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.
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References
S. Coleman, Phys. Rev. D15 (1977), 2929.
C. Callan and S. Coleman, Phys. Rev. D16 (1977), 1762.
See e.g. S. Weinberg, Phys. Rev. Letters 37 (1976), 657–
S. Weinberg, Phys. Rev. Letters 19 (1967), 1264.
S. Weinberg, Phys. Rev. Letters 19 (1967), 1264. A. Salam, Elementary Particle Theory, ed. by N. Svartholm (Stockholm, 1968)
S.L. Glasnow, J. Iliopoulos and L. Maiani, Phys. Rev., D2 (1970), 1285.
S. Weinberg, Phys. Rev. Letters 29 (1972), 388.
J.C. Pati and A. Salam, Phys. Rev. D10 (1974), 275.
R.N. Mohapatra and J.C. Pati, Phys. Rev. D11 (1975), 566 and 2558.
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.
S.L. Glashow and S. Weinberg, Phys. Rev. D15 (1977), 1958.
See e.g. A. de Rujula, H. Georgi and S.L. Glashow, Ann. of Phys. 109 (1977), 258.
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.
M. Gell-Mann, R.J. Oakes and B. Renner, Phys. Rev. 175 (1968), 2195
S. Weinberg, “The problem of Mass”, Festschrift for I.I. Rabi, to be published by N.Y. Academy of Sciences (1978).
H. Georgi and H.D. Politzer, Phys. Rev. D14 (1976), 1829.
R. F. Dashen, Phys. Rev. 183 (1969), 1245.
G. Segré and J. Weyers, Phys. Lett. 62B (1976), 91.
Figure I is reproduced from relerence(12) without any change.
S. Weinberg, Phys. Rev. D7 (1973), 2887.
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.
See e.g. S. Weinberg, Phys. Rev. Letters 29 (1972), 368.
A. Duncan and P. Schattner, Phys. Rev. D7 (1973),1861.
D.Z.Freedman and W.Kummer, Phys. Rev.D7 (1973), 1829.
S.Y. Pi, Phys. Rev. D7 (1973), 3750.
J. Liberman, Phys. Rev. D9 (1974), 1749.
D.Wilkinson, Ph. D. Thesis, University of Pennsylvania (1975).
M. de Crombrugghe, H. Haut and J. Weyers, Phys. Lett. 71B (1977), 400.
H. Haut, Ph.D. Thesis, University of Louvain (1978).
The only exception which is in itself quite interesting is when m = 0!
See e.g. J. Ellis, Charm and beyond, Lectures given at the Cargèse Summer School 1977.
F. Wilczek and A. Zee, Phys. Rev. Letters 42 (1979), 421.
For a beautiful review and references to earlier work, see R. Gatto, The Mass Matrix, Université de Genève, preprint UGVADPT 1979/04–199.
This relation was originally derived by R. Gatto, G. Sartori and N. Tonin, Phys. Rev. Lett. 28b (1968), 128.
H. Fritzsch, Phys. Lett. 70B (1977), 436.
F. Wilczek and A. Zee, Phys. Letters 70B (1977), U18.
M. de Crombrugghe, Phys. Letters 80B (1979), 365 and Ph.D. Thesis, University of Leuven (1979).
H. Fritzsch, Phys. Lett. 73B (1978), 317. CERN Preprint TH 2640 (1979).
The matrix for example is not acceptable since mb ≠ ms + md and mt ≠ mc + mu.
Some recent applications of permutation symmetry can be found in E. Derman,Phys. Letters 78B (1978) 797.
S. Pakvasa and H. Sugawara, Phys. Letters 78B (1978) 497.
H. Sato, Nuclear Phys. B152 (1979), 36.
See also references (30) and (34). Other discrete symmetries have also been considered, See e.g. P. Krawczyk, Warsaw University Preprint 1979.
H. Harari, H. Haut and J. Weyers, Phys. Lett. 78b (1978), 459.
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.
G. Segré, H.A. Weldon and J. Weyers, Phys. Lett. 83B (1979), 351.
The uniqueness follows from the choice of eq. (75).
In other words we choose an extra discrete symmetry for the leptons which forces their mass matrix to be diagonal, see rel.(31).
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.
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).
For a simple way out, using soft breakings(10), see e.g. H. Georgi and V. Nanopoulos, Phys. Lett. 82B (1979), 98.
S. Coleman and E. Weinberg, Phys. Rev. D7 (1973), 1888.
E. Gildener and S. Weinberg, Phys. Rev. D13 (1976), 3333.
H. Sato, Nuclear Phys. B148 (1979), 433.
e.g. S. Barr and A. Zee, Phys. Rev. D18 (1978) 4213 and references quoted therein.
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Weyers, J. (1980). The Spectrum of Leptons and Quarks. In: Lévy, M., Basdevant, JL., Speiser, D., Weyers, J., Gastmans, R., Jacob, M. (eds) Quarks and Leptons. NATO Advanced Study Institutes Series, vol 61. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-7197-7_10
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