Renormalization-group equations in the [SU(6)<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mo>]</mo></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span> model

A. Hernández; R. Martínez

doi:10.1103/PhysRevD.51.3962

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Renormalization-group equations in the [SU(6) $]^{3}$ model

A. Hernández

R. Martínez

Departamento de Física, CINVESTAV Apartado Postal 14-740, México D.F.
Escuela de Ciencias, UAEM, Instituto Literario 100, C.P. 50000 Toluca, Edificio de México

Departamento de Física, CINVESTAV, Apartado Postal 14-740, México D.F.
Departamento de Física, Universidad Nacional, A 14490, Bogotá, Columbia

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Phys. Rev. D 51, 3962 – Published 1 April, 1995

DOI: https://doi.org/10.1103/PhysRevD.51.3962

Abstract

We use the renormalization-group equations to calculate the symmetry-breaking scales in the [SU(6) $]^{3}$ Pati-Salam model. Using only known parameters, we predict the mass scales consistent with very small values for the light-neutrino masses and rare processes decay such as $K^{+}$ → $π^{+}$ $e^{-}$ $μ^{+}$ for three steps of symmetry breaking. We also find that the proton is stable by gauge and Higgs boson exchange.

References (15)

S. 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).
H. Georgi and S. L. Glashow, Phys. Rev. Lett. 32, 438 (1974).
J. C. Pati and A. Salam, Phys. Rev. D 8, 1240 (1973); ibid. 10, 275 (1974); R. Foot, H. Lew and R. R. Volkas, ibid. 44, 859 (1991).
A. H. Galeana, R. Martínez, W. Ponce and A. Zepeda, Phys. Rev. D 44, 2166 (1991).
A. Galli, Nuovo Cimento 106A, 1309 (1993).
H. Georgi, H. Quinn and S. Weinberg, Phys. Rev. Lett. 33, 451 (1974); H. Fritzsch and P. Minkowski, Ann. Phys. (N.Y.) 93, 193 (1975); P. Langacker, Phys. Rep. 72, 1 (1981); R. W. Robinett and J. Rosner, Phys. Rev. D 30, 1470 (1984).
M. Gell Mann, P. Ramond, and R. Slansky, in Supergravity, Proceedings of the Conference, Stony Brook, New York, 1979, edited by P. van Nieuwenhuizen and D. Freedman (North Holland, Amsterdam, 1979), p. 315; T. Yanagida, in Proceedings of the Workshop on Unified Theory and Baryon Number of the Universe, Tsukuba, Japan, 1979, edited by A. Sawada and A. Sugamoto (KEK Report No. 79 18, Tsukuba, Japan, 1979); A. Davidson and K. Wali, Phys. Rev. Lett. 59, 393 (1987).
R. N. Mohapatra and R. E. Marshak, Phys. Rev. Lett. 44, 1316 (1980).
M. Gell Mann and F. E. Low, Phys. Rev. 95, 1300 (1954); C. G. Callan, Phys. Rev. D 2, 1541 (1970); D. J. Gross and F. Wilczek, ibid. 8, 3633 (1973).
T. Appelquist and J. Carazzone, Phys. Rev. D 11, 2856 (1975).
N. G. Deshpande, E. Keith and Palash B. Pal, Phys. Rev. Lett. 46, 2261 (1992).
P. Langacker and M. Luo, Phys. Rev. D 44, 817 (1991); G. Degrassi, S. Fanchiotti and A. Sirlin, Nucl. Phys. B351, 49 (1991); LEP Collaborations ALEPH, DELPHI, L3, and OPAL, Phys. Lett. B 276, 247 (1992).
Particle Data Group, K. Hikasa et al., Phys. Rev. D 45, S1 (1992).
R. Gaitán, Ph.D. thesis, CINVESTAV, 1993; N. G. Deshpande and R. J. Johnson, Phys. Rev. D 27, 1193 (1983).
J. C. Pati and A. Salam, Phys. Rev. Lett. 31, 661 (1973).

[c1] S. 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).

[c2] H. Georgi and S. L. Glashow, Phys. Rev. Lett. 32, 438 (1974).

[c3] J. C. Pati and A. Salam, Phys. Rev. D 8, 1240 (1973); ibid. 10, 275 (1974); R. Foot, H. Lew and R. R. Volkas, ibid. 44, 859 (1991).

[c4] A. H. Galeana, R. Martínez, W. Ponce and A. Zepeda, Phys. Rev. D 44, 2166 (1991).

[c5] A. Galli, Nuovo Cimento 106A, 1309 (1993).

[c6] H. Georgi, H. Quinn and S. Weinberg, Phys. Rev. Lett. 33, 451 (1974); H. Fritzsch and P. Minkowski, Ann. Phys. (N.Y.) 93, 193 (1975); P. Langacker, Phys. Rep. 72, 1 (1981); R. W. Robinett and J. Rosner, Phys. Rev. D 30, 1470 (1984).

[c7] M. Gell Mann, P. Ramond, and R. Slansky, in Supergravity, Proceedings of the Conference, Stony Brook, New York, 1979, edited by P. van Nieuwenhuizen and D. Freedman (North Holland, Amsterdam, 1979), p. 315; T. Yanagida, in Proceedings of the Workshop on Unified Theory and Baryon Number of the Universe, Tsukuba, Japan, 1979, edited by A. Sawada and A. Sugamoto (KEK Report No. 79 18, Tsukuba, Japan, 1979); A. Davidson and K. Wali, Phys. Rev. Lett. 59, 393 (1987).

[c8] R. N. Mohapatra and R. E. Marshak, Phys. Rev. Lett. 44, 1316 (1980).

[c9] M. Gell Mann and F. E. Low, Phys. Rev. 95, 1300 (1954); C. G. Callan, Phys. Rev. D 2, 1541 (1970); D. J. Gross and F. Wilczek, ibid. 8, 3633 (1973).

[c10] T. Appelquist and J. Carazzone, Phys. Rev. D 11, 2856 (1975).

[c11] N. G. Deshpande, E. Keith and Palash B. Pal, Phys. Rev. Lett. 46, 2261 (1992).

[c12] P. Langacker and M. Luo, Phys. Rev. D 44, 817 (1991); G. Degrassi, S. Fanchiotti and A. Sirlin, Nucl. Phys. B351, 49 (1991); LEP Collaborations ALEPH, DELPHI, L3, and OPAL, Phys. Lett. B 276, 247 (1992).

[c13] Particle Data Group, K. Hikasa et al., Phys. Rev. D 45, S1 (1992).

[c14] R. Gaitán, Ph.D. thesis, CINVESTAV, 1993; N. G. Deshpande and R. J. Johnson, Phys. Rev. D 27, 1193 (1983).

[c15] J. C. Pati and A. Salam, Phys. Rev. Lett. 31, 661 (1973).

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Renormalization-group equations in the [SU(6) $]^{3}$ model

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Renormalization-group equations in the [SU(6) $]^{3}$ model