Summary
In terms of an intergenerationU(3) algebra, a numerical model is constructed for quark mass matrices, predicting the top-quark mass around 108 GeV and theCP-violating phase around 71°. The CKM matrix is nonsymmetric in moduli with |V ub| being very small. The model is motivated by the author's previous work on three replicas of the Dirac particle, presumably resulting into three generations of leptons and quarks. The paper may be also viewed as an introduction to a new method of intrinsic dynamical description of lepton and quark mass matrices.
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References
H. Fritzsch:Nucl. Phys. B,155, 189 (1979).
H. Fritzsch andJ. Plankl:Flavour democracy and the lepton-quark hierarchy, CERN-TH 5612/89 (December 1989).
W. Kròlikowski:Semiempirical sum rule for electron, muon and tau masses, Aachen report PITHA 90/7 (March 1990), unpublished.
W. Kròlikowski:Acta Phys. Pol. B,21, 871 (1990).
Particle Data Group:Phys. Lett. B,204, 1 (1988).
For this point cf.Y. Nir andH. R. Quinn:Learning about the CKM matrix from CP asymmetries, SLAC-PUB-5223 (April 1990).
For a general discussion of Cabibbo-Kobayashi-Maskawa matrix with symmetric moduli cf.G. C. Branco andP. A. Parada:Is the CKM matrix symmetric? CERN-TH 5679/90 (March 1990); for an interesting example cf.P. Kielanowski:Phys. Rev. Lett.,63, 2189 (1989).
G. Buchalla, A. Buras andM. Harlander: The anatomy of\ge’/\ge in the standard model, MIP-PAE/PTh 63/89 (October 1989).
W. A. Bardeen, C. T. Hill andM. Lindner:Minimal dynamical symmetry breaking of the standard model, FERMI-PUB-89/127-T (July 1989).
F. J. Gilman:CP violation, SLAC-PUB-5156 (December 1989).
ForN=1 eq. (A.5) is the usual Dirac equation and forN=2 it is equivalent to the Kähler equation,E. Kähler:Rend. Mat.,21, 425 (1962). Note that the latter equation was essentially discovered as early as 1928 by Ivanenko and Landau (Z. Phys.,48, 341 (1928)), soon after the Dirac equation (Proc. R. Soc. London,117, 610 (1928)).
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Supported by the Deutsche Forschungsgemeinschaft.
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Kròlikowski, W. An algebraic model for quark mass matrices. Nuov Cim A 104, 1321–1335 (1991). https://doi.org/10.1007/BF02789575
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DOI: https://doi.org/10.1007/BF02789575