Advertisement

Dynamical Problems of the Relativistic Quark Model

  • M. Böhm
  • H. Joos
  • M. Krammer
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 11/1973)

Abstract

In our lectures we deal with the specific dynamical problems arising in the formulation of the relativistic quark model in the framework of field theory1. After the discussion of some basic questions occurring in this particular attempt towards a foundation of hadron dynamics, we develop extensively the methods for the description of mesons as quark-antiquark bound-states and give some illuminating phenomenological applications. In order to outline the spirit of our approach, let us first answer some general questions.

Keywords

Heavy Quark Vector Meson Quark Model Single Particle State Relativistic Quark Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chapter A is partly based on Lectures by H. Joos, Quark Theory of Elementary Particles, Instituto de Fisica Teorica, Sao Paulo (1969).Google Scholar
  2. 2.
    Textbooks on general Quantum Field Theory, for example, L. Klein (Editor), “Dispersion Relations and the Abstract Approach to Field Theory” ( New York, Gordon and Breach Publishers Inc. 1961 ).Google Scholar
  3. R. Jost, “The General Theory of Quantized Fields”, Providence: American Mathematical Soc. (1965).MATHGoogle Scholar
  4. R. Jost (Editor), Teoria quantistica locale, New York and London, Academic Press (1969).Google Scholar
  5. 3.
    R. Haag, Phys. Rev. 112, (1958) 669.MATHADSMathSciNetCrossRefGoogle Scholar
  6. W. Zimmermann, Nuovo Cim. X, (1958) 597.CrossRefGoogle Scholar
  7. D. Ruelle, Hely. Phys. Acta 35 (1962) 147.MATHMathSciNetGoogle Scholar
  8. 4.
    W. Zimmermann, Nuovo Cim. 13 (1959) 503MATHCrossRefGoogle Scholar
  9. W. Zimmermann, ibid. 16 (1960) 690.MATHGoogle Scholar
  10. 5.
    For a review on this work see: R. Haag, Brandeis Lectures 1970.Google Scholar
  11. 6.
    W. Thirring, Nuclear Phys. 10, 97 (1959).MATHADSMathSciNetCrossRefGoogle Scholar
  12. 7.
    S. Sakata, Progr. Theor. Phys. 16, 686 (1956).ADSCrossRefGoogle Scholar
  13. 8.
    J. Wess, Nuovo Cim. 15, 52 (1960).MathSciNetCrossRefGoogle Scholar
  14. 9.
    M. Gell-Mann, Physics Lett. 8, 214 (1964).ADSCrossRefGoogle Scholar
  15. G. Zweig, CERN preprints TH 401, 412 (1964) (unpublished).Google Scholar
  16. 10.
    H. J. Lipkin, Proc. of the Lund Int. Conf. on Elementary Particles, p. 51 (Lund 1969 ).Google Scholar
  17. 11.
    G. Preparata, Massive Quarks and Deep Inelastic Phenomena, Universita di Roma (Preprint).Google Scholar
  18. 12.
    O. W. Greenberg, Phys. Rev. Lett. 13, 598 (1964).ADSCrossRefGoogle Scholar
  19. T. Goto, O. Hara, and S. Ishida, Progr. Theor. Phys. 43, 849 (1970).ADSCrossRefGoogle Scholar
  20. J. G. Körner, Nuclear Phys. B25, 282 (1970).Google Scholar
  21. 13.
    M. Y. Han and Y. Nambu, Phys. Rev. 139B, 1006 (1965).ADSMathSciNetCrossRefGoogle Scholar
  22. 14.
    M. Gell-Mann, in “Elementary Particle Physics”, p.733 (P. Urban ed., Springer, Wien-New York, 1972 ).Google Scholar
  23. 15.
    We thank Prof. K. Symanzik for a hint in this direction.Google Scholar
  24. 16.
    Dynamics based on generalized Veneziano formulas seem to correspond to infinite component fields. For ref. see: V. Alessandrini, D. Amati, M. Le Bellac, D. Olive, Phys. Rep. lc, No. 6 (1971).Google Scholar
  25. R. J. Rivers, Nuovo Cim. 11A, 178 (1972).ADSCrossRefGoogle Scholar
  26. For dynamical quark n-point functions based on the Veneziano formula see: M. Bando, S. Machida, H. Nakkagawe, and K. Yamawaki, Progr. Theor. Phys. 47, 626 (1972) and literature quoted there.ADSCrossRefGoogle Scholar
  27. 17.
    On a more kinematical level, phenomenological questions in the framework of QUARFT were discussed by: T. Gudehus, DESY 68/11.Google Scholar
  28. C. H. Llewellyn-Smith, Ann. Phys. (N.Y.) 53, 521 (1969).CrossRefGoogle Scholar
  29. 18.
    M. Gell-Mann, Physica 1, 63 (1964).Google Scholar
  30. 19.a)
    J. V. Allaby et al., Nuovo Cim. 64A, 75 (1969).ADSCrossRefGoogle Scholar
  31. b).
    Yu. M. Antipov et al., Physics Lett. 29B, 245 (1969).ADSCrossRefGoogle Scholar
  32. M. Bott-Bodenhausen et al., Physics Lett. 40B, 693 (1972).ADSGoogle Scholar
  33. 20.
    R. Hagedorn, Nuovo Cim. Suppl. 6, 311 (1968).Google Scholar
  34. V. M. Maksimenko et al., Sov. Phys. - JETP Lett. 3, 214 (1966).ADSGoogle Scholar
  35. 21.
    T. Massam, The Quark Hunters’ Progress, CERN 68–24.Google Scholar
  36. T. Massam, The Quark Hunters’ Progress, CERN 68–24. Y. S. Kim, N. Kwak, Fields and Quanta 3, 1 (1972).Google Scholar
  37. 22.
    J. J. de Swart, Phys. Rev. Lett. 18, 618 (1967).ADSCrossRefGoogle Scholar
  38. 23.
    F. Low, Comments Nucl. and Part. Phys. 1, 52, 85 (1967).MathSciNetGoogle Scholar
  39. H. Fritzsch, M. Gell-Mann, Proc. of the XVI Int. Conference on High Energy Physics, Chicago-Batavia, Vol. 2, 135 (1972).Google Scholar
  40. 24.
    K. Johnson, Phys. Rev. D6, 1101 (1972).ADSGoogle Scholar
  41. 25.
    Similar ideas were proposed by: H. Suura, Physics Lett. 42B, 237 (1972).Google Scholar
  42. 26.
    Heavy quarks were introduced in a non-relativistic framework by: G. Morpurgo, Physics 2, 95 (1965).Google Scholar
  43. 27.
    G. Källen, Helv. Phys. Acta, 25, 417 (1952).MATHGoogle Scholar
  44. H. Lehmann, Nuovo Cim. 11, 342 (1954).MATHMathSciNetCrossRefGoogle Scholar
  45. S. S. Schweber, Relativistic Quantum Field Theory, p. 659 ( Harper and Row, New York 1961 ).Google Scholar
  46. 28.
    We thank G. Preparata for a clarifying discussion on this point.Google Scholar
  47. 29.
    We omit technical details. In view of the fact, that all hadrons may be generated by a+e annihilation, this assumption might be even justified in physics. Compare also: R. F. Dashen, D.H. Sharp, Phys. Rev. 165, 1857 (1968).ADSCrossRefGoogle Scholar
  48. 30.
    J. M. G. Fell, Transact. Am. Math. Soc. 94, 365 (1960).MATHMathSciNetGoogle Scholar
  49. R. Haag, D. Kastler, Journ. Math. Phys. 5, 848 (1964).MATHADSMathSciNetCrossRefGoogle Scholar
  50. S. Doplicher, R. Haag, J. E. Roberts, Commun. Math. Phys. 23, 199 (1971).ADSMathSciNetCrossRefGoogle Scholar
  51. 31.
    K. Symanzik, Journ. Math. Phys. 1, 249 (1960).ADSMathSciNetCrossRefGoogle Scholar
  52. for references see: K. Symanzik, “Many-Particle Structure of Green’s Functions”, Symposia on Theoretical Physics, Vol.3, 121 (1967), (Plenum Press, 1967 ).Google Scholar
  53. 32.
    J. G. Taylor, Phys. Rev. 150, 1321 (1966).ADSCrossRefGoogle Scholar
  54. D. Z. Freedman, C. Lovelace and J. M. Namyslowski, Nuovo Cim. 43A, 258 (1966).ADSCrossRefGoogle Scholar
  55. 33.
    This form is due to K. Symanzik (unpublished).Google Scholar
  56. 34.
    H. A. Bethe, E. E. Salpeter, Phys. Rev. 84, 1232 (1951).MATHADSMathSciNetCrossRefGoogle Scholar
  57. 1.
    M. Gell-Mann, F. Low, Phys. Rev. 84, 350 (1951).MATHADSMathSciNetCrossRefGoogle Scholar
  58. 35.
    S. Mandelstam, Proc. Roy. Soc. A233, 248 (1955).MATHADSMathSciNetCrossRefGoogle Scholar
  59. R. E. Cutkosky, M. Leon, Phys. Rev. 135B, 1445 (1964).ADSMathSciNetCrossRefGoogle Scholar
  60. 36.
    R. Meyer, Dissertation, Hamburg (1972); internal report DESY-T-72/10.Google Scholar
  61. 37.
    R. Dolen, D. Horn, and C. Schmid, Phys. Rev. Lett. 19, 402 (1967)ADSCrossRefGoogle Scholar
  62. R. Dolen, D. Horn, and C. Schmid, Phys. Rev. 166, 1772 (1968).ADSGoogle Scholar
  63. Application to meson-meson scattering: C. Lovelace, Physics Lett. 28B, 264 (1968).ADSGoogle Scholar
  64. 38.
    E. D. Bloom, F. J. Gilman, Phys. Rev. Lett. 25, 1140 (1970)ADSCrossRefGoogle Scholar
  65. E. D. Bloom, F. J. Gilman, Phys. Rev. D4, 2901 (1971).ADSGoogle Scholar
  66. 39.
    M. Böhm, H. Joos, M. Krammer, DESY 72 /62 (1972).Google Scholar
  67. A. Bramon, E. Etim, M. Greco, Physics Lett. 41B, 609 (1972).Google Scholar
  68. 40.
    A. Salam, R. Delbourgo, J. Strathdee, Proc. Roy. Soc. (London) A284, 146 (1965).ADSMathSciNetCrossRefGoogle Scholar
  69. 41.
    T. Gudehus, DESY-Report 68 /11 (1968).Google Scholar
  70. M. Böhm, T. Gudehus, Nuovo Cim. 57A, 578 (1968).ADSCrossRefGoogle Scholar
  71. H. Suura, B.-L. Young, Nuovo Cim. 11A, 101 (1972).ADSCrossRefGoogle Scholar
  72. 42.
    see f.i.: G. Morpurgo in “Theory and Phenomenology in Particle Physics” part A, p. 84 (Editor A. Zichichi, Academic Press New York, London (1969)).Google Scholar
  73. J. J. J. Kokkedee, “The Quark Model” (W. A. Benjamin, Inc. New York (1969)).Google Scholar
  74. 43.
    H. Harari, Phys. Rev. Lett. 22, 562 (1969).ADSCrossRefGoogle Scholar
  75. J. Rosner, Phys. Rev. Lett. 22, 689 (1969).ADSCrossRefGoogle Scholar
  76. 44.
    Y. Takahashi, Nuovo Cim. 6, 370 (1957).Google Scholar
  77. 45.
    F. Gutbrod told us about the importance of considering modifications of S’(q) according to (3.14) in phenomenological bound state models of e.m. interactions. (Compare F. Gutbrod, DESY 72 /74 (1972).Google Scholar
  78. 46.
    M. Gell-Mann, Ref. 14, for the relation between constituent quarks and current quarks.Google Scholar
  79. 47.
    J. J. J. Kokkedee, l.c.; O.W. Greenberg, Proc. of the Lund Int. Conf. on Elementary Particles, p. 385 (Lund 1969 ).Google Scholar
  80. 48.
    R. H. Dalitz, “Symmetries and the Strong Interactions”, Proc. of the XIIIth International Conference on High Energy Physics, Berkeley (1966) 215.Google Scholar
  81. R. H. Dalitz, “Mesonic Resonance States”, Meson Spectroscopy, p. 497 (C. Baltay, A. H. Rosenfeld ed., New York (1968)).Google Scholar
  82. 49.
    Ref. 34. An extensive review of the theory of the B S equation has been given by: N. N. kanishi, Progr. Theor. Phys. Suppl. 43, 1 (1969).ADSCrossRefGoogle Scholar
  83. 50.
    M. Böhm, H. Joos, M. Krammer, Nuovo Cim. 7A, 21 (1972)ADSCrossRefGoogle Scholar
  84. M. Böhm, H. Joos, M. Krammer, “Concepts in Hadron Physics”, p. 407 (Springer-Verlag, Wien, New York, 1971 ).Google Scholar
  85. 51.
    M. K. Sundaresan, P. J. S. Watson, Ann. Phys. (N.Y.) 59, 375 (1970).ADSMathSciNetCrossRefGoogle Scholar
  86. G. Preparata, in “Subnuclear Phenomena”, p. 240 (1969 International School of Physics E. Majorana, Erice).Google Scholar
  87. 52.
    G. C. Wick, Phys. Rev. 96, 1124 (1954).MATHADSMathSciNetCrossRefGoogle Scholar
  88. 53.
    M. Gourdin, Nuovo Cim. 7, 338 (1958).MATHCrossRefGoogle Scholar
  89. 54.
    A. Erdelyi, ed., “Higher Transcendental Functions”, Vol. 2 ( McGraw-Hill, New York, 1953 ).Google Scholar
  90. 55.
    E. Zur Linden, H. Mitter, Nuovo Cim. 61B, 389 (1969).ADSCrossRefGoogle Scholar
  91. 56.
    A. Pagnamenta, Nuovo Cim. 53A, 30 (1968).ADSCrossRefGoogle Scholar
  92. 57.
    See Ref. 51 and P. Becher, Diplomarbeit, Würzburg (1972).Google Scholar
  93. 58.
    M. Ciafaloni, P. Menotti, Phys. Rev. 1408, 929 (1965).ADSMathSciNetCrossRefGoogle Scholar
  94. 59.
    R. P. Feynman, M. Kislinger, F. Ravndal, Phys. Rev. D3, 2706 (1971).ADSCrossRefGoogle Scholar
  95. 60.
    M. Böhm, H. Joos, M. Krammer, Nuclear Phys. B51, 397 (1973).ADSCrossRefGoogle Scholar
  96. 61.
    M. K. Sundaresan and P. J. S. Watson, Ref. 51.Google Scholar
  97. 62.
    B. L. v. d. Waerden, “Die gruppentheoretische Methode in der Quantenmechanik”, p. 78… (Springer, Berlin 1932 ).Google Scholar
  98. 63.
    See f.i.: A. R. Edmonds, “Angular Momentum in Quantum Mechanics” (Princeton Univ. Press, 1957 ).Google Scholar
  99. 64.
    S. Mandelstam, Proc. Roy. Soc. A237, 496 (1956).MATHADSMathSciNetCrossRefGoogle Scholar
  100. 65.
    H. M. Lipinski, D. R. Snider, Phys. Rev. 176, 2055 (1968).ADSCrossRefGoogle Scholar
  101. a).
    R. F. Keam, Journ. Math. Phys. 9, 1462 (1968).Google Scholar
  102. b).
    R. F. Keam, ibid. 10, 594 (1969).Google Scholar
  103. c).
    R. F. Keam, ibid. 11, 394 (1970).Google Scholar
  104. d).
    R. F. Keam, ibid. 12, 515 (1971).MathSciNetGoogle Scholar
  105. R. Delbourgo, A. Salam, J. Strathdee, Nuovo Cim. 50A, 193 (1967).CrossRefGoogle Scholar
  106. P. Breitenlohner, MPI-Preprint (1970).Google Scholar
  107. P. Narayanaswamy, A. Pagnamenta, Nuovo Cim, 53A, 635 (1968).ADSCrossRefGoogle Scholar
  108. K. Ladânyi, Preprint, Tübingen (1972).Google Scholar
  109. 66.
    J. S. Goldstein, Phys. Rev. 91, 1516 (1953).MATHADSCrossRefGoogle Scholar
  110. S. N. Biswas, H. S. Green, Nuclear Phys. 2, 177 (1956)MATHADSCrossRefGoogle Scholar
  111. A. Bastai, L. Bertocchi, G. Furlan, M. Tonin, Nuovo Cim. 30, 1532 (1963).MATHMathSciNetCrossRefGoogle Scholar
  112. W. Kummer, Nuovo Cim. 31, 219 (1964);MathSciNetCrossRefGoogle Scholar
  113. W. Kummer, ibid. 34, 1840 (1964).Google Scholar
  114. K. Seto, Progr. Theor. Phys. 42, 1394 (1969).Google Scholar
  115. H. Ito, Progr. Theor. Phys. 43, 1035 (1970).MATHADSCrossRefGoogle Scholar
  116. N. Nakanishi, Journ. Math. Phys. 12, 1578 (1971).MATHGoogle Scholar
  117. 67.
    D. Zum Winkel, Diplomarbeit, Hamburg (in preparation).Google Scholar
  118. 68.
    H. Harari, Proc. of the 14th International Conference on High-Energy Physics, Vienna (1968), p. 195.Google Scholar
  119. H. J. Lipkin, Ref. 10.Google Scholar
  120. 69.
    W. Thirring, in “Subnuclear Phenomena” (1.c.) p.200.Google Scholar
  121. 70.
    M. Krammer, internal report DESY-T 73/1.Google Scholar
  122. 71.
    H. Joos, Fortschritte der Physik 10, 65 (1962).MATHCrossRefGoogle Scholar
  123. 72.
    Review of particle properties, Particle Data Group, Physics Lett. 39B, 1 (1972).CrossRefGoogle Scholar
  124. 73.
    M. Böhm, H. Joos, M. Krammer, DESY 72 /62 (1972).Google Scholar
  125. T. Kobayashi, Progr. Theor. Phys. 48, 335 (1972).ADSCrossRefGoogle Scholar
  126. 74.
    H. Pietschmann, W. Thirring, University of Vienna, Scientific Note No. 32 (1965).Google Scholar
  127. R. van Royen, V. F. Weisskopf, Nuovo Cim. 50, 617 (1967);ADSCrossRefGoogle Scholar
  128. R. van Royen, V. F. Weisskopf, ibid. 51, 583 (1967).ADSGoogle Scholar
  129. 75.
    J. Lefrancois, Proc. of the 1971 Int. Symposium on Electron and Photon Interactions at High Energies, p. 51 (Cornell Univ.).Google Scholar
  130. 76.
    G. Barbarino et al., Lett. Nuovo Cim. 3, 689 (1972).CrossRefGoogle Scholar
  131. 77.
    G. Smadja et al., in “Experimental Meson Spectroscopy 1972” (Third Philadelphia Conference) p. 349.Google Scholar
  132. 78.
    F. Ceradini et al., Physics Lett. 43B, 341 (1973).ADSCrossRefGoogle Scholar
  133. 79.
    J. J. Sakurai, D. Schildknecht, Physics Lett. 40B, 121 (1972).ADSGoogle Scholar
  134. 80.
    N. Cabibbo, R. Gatto, Phys. Rev. 124, 1577 (1961).ADSCrossRefGoogle Scholar
  135. 81.
    R. P. Feynman, Proc. of the Third Topical Conference on High Energy Collisions of Hadrons, Stony Brook. ( Gordon and Breach, New York, 1969 ).Google Scholar
  136. 82.
    H. Fritzsch, M. Gell-Mann, Proc. of the Coral Gables Conference on Fundamental Interactions at High Energy, Vol. 2, p. 1 ( Gordon and Breach, New York, London, Paris, 1971 ).Google Scholar
  137. 83.
    S. Weinberg, Phys. Rev. Lett. 18, 507 (1967).ADSCrossRefGoogle Scholar
  138. 84.
    Electromagnetic meson decays in the P+V-S model were discussed recently by D. Flamm and J. Sanchez; Lett. Nuovo Cim. 6, 129 (1973).CrossRefGoogle Scholar
  139. 85.
    R. Delbourgo, M. A. Rashid, A. Salam, J. Strathdee, Proc. of the Seminar on High Energy Physics and Elementary Particles (Trieste 1965 ) p. 455.Google Scholar
  140. 86.
    For a review on relativistic generalizations of SU(6) we refer to: H. Ruegg, W. Rühl, T.S. Santhanam, H.lv. Phys. Acta 40, 9 (1967).Google Scholar
  141. 87.
    L. I. Schiff, Phys. Rev. Lett. 17, 612 (1966).ADSCrossRefGoogle Scholar
  142. O. W. Greenberg, Phys. Rev. 150, 1177 (1966).ADSCrossRefGoogle Scholar
  143. 1.
    G. Morpurgo, Physics Lett. 20, 684 (1966).ADSCrossRefGoogle Scholar
  144. 88.
    G. Morpurgo, Ref. 42. H. J. Lipkin, Phys. Rev. 159, 1303 (1967).CrossRefGoogle Scholar
  145. 89.
    Such modified couplings are suggested by experiment: M. Afzal et al., Nuovo Cim. 15A, 61 (1973).ADSCrossRefGoogle Scholar
  146. 90.
    J. Nuttal, Phys. Rev. 160, 1459 (1967).ADSCrossRefGoogle Scholar
  147. 91.
    D. B. Lichtenberg, Phys. Rev. 178, 2197 (1969).ADSCrossRefGoogle Scholar
  148. A. N. Mitra, Nuovo Cim. 56A, 1164 (1968).ADSCrossRefGoogle Scholar
  149. 92.
    For a review of three-particle scattering we refer to: W. Sandhas, in “Elementary Particle Physics” (l.c.) p. 57.Google Scholar
  150. J. G. Taylor, Ref. 32.Google Scholar
  151. 93.
    O. W. Greenberg, Ref. 12.Google Scholar
  152. 94.
    G. Berendt, E. Weimar, private communication.Google Scholar
  153. 95.
    G. Berendt, E. Weimar, Lett. Nuovo Cim. 5, 613 (1972).CrossRefGoogle Scholar
  154. 96.
    L. Susskind, Phys. Rev. Lett. 23, 545 (1969).ADSCrossRefGoogle Scholar
  155. D. Geffen (private communication).Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • M. Böhm
    • 1
  • H. Joos
    • 2
  • M. Krammer
    • 2
  1. 1.Physikalisches InstitutUniversität WürzburgGermany
  2. 2.Deutsches Elektronen-SynchrotronDESYHamburgGermany

Personalised recommendations