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The Spectrum of Leptons and Quarks

  • J. Weyers
Conference paper
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 61)

Abstract

The proliferation of quarks and leptons remains one of the least understood features in our present day description of the fundamental structure of matter. The only distinguishing property of the successive generations of fermions seems to be their mass. The purpose of these lectures is to review what is known — or believed — about quark and lepton masses. In the first section we briefly recall the role of the Higgs sector in a spontaneously broken gauge theory of the electroweak force and in section II we review the conventional wisdom on quark masses from current algebra and in a confining theory such as QCD. At this stage all quark (and lepton) masses and mixing angles are unrelated and fundamental parameters in our theory! In section III we then define rather sketchily what a natural symmetry is and under which conditions it allows certain parameters to be calculated; section IV, finally is devoted to a very biased and non exhaustive list of models which attempt to relate ?ermion masses and mixing angles.

Keywords

Yukawa Coupling Quark Masse Mass Matrice Higgs Sector Vacuum Expectation Value 
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.

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References

  1. (1).
    S. Coleman, Phys. Rev. D15 (1977), 2929.ADSGoogle Scholar
  2. C. Callan and S. Coleman, Phys. Rev. D16 (1977), 1762.ADSGoogle Scholar
  3. 2).
    See e.g. S. Weinberg, Phys. Rev. Letters 37 (1976), 657–ADSCrossRefGoogle Scholar
  4. 2a).
    S. Weinberg, Phys. Rev. Letters 19 (1967), 1264.ADSCrossRefGoogle Scholar
  5. 2b).
    S. Weinberg, Phys. Rev. Letters 19 (1967), 1264. A. Salam, Elementary Particle Theory, ed. by N. Svartholm (Stockholm, 1968)Google Scholar
  6. 2b).
    S.L. Glasnow, J. Iliopoulos and L. Maiani, Phys. Rev., D2 (1970), 1285.ADSGoogle Scholar
  7. (4).
    S. Weinberg, Phys. Rev. Letters 29 (1972), 388.ADSCrossRefGoogle Scholar
  8. (4).
    J.C. Pati and A. Salam, Phys. Rev. D10 (1974), 275.ADSGoogle Scholar
  9. (4).
    R.N. Mohapatra and J.C. Pati, Phys. Rev. D11 (1975), 566 and 2558.ADSGoogle Scholar
  10. (5).
    See e.g. Proceedings of the International V-Conlerence (Bergen, 1979) earlier values can be found in C. Baltay, Proceedings of the XIXth International Conference on High Energy Physics, Tokyo 1978.Google Scholar
  11. 6).
    S.L. Glashow and S. Weinberg, Phys. Rev. D15 (1977), 1958.ADSGoogle Scholar
  12. 7).
    See e.g. A. de Rujula, H. Georgi and S.L. Glashow, Ann. of Phys. 109 (1977), 258.ADSCrossRefGoogle Scholar
  13. 8).
    M. Kobayashi and K. Maskawa, Prog. Theor. Phys. 49 (1973), 652. For recent reviews on the values of the mixing angles see e.g. H. Harari, Phys. Reports 42C (1978), 235. L. Maiani, Proceedings of the Cargèse Summer School, 1979. V. Barger, W.F. Long and S. Pakvasa, preprint UH 511 - 335 - 79 UW-COO-881–90 (1979). See e.g. M.K. Gaillard, Proceedings of the Cargèse Summer School 1979.ADSCrossRefGoogle Scholar
  14. 9).
    M. Gell-Mann, R.J. Oakes and B. Renner, Phys. Rev. 175 (1968), 2195ADSCrossRefGoogle Scholar
  15. 10).
    S. Weinberg, “The problem of Mass”, Festschrift for I.I. Rabi, to be published by N.Y. Academy of Sciences (1978).Google Scholar
  16. 11).
    H. Georgi and H.D. Politzer, Phys. Rev. D14 (1976), 1829.ADSGoogle Scholar
  17. 12).
    R. F. Dashen, Phys. Rev. 183 (1969), 1245.ADSCrossRefGoogle Scholar
  18. (14).
    G. Segré and J. Weyers, Phys. Lett. 62B (1976), 91.ADSGoogle Scholar
  19. 15).
    Figure I is reproduced from relerence(12) without any change.Google Scholar
  20. 16).
    S. Weinberg, Phys. Rev. D7 (1973), 2887.ADSGoogle Scholar
  21. (17).
    K. Symanzik in Coral Gables Conference on Fundamental Interactions at High Energies II edited by A. Perlmutter et al., Gordon and Breach, New York 1970.Google Scholar
  22. (18).
    See e.g. S. Weinberg, Phys. Rev. Letters 29 (1972), 368.ADSGoogle Scholar
  23. (18a).
    A. Duncan and P. Schattner, Phys. Rev. D7 (1973),1861.ADSGoogle Scholar
  24. (18b).
    D.Z.Freedman and W.Kummer, Phys. Rev.D7 (1973), 1829.ADSGoogle Scholar
  25. (18c).
    S.Y. Pi, Phys. Rev. D7 (1973), 3750.ADSGoogle Scholar
  26. (18d).
    J. Liberman, Phys. Rev. D9 (1974), 1749.ADSGoogle Scholar
  27. (18e).
    D.Wilkinson, Ph. D. Thesis, University of Pennsylvania (1975).Google Scholar
  28. (18f).
    M. de Crombrugghe, H. Haut and J. Weyers, Phys. Lett. 71B (1977), 400.ADSGoogle Scholar
  29. (18g).
    H. Haut, Ph.D. Thesis, University of Louvain (1978).Google Scholar
  30. 19).
    The only exception which is in itself quite interesting is when m = 0!Google Scholar
  31. 20).
    See e.g. J. Ellis, Charm and beyond, Lectures given at the Cargèse Summer School 1977.Google Scholar
  32. 21).
    F. Wilczek and A. Zee, Phys. Rev. Letters 42 (1979), 421.ADSCrossRefGoogle Scholar
  33. 22).
    For a beautiful review and references to earlier work, see R. Gatto, The Mass Matrix, Université de Genève, preprint UGVADPT 1979/04–199.Google Scholar
  34. 23).
    This relation was originally derived by R. Gatto, G. Sartori and N. Tonin, Phys. Rev. Lett. 28b (1968), 128.ADSGoogle Scholar
  35. (24).
    H. Fritzsch, Phys. Lett. 70B (1977), 436.ADSGoogle Scholar
  36. 25).
    F. Wilczek and A. Zee, Phys. Letters 70B (1977), U18.Google Scholar
  37. 26).
    M. de Crombrugghe, Phys. Letters 80B (1979), 365 and Ph.D. Thesis, University of Leuven (1979).ADSGoogle Scholar
  38. (27).
    H. Fritzsch, Phys. Lett. 73B (1978), 317. CERN Preprint TH 2640 (1979).ADSGoogle Scholar
  39. (28).
    The matrix for example is not acceptable since mb ms + md and mt mc + mu.Google Scholar
  40. (29).
    Some recent applications of permutation symmetry can be found in E. Derman,Phys. Letters 78B (1978) 797.Google Scholar
  41. S. Pakvasa and H. Sugawara, Phys. Letters 78B (1978) 497.MathSciNetGoogle Scholar
  42. H. Sato, Nuclear Phys. B152 (1979), 36.ADSGoogle Scholar
  43. (29).
    See also references (30) and (34). Other discrete symmetries have also been considered, See e.g. P. Krawczyk, Warsaw University Preprint 1979.Google Scholar
  44. (30).
    H. Harari, H. Haut and J. Weyers, Phys. Lett. 78b (1978), 459.ADSGoogle Scholar
  45. (30).
    S. Meljanac and S. Pallua,University of Zagreb, preprint 1979. The discrete symmetry in this case in S3L x S3R. One of the most interesting aspects of this approach is that it led to a numerical value for the Cabibbo angle.Google Scholar
  46. 31).
    G. Segré, H.A. Weldon and J. Weyers, Phys. Lett. 83B (1979), 351.ADSGoogle Scholar
  47. 32).
    The uniqueness follows from the choice of eq. (75).Google Scholar
  48. 33).
    In other words we choose an extra discrete symmetry for the leptons which forces their mass matrix to be diagonal, see rel.(31).Google Scholar
  49. (34).
    This relation was first obtained, I believe, by S. Pakvasa and H. Sugawara, reference (29). See e.g. the talk by S. Pakvasa at 1979, Bergen, to be published.Google Scholar
  50. 35).
    It is probably fair to estimate the theoretical errors on this number to be of the order of 10–20 %. For other estimates see e.g. ref. (34).Google Scholar
  51. 36).
    For a simple way out, using soft breakings(10), see e.g. H. Georgi and V. Nanopoulos, Phys. Lett. 82B (1979), 98.ADSGoogle Scholar
  52. 37).
    S. Coleman and E. Weinberg, Phys. Rev. D7 (1973), 1888.ADSGoogle Scholar
  53. 37a).
    E. Gildener and S. Weinberg, Phys. Rev. D13 (1976), 3333.ADSGoogle Scholar
  54. 37b).
    H. Sato, Nuclear Phys. B148 (1979), 433.ADSGoogle Scholar
  55. (38).
    e.g. S. Barr and A. Zee, Phys. Rev. D18 (1978) 4213 and references quoted therein.ADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • J. Weyers
    • 1
  1. 1.Institut de Physique ThéoriqueUniversité de LouvainLouvain-la-NeuveBelgium

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