute for Theoretical Physics and Department of PhysicsStanford UniversityStanford
  2. 2.Enrico Fermi Institute for Nuclear Studies and Department of PhysicsUniversity of ChicagoChicago
  3. 3.Department of PhysicsCalifornia Institute of TechnologyPasadena

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