Unified gauge theories with right-handed currents and heavy fermions

Rabindra N. Mohapatra

doi:10.1103/PhysRevD.13.113

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Unified gauge theories with right-handed currents and heavy fermions

Rabindra N. Mohapatra

Department of Physics, City College of the City University of New York, New York, New York 10031

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Phys. Rev. D 13, 113 – Published 1 January, 1976

DOI: https://doi.org/10.1103/PhysRevD.13.113

Abstract

Gauge models with heavy fermions and right-handed currents are discussed based on the gauge groups ${SU (2)}_{A} \times U (1) \times {SU (4)}^{'}, {SU (2)}_{A} \times {SU (2)}_{B} \times {SU (4)}^{'}$ , and SU(4) × SU ${(4)}^{'}$ and are constructed so as to lead to the $Δ I = \frac{1}{2}$ rule. SU(4) × SU ${(4)}^{'}$ is advocated as the ultimate unifying gauge group of nature, and it is shown how at various stages of spontaneous breakdown both the ${SU (2)}_{A} \times {SU (2)}_{B} \times {SU (4)}^{'}$ and ${SU (2)}_{A} \times U (1) \times {SU (4)}^{'}$ groups manifest themselves. We also show that $CP$ violation takes an interesting complexion in these models and leads to exactly the relations $η_{+ -} ≃ η_{00}$ in $K_{L} \to 2 π$ decays. Furthermore, we show that the magnitude of $CP$ violation is related to gauge interactions that violate the heavy quark degeneracy.

References (39)

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S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D 2, 1285 (1970)
A. Gamba, R. E. Marshak, and S. Okubo, Proc. Natl. Acad. Sci. USA 45, 881 (1959) J. D. Bjorken and S. L. Glashow, Phys. Lett. 11, 255 (1964)
M. Y. Han and Y. Nambu, Phys. Rev. 139, B1006 (1965) A. Tavkhelidz̆e et al., in proceedings of the Conference on High Energy Physics, (unpublished) O. W. Greenberg, Phys. Rev. Lett. 13, 596 (1964)
J. Aubert et al., Phys. Rev. Lett. 33, 1406 (1974) G. S. Abrams et al., ibid. 33, 1453 (1974)
F. J. Gilman, SLAC report, 1975 (unpublished)
R. M. Barnett, Phys. Rev. Lett. 34, 41 (1975) H. Harari, Phys. Lett. 57B, 265 (1975) F. Wilczek, 59B, 105 (1975)
G. Feldman, report of SPEAR results given at the Palermo International Conference, 1975 (unpublished)
J. C. Pati and A. Salam, Phys. Rev. D 10, 275 (1974)
[9] R. N. Mohapatra and J. C. Pati, Phys. Rev. D 11, 566 (1975) ibid.112588 (1975) G. Senjanovic and R. N. Mohapatra, ibid. 12, 1502 (1975) R. N. Mohapatra, ibid. 9, 3558 (1974) R. N. Mohapatra, J. C. Pati, and L. Wolfenstein, ibid. 11, 3319 (1975)
([10]) R. N. Mohapatra and J. C. Pati, Phys. Rev. D 11, 2588 (1975) H. Fritzsuch and P. Minkowski, Phys. Lett. 56B, 69 (1975)
J. C. Pati and A. Salam, Phys. Lett. 58B, 333 (1975)
D. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973) H. D. Politzer, ibid. 30, 1346 (1973)
S. Weinberg, Rev. Mod. Phys. 46, 255 (1974) M. A. B. Bég and A. Sirlin, Annu. Rev. Nucl. Sci. 24, 379 (1974) J. Iliopoulos, in Proceedings of the XVII International Conference on High Energy Physics, London, 1974, edited by J. R. Smith (Rutherford Laboratory, Chilton, Didcot, Berkshire, England, 1974), p. III-89
R. N. Mohapatra, Phys. Rev. D 6, 2023 (1972)
A. De Rújula, H. Georgi and S. L. Glashow, Phys. Rev. Lett. 35, 69 (1975)
H. Fritzsch and P. Minkowski, Caltech Report No. 68-503, 1975 (unpublished)
F. Wilczek, A. Zee, R. Kingsley and S. Treiman, Phys. Rev. D 12, 2768 (1975)
G. Branco, T. Hagiwara and R. N. Mohapatra, preceding paper, Phys. Rev. D 13, 104 (1976)
A. De Rújula, H. Georgi, and S. L. Glashow, Phys. Rev. D 12, 3589 (1975)
S. Pakvasa, W. A. Simmons, and S. F. Tuan, Phys. Rev. Lett. 35, 702 (1975)
M. R. Krishnaswamy, M. G. K. Menon, V. S. Narashinham, N. Ito, S. Kawakami, and S. Miyake, TIFR report (to be published in Pramana) Phys. Lett. 57B, 105 (1975)
J. C. Pati and A. Salam, ICTP report, 1975 (unpublished) O. W. Greenberg, Phys. Rev. Lett. 35, 1120 (1975) J. D. Bjorken and C. H. Woo. C. K. Chang, Phys. Rev. D 5, 950 (1972) J. Bartelski and W. Krolikowski, Warsaw report (unpublished)
R. E. Marshak, Riazuddin, and C. P. Ryan, Theory of Weak Interactions in Particle Physics (Wiley, New York, 1969)
G. Snow, Nucl. Phys. B55, 445 (1973) M. Gaillard, B. W. Lee, and J. Rosner, Rev. Mod. Phys. 47, 277 (1975)
A. De Rújula, H. Georgi, and S. L. Glashow, Phys. Rev. Lett. 35, 628 (1975)
Omitted endnote
V. Barger, R. Weiler, and R. J. N. Phillips, Phys. Rev. Lett. 35, 692 (1975)
A. Benvenuti et al., Phys. Rev. Lett. 35, 1249 (1975)
L. Wolfenstein, in Particles and Fields—1974, proceedings of the 1974 Williamsburg meeting of the Division of Particles and Fields of the American Physical Society, edited by Carl E. Carlson (A. I. P., New York, 1975)
E. A. Paschos, Brookhaven report, 1975 (unpublished)
R. Kingsley, F. Wilczek, S. Treiman, and A. Zee, Phys. Rev. D 11, 1919 (1975) M. B. Einhorn and C. Quigg, 12, 2015 (1975) A. Pais and V. Rittenberg, Phys. Rev. Lett. 34, 707 (1975)
T. Hagiwara, G. Branco, R. N. Mohapatra, and D. P. Sidhu, Phys. Rev. D (to be published)
A. M. Boyarski et al., Phys. Rev. Lett. 35, 195, (1975)
M. B. Einhorn and C. Quigg, Phys. Rev. Lett. 35, 1114 (1975)
R. N. Mohapatra, J. S. Rao, and R. E. Marshak, Phys. Rev. Lett. 20, 1081 (1968) B. L. Ioffe and E. P. Shabalin, Yad. Fiz. 6, 828 (1967) [Sov. J. Nucl. Phys. 6, 603 (1968)]
R. N. Mohapatra, in Particles and Fields—1974, proceedings of the 1974 Williamsburg meeting of the Division of Particles and Fields of the American Physical Society, edited by Carl E. Carlson ([30])
L. Wolfenstein, CERN report, 1974 (unpublished)
E. Golowich and B. Holstein, Phys. Rev. Lett. 35, 831 (1975)

[c1] S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967) A. Salam, in Elementary Particle Physics: General Relativity and Analyticity (Nobel Symposium No. 8), edited by N. Svartholm (Almqvist and Wiksells, Stockholm, 1968), p. 367

[c2] S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D 2, 1285 (1970)

[c3] A. Gamba, R. E. Marshak, and S. Okubo, Proc. Natl. Acad. Sci. USA 45, 881 (1959) J. D. Bjorken and S. L. Glashow, Phys. Lett. 11, 255 (1964)

[c4] M. Y. Han and Y. Nambu, Phys. Rev. 139, B1006 (1965) A. Tavkhelidz̆e et al., in proceedings of the Conference on High Energy Physics, (unpublished) O. W. Greenberg, Phys. Rev. Lett. 13, 596 (1964)

[c5] J. Aubert et al., Phys. Rev. Lett. 33, 1406 (1974) G. S. Abrams et al., ibid. 33, 1453 (1974)

[c6] F. J. Gilman, SLAC report, 1975 (unpublished)

[c7] R. M. Barnett, Phys. Rev. Lett. 34, 41 (1975) H. Harari, Phys. Lett. 57B, 265 (1975) F. Wilczek, 59B, 105 (1975)

[c8] G. Feldman, report of SPEAR results given at the Palermo International Conference, 1975 (unpublished)

[c9] J. C. Pati and A. Salam, Phys. Rev. D 10, 275 (1974)

[c10] [9] R. N. Mohapatra and J. C. Pati, Phys. Rev. D 11, 566 (1975) ibid.112588 (1975) G. Senjanovic and R. N. Mohapatra, ibid. 12, 1502 (1975) R. N. Mohapatra, ibid. 9, 3558 (1974) R. N. Mohapatra, J. C. Pati, and L. Wolfenstein, ibid. 11, 3319 (1975)

[c11] ([10]) R. N. Mohapatra and J. C. Pati, Phys. Rev. D 11, 2588 (1975) H. Fritzsuch and P. Minkowski, Phys. Lett. 56B, 69 (1975)

[c12] J. C. Pati and A. Salam, Phys. Lett. 58B, 333 (1975)

[c13] D. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973) H. D. Politzer, ibid. 30, 1346 (1973)

[c14] S. Weinberg, Rev. Mod. Phys. 46, 255 (1974) M. A. B. Bég and A. Sirlin, Annu. Rev. Nucl. Sci. 24, 379 (1974) J. Iliopoulos, in Proceedings of the XVII International Conference on High Energy Physics, London, 1974, edited by J. R. Smith (Rutherford Laboratory, Chilton, Didcot, Berkshire, England, 1974), p. III-89

[c15] R. N. Mohapatra, Phys. Rev. D 6, 2023 (1972)

[c16] A. De Rújula, H. Georgi and S. L. Glashow, Phys. Rev. Lett. 35, 69 (1975)

[c17] H. Fritzsch and P. Minkowski, Caltech Report No. 68-503, 1975 (unpublished)

[c18] F. Wilczek, A. Zee, R. Kingsley and S. Treiman, Phys. Rev. D 12, 2768 (1975)

[c19] G. Branco, T. Hagiwara and R. N. Mohapatra, preceding paper, Phys. Rev. D 13, 104 (1976)

[c20] A. De Rújula, H. Georgi, and S. L. Glashow, Phys. Rev. D 12, 3589 (1975)

[c21] S. Pakvasa, W. A. Simmons, and S. F. Tuan, Phys. Rev. Lett. 35, 702 (1975)

[c22] M. R. Krishnaswamy, M. G. K. Menon, V. S. Narashinham, N. Ito, S. Kawakami, and S. Miyake, TIFR report (to be published in Pramana) Phys. Lett. 57B, 105 (1975)

[c23] J. C. Pati and A. Salam, ICTP report, 1975 (unpublished) O. W. Greenberg, Phys. Rev. Lett. 35, 1120 (1975) J. D. Bjorken and C. H. Woo. C. K. Chang, Phys. Rev. D 5, 950 (1972) J. Bartelski and W. Krolikowski, Warsaw report (unpublished)

[c24] R. E. Marshak, Riazuddin, and C. P. Ryan, Theory of Weak Interactions in Particle Physics (Wiley, New York, 1969)

[c25] G. Snow, Nucl. Phys. B55, 445 (1973) M. Gaillard, B. W. Lee, and J. Rosner, Rev. Mod. Phys. 47, 277 (1975)

[c26] A. De Rújula, H. Georgi, and S. L. Glashow, Phys. Rev. Lett. 35, 628 (1975)

[c27] Omitted endnote

[c28] V. Barger, R. Weiler, and R. J. N. Phillips, Phys. Rev. Lett. 35, 692 (1975)

[c29] A. Benvenuti et al., Phys. Rev. Lett. 35, 1249 (1975)

[c30] L. Wolfenstein, in Particles and Fields—1974, proceedings of the 1974 Williamsburg meeting of the Division of Particles and Fields of the American Physical Society, edited by Carl E. Carlson (A. I. P., New York, 1975)

[c31] E. A. Paschos, Brookhaven report, 1975 (unpublished)

[c32] R. Kingsley, F. Wilczek, S. Treiman, and A. Zee, Phys. Rev. D 11, 1919 (1975) M. B. Einhorn and C. Quigg, 12, 2015 (1975) A. Pais and V. Rittenberg, Phys. Rev. Lett. 34, 707 (1975)

[c33] T. Hagiwara, G. Branco, R. N. Mohapatra, and D. P. Sidhu, Phys. Rev. D (to be published)

[c34] A. M. Boyarski et al., Phys. Rev. Lett. 35, 195, (1975)

[c35] M. B. Einhorn and C. Quigg, Phys. Rev. Lett. 35, 1114 (1975)

[c36] R. N. Mohapatra, J. S. Rao, and R. E. Marshak, Phys. Rev. Lett. 20, 1081 (1968) B. L. Ioffe and E. P. Shabalin, Yad. Fiz. 6, 828 (1967) [Sov. J. Nucl. Phys. 6, 603 (1968)]

[c37] R. N. Mohapatra, in Particles and Fields—1974, proceedings of the 1974 Williamsburg meeting of the Division of Particles and Fields of the American Physical Society, edited by Carl E. Carlson ([30])

[c38] L. Wolfenstein, CERN report, 1974 (unpublished)

[c39] E. Golowich and B. Holstein, Phys. Rev. Lett. 35, 831 (1975)

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Unified gauge theories with right-handed currents and heavy fermions

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