Variations on a theme: The ansatz of Stech for the quark mass matrices

L. Lavoura

doi:10.1103/PhysRevD.41.2275

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Variations on a theme: The ansatz of Stech for the quark mass matrices

L. Lavoura

Instituto Nacional de Investigação Científica, Centro de Física da Matéria Condensada, Avenida do professor Gama Pinto, 2, P-1699 Lisboa Codex, Portugal

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Phys. Rev. D 41, 2275 – Published 1 April, 1990

DOI: https://doi.org/10.1103/PhysRevD.41.2275

Abstract

I analyze the Ansatz of Stech for the quark mass matrices, showing that it is equivalent to a system of three linear equations among the squared moduli of the Cabibbo-Kobayashi-Maskawa matrix elements. I show that in the Ansatz of Stech the roles of $M_{U}$ and $M_{D}$ may be exchanged, and suggest a generalization of the Ansatz of Stech in which the top-quark mass may be higher than 100 GeV.

References (24)

B. Stech, Phys. Lett. 130B, 189 (1983).
H. Fritzsch, Phys. Lett. 73B, 317 (1978); Nucl. Phys. B155, 189 (1979); L. F. Li, Phys. Lett. 84B, 461 (1979).
M. Gronau, R. Johnson and J. Schechter, Phys. Rev. Lett. 54, 2176 (1985).
J. Yoh, recent results of the Collider Detector at Fermilab (CDF) Collaboration, talk presented at the 1989 DESY Theory Workshop (unpublished). The bound is $m_{t}$ > 72 GeV, 95% C.L.
H. Fritzsch, Report No. MPI-PAE/PTh 26/89, 1989 (unpublished).
N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963); S. L. Glashow, J. Iliopoulos and L. Maiani, Phys. Rev. D 2, 1285 (1970); M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973).
H. Harari, H. Haut and J. Weyers, Phys. Lett. 78B, 459 (1978).
S. L. Glashow, Nucl. Phys. 22, 579 (1961); S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967); A. Salam, in Elementary Particle Theory: Relativistic Groups and Analyticity (Nobel Symposium No. 8), edited by N. Svartholm (Almqvist and Wiksell, Stockholm, 1968).
G. C. Branco and L. Lavoura, Phys. Lett. B 208, 123 (1988).
G. C. Branco and D. D. Wu, Phys. Lett. B 205, 353 (1988).
C. Jarlskog and A. Kleppe, Nucl. Phys. B286, 245 (1987); C. Jarlskog, Phys. Rev. D 35, 1685 (1987).
L. Lavoura, Phys. Lett. B 228, 245 (1989).
J. Gasser and H. Leutwyler, Phys. Rep. 87, 77 (1982).
K. R. Schubert, in Proceedings of the 1988 Summer School in High Energy Physics and Cosmology, edited by J. C. Pati and Q. Shafi (World Scientific, Singapore, 1989). In this paper I do not take into account the recent analysis of the ARGUS Collaboration which indicates that | $V_{ub}$ | is nonzero, but is much smaller than the previous upper bound. See M. Danilov, in Proceedings of the XIV International Symposium on Lepton and Photon Interactions, Stanford, California, edited by M. Riordan (World Scientific, Singapore, in press). See also CLEO Collaboration, R. Fulton et al.., Report No. CLNS-89/951 (unpublished).
G. Ecker, Z. Phys. C 24, 353 (1984).
X. G. He and W. S. Hou, Phys. Rev. D 41, 1517 (1990).
M. Gronau, V. Gupta, R. Johnson and J. Schechter, Phys. Rev. D 33, 3368 (1986).
M. Gronau and J. Schechter, Phys. Rev. Lett. 54, 385 (1985); ibid. 54, 1209(E) (1985).
C. Jarlskog, Phys. Rev. Lett. 55, 1039 (1985); I. Dunietz, O. W. Greenberg and D. D. Wu, 55, 2935 (1985).
A model which may yield this Ansatz was proposed by G. Ecker, W. Grimus and H. Neufeld, Nucl. Phys. B247, 70 (1984).
For a review, see R. Peccei, in CP Violation, edited by C. Jarlskog (World Scientific, Singapore, 1989).
S. Weinberg, Trans. N.Y. Acad. Sci. Series II, 38 (1977).
K. Sasaki, Z. Phys. C 32, 149 (1986); B. Grzadkowski and M. Linder, Phys. Lett. B 193, 71 (1987); C. H. Albright and M. Lindner, ibid. 213, 347 (1988).
H. Albrecht et al., Phys. Lett. B 192, 245 (1987); M. Artuso et al., Phys. Rev. Lett. 62, 2233 (1989).

[c1] B. Stech, Phys. Lett. 130B, 189 (1983).

[c2] H. Fritzsch, Phys. Lett. 73B, 317 (1978); Nucl. Phys. B155, 189 (1979); L. F. Li, Phys. Lett. 84B, 461 (1979).

[c3] M. Gronau, R. Johnson and J. Schechter, Phys. Rev. Lett. 54, 2176 (1985).

[c4] J. Yoh, recent results of the Collider Detector at Fermilab (CDF) Collaboration, talk presented at the 1989 DESY Theory Workshop (unpublished). The bound is $m_{t}$ > 72 GeV, 95% C.L.

[c5] H. Fritzsch, Report No. MPI-PAE/PTh 26/89, 1989 (unpublished).

[c6] N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963); S. L. Glashow, J. Iliopoulos and L. Maiani, Phys. Rev. D 2, 1285 (1970); M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973).

[c7] H. Harari, H. Haut and J. Weyers, Phys. Lett. 78B, 459 (1978).

[c8] S. L. Glashow, Nucl. Phys. 22, 579 (1961); S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967); A. Salam, in Elementary Particle Theory: Relativistic Groups and Analyticity (Nobel Symposium No. 8), edited by N. Svartholm (Almqvist and Wiksell, Stockholm, 1968).

[c9] G. C. Branco and L. Lavoura, Phys. Lett. B 208, 123 (1988).

[c10] G. C. Branco and D. D. Wu, Phys. Lett. B 205, 353 (1988).

[c11] C. Jarlskog and A. Kleppe, Nucl. Phys. B286, 245 (1987); C. Jarlskog, Phys. Rev. D 35, 1685 (1987).

[c12] L. Lavoura, Phys. Lett. B 228, 245 (1989).

[c13] J. Gasser and H. Leutwyler, Phys. Rep. 87, 77 (1982).

[c14] K. R. Schubert, in Proceedings of the 1988 Summer School in High Energy Physics and Cosmology, edited by J. C. Pati and Q. Shafi (World Scientific, Singapore, 1989). In this paper I do not take into account the recent analysis of the ARGUS Collaboration which indicates that | $V_{ub}$ | is nonzero, but is much smaller than the previous upper bound. See M. Danilov, in Proceedings of the XIV International Symposium on Lepton and Photon Interactions, Stanford, California, edited by M. Riordan (World Scientific, Singapore, in press). See also CLEO Collaboration, R. Fulton et al.., Report No. CLNS-89/951 (unpublished).

[c15] G. Ecker, Z. Phys. C 24, 353 (1984).

[c16] X. G. He and W. S. Hou, Phys. Rev. D 41, 1517 (1990).

[c17] M. Gronau, V. Gupta, R. Johnson and J. Schechter, Phys. Rev. D 33, 3368 (1986).

[c18] M. Gronau and J. Schechter, Phys. Rev. Lett. 54, 385 (1985); ibid. 54, 1209(E) (1985).

[c19] C. Jarlskog, Phys. Rev. Lett. 55, 1039 (1985); I. Dunietz, O. W. Greenberg and D. D. Wu, 55, 2935 (1985).

[c20] A model which may yield this Ansatz was proposed by G. Ecker, W. Grimus and H. Neufeld, Nucl. Phys. B247, 70 (1984).

[c21] For a review, see R. Peccei, in CP Violation, edited by C. Jarlskog (World Scientific, Singapore, 1989).

[c22] S. Weinberg, Trans. N.Y. Acad. Sci. Series II, 38 (1977).

[c23] K. Sasaki, Z. Phys. C 32, 149 (1986); B. Grzadkowski and M. Linder, Phys. Lett. B 193, 71 (1987); C. H. Albright and M. Lindner, ibid. 213, 347 (1988).

[c24] H. Albrecht et al., Phys. Lett. B 192, 245 (1987); M. Artuso et al., Phys. Rev. Lett. 62, 2233 (1989).

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Variations on a theme: The ansatz of Stech for the quark mass matrices

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