Skip to main content
SpringerLink
Log in

Low-energy properties of a relativistic quark model with linear scalar potential

Свойства релятивистской модели кварков с линейным скалярным потенциалом

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

A simple quark model with a linear rising scalar confining potential and an additional Coulomb potential is discussed. The eigenvalues of the appropriate Dirac equation are studied with respect to variations of the quark bare mass and to the potential parameters. The model is able to account for the static properties of the nucleon.

Riassunto

Si discute un semplice modello a quark con un potenziale a crescita lineare e a confinamento scalare e un potenziale addizionale di Coulomb. Si studiano gli autovalori dell’equazione di Dirac appropriata in rapporto alle variazioni della massa pura del quark e ai parametri di potenziale. Il modello è in grado di dare una spiegazione delle proprietà statiche del nucleone.

Реэюме

Обсуждается простая модель кварков с линейным воэрастаюшим скалярным ограниченным потенциалом с добавлением кулоновского потенциала. Исследуются собственные эначения соответствуюшего уравнения Дирака в отно-щении иэменений эатравочной массы кварков и параметров потенциала. Предло-женная модель может общяснить статические свойства нуклона.

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

  1. For a review of deep inelastic electron-nucleon scattering seeH. W. Kendall:Proceedings of the 1971 International Symposium on Electron and Photon Interactions at High Energies, edited byN. B. Mistry (Ithaca, N. Y., 1971); the deep inelastic neutrino-nucleon scattering is summarized inD. H. Perkins:Proceedings of the XVI International Conference, Vol.4 (Batavia, Ill., 1972);Proceedings of the V Hawaii Topical Conference in Particle Physics, edited byP. N. Dobson, V. Z. Peterson andS. F. Tuan (1973).

  2. R. P. Feynman:Proceedings of the Neutrino 72 Conference, edited byA. Frenkel andG. Marx, Vol.2 (Balatonfüred, 1972).

  3. J. Kuti andV. F. Weisskopf:Phys. Rev. D,4, 3418 (1971). See alsoH. Faissner: PITHA-60, Aachen, 1972, unpublished;D. Rein:Phys. Lett.,43 B, 209 (1973).

    Article  ADS  Google Scholar 

  4. J. J. Aubert, U. Becker, P. J. Biggs, J. Burger, M. Chen, G. Everhart, P. Goldhagen, J. Leong, T. Mc Corriston, T. G. Rhoades, M. Rohde, S. C. C., Ting, S. L. Wu andY. Y. Lee:Phys. Rev. Lett.,33, 1404 (1974);J. E. Augustin. A. M. Boyarski, M. Breidenbach, F. Bulos, J. T. Dakin, G. J. Feldman, G. E. Fischer, D. Fryberger, G. Hanson, B. Jean-Marie, R. R. Larsen, V. Lüth, H. L. Lynch, D. Lyon, C. C. Morehouse, J. M. Paterson, M. L. Perl, B. Richter, P. Rapidis, R. F. Schwitters, W. M. Tannenbaum, F. Vanucci, G. S. Abrams, D. Briggs, W. Chinowsky, C. E. Friedberg, G. Goldhaber, R. J. Hollebeek, J. A. Kadyk, B. Lulu, F. Pierre, G. H. Trilling, J. S. Whitaker, J. Wiss andJ. E. Zipse:Phys. Rev. Lett.,33, 1406 (1974).

    Article  ADS  Google Scholar 

  5. A. Benvenuti, D. Cline, W. Ford, R. Imlay, T. Y. Ling, A. K. Mann, F. Messing, R. Orr, D. D. Reeder, C. Rubbia, R. Stefanski, L. Sulak andP. Wanderer:Phys. Rev. Lett.,34, 419 (1975).

    Article  ADS  Google Scholar 

  6. V. Lüth: talk at theInternational Neutrino Conference, Aachen, 1976, to appear in theProceedings.

  7. SeeM. K. Gaillard, B. W. Lee andL. L. Rosner:Rev. Mod. Phys.,47, 112 (1975).

    Article  Google Scholar 

  8. SeeK. Krisor:Nuovo Cimento,27 A, 132 (1975), and literature quoted therein.

    Article  ADS  Google Scholar 

  9. A. Chodos, R. L. Jaffe, K. Johnson, C. B. Thorn andV. F. Weisskopf:Phys. Rev. D,9, 3471 (1974);W. A. Bardeen, M. S. Chanowitz, S. D. Drell, M. Weinstein andT. N. Yan:Phys. Rev. D,11, 1094 (1975).

    Article  MathSciNet  ADS  Google Scholar 

  10. G. Morpurgo:Physics,2, 95 (1965).

    Google Scholar 

  11. P. N. Bogoliubov:Ann. Inst. Henri Poincaré,8 A, 162 (1968).

    Google Scholar 

  12. One can imagine that self-interacting vector gluon fields could provide for a baglike solution where gluons and quarks are confined to a certain volume of space. See f.i.G. t’Hooft: CERN-TH-1902 (1974);J. Kuti:Proceedings of the Neutrino 75 Conference, edited byA. Frenkel andG. Marx, Vol.2 (Balatonfüred, 1975).

  13. J. F. Gunion andL. F. Li:Phys. Rev. D,12, 3583 (1975).

    Article  ADS  Google Scholar 

  14. J. J. Kokkedee:The Quark Model (New York, N. Y., and Amsterdam, 1969).

  15. J. Kogut andL. Susskind:Phys. Rev. D,9, 3501 (1974);J. Schwinger:Phys. Rev.,128, 2425 (1962).

    Article  ADS  Google Scholar 

  16. K. Wilson:Phys. Rev. D,10, 2445 (1974).

    Article  ADS  Google Scholar 

  17. E. Eichten, K. Gottfried, T. Kinoshita, J. Kogut, K. D. Lane andT. M. Yan:Phys. Rev. Lett.,34, 369 (1975);B. J. Harrington, S. Y. Park andA. Yildiz:Phys. Rev. Lett.,34, 168 (1975);T. Appelquist andH. D. Politzer:Phys. Rev. Lett.,34, 41 (1975);T. Appelquist, A. De Rújula, H. D. Politzer andS. L. Glashow:Phys. Rev. Lett.,34, 365 (1975).

    Article  ADS  Google Scholar 

  18. C. L. Critchfield:Phys. Rev. D,12, 923 (1975).

    Article  ADS  Google Scholar 

  19. After completion of this work a paper ofJ. Critchfield came to my attention which deals also with a nonvanishing mass parameter andα s ≠ 0; his article, however, is mainly concerned with the mathematical implications of such an approach. SeeJ. Critchfield:Journ. Math. Phys.,17, 261 (1976).

    Article  MathSciNet  ADS  Google Scholar 

  20. G. Köpp, T. F. Walsh andP. Zerwas:Nucl. Phys.,42 B, 109 (1972).

    Article  ADS  Google Scholar 

  21. This is of course due to the mass difference between strange and nonstrange quarks. SeeA. De Rújula, H. Georgi andS. L. Glashow:Phys. Rev. D,12, 147 (1975). See alsoR. Davis:Nucl. Phys.,11 B, 249 (1969). A very interesting contribution to this field has also been made byL. M. Sehgal:Phys. Rev. D,10, 1663 (1974).

    Article  ADS  Google Scholar 

  22. We follow the notation ofH. A. Bethe andE. E. Salpeter:Quantum Mechanics of One and Two Electron Atoms (Berlin and Heidelberg, 1957).

  23. The termL k proportional tom could be avoided by inclusion of a mass-dependent term exp [-mr] in the large-distance behaviour of the wave functions (4); compare ref. (19) After completion of this work a paper ofJ. Critchfield came to my attention which deals also with a nonvanishing mass parameter andα s ≠ 0; his article, however, is mainly concerned with the mathematical implications of such an approach. See.

    Article  MathSciNet  ADS  Google Scholar 

  24. W. Braunschweig, H. U. Martyn, H. G. Sander, D. Schmitz, W. Sturm, W. Wallraff, K. Berkelman, D. Cords, R. Felst, E. Gadermann, G. Grindhammer, H. Hultschig, P. Joos, W. Koch, U. Kötz, H. Krehbiel, D. Kreinick, J. Ludwig, K. H. Mess, K. C. Moffeit, A. Petersen, G. Poelz, J. Ringel, K. Sauerberg, P. Schmüser, G. Vogel, B. H. Wiik, G. Wolf, G. Buschhorn, R. Kotthaus, U. E. Kruse, H. Lierl, H. Oberlack, K. Pretzl, M. Schliewa, S. Orito, T. Suda, Y. Totsuka andS. Yamada:Phys. Lett.,57 B, 407 (1975).

    Article  ADS  Google Scholar 

  25. E. Dahl-Jensen, N. Doble, D. Evans, A. D. Herz, U. Liebermeister, Ph. Rosselet, C. Busi, G. Önengüt, P. Tolun, M. Gailloud, R. Weill, G. Hansl, A. Manz, W. Püschel, R. Settles, G. Baroni, G. Romano andV. Rossi:Nuovo Cimento,3 A, 1 (1971).

    Article  ADS  Google Scholar 

  26. B. Borkowski, P. Peuser, G. G. Simon, V. W. Walther andR. D. Wendling:Nucl. Phys.,222 A, 269 (1974).

    Article  ADS  Google Scholar 

  27. SeeParticle Data Group:Rev. Mod. Phys.,45, No. 2, Part II (1973).

Download references

Author information

Authors and Affiliations

  1. Technische Hochschule, III. Physikalisches Institut, Aachen, Germany

    D. W. Rein

Authors
  1. D. W. Rein
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

To speed up publication, the author of this paper has agreed to not receive the proofs for correction.

Work supported by the German Bundesministerium für Forschung und Technologie.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rein, D.W. Low-energy properties of a relativistic quark model with linear scalar potential. Nuov Cim A 38, 19–37 (1977). https://doi.org/10.1007/BF02734126

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02734126

Search

Navigation