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The golden ratio prediction for the solar neutrino mixing · Around

2007

The golden ratio prediction for the solar neutrino mixing

Kajiyama, Yuji, Raidal, Martti, Strumia, Alessandro

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We present a simple texture that predicts the cotangent of the solar neutrino mixing angle to be equal to the golden ratio.

This prediction is 1.4 standard deviations below the present best-fit value and final SNO and KamLAND data could discriminate it from tri-bi-maximal mixing.
The neutrino mass matrix is invariant under a Z_2 x Z'_2 symmetry: that geometrically is a reflection along the diagonal of the golden rectangle.
Assuming an analogous structure in the quark sector suggests a golden prediction for the Cabibbo angle, theta_C = pi/4- theta_12 = 13.3 degree, up to uncertainties comparable to V_{ub}.

Built on

P. Minkowski, Phys. Lett. B 67 (1977) 421; M. Gell-Mann, P. Ramond and R. Slansky, Proceedings of the Supergravity Stony Brook Workshop, New York, 1979, eds. P. Van Nieuwenhuizen and D. Freedman (North-Holland, Amsterdam); T. Yanagida, Proceedings of the Workshop on Unified Theories and Baryon Number in the Universe, Tsukuba, Japan 1979 (eds. A. Sawada and A. Sugamoto, KEK Report No. 79-18, Tsukuba); R. Mohapatra and G. Senjanovic, Phys. Rev. Lett. 44, (1980) 912
1980
Earlier work this paper cites.
P. F. Harrison, D. H. Perkins and W. G. Scott, Phys. Lett. B 530 (2002) 167 [arXiv:hep-ph/0202074]
2002
Earlier work this paper cites.
The golden prediction
Original
2003
Earlier work this paper cites.
A. Y. Smirnov, arXiv:hep-ph/0402264. See also the talk by P. Ramond at the
2004
Earlier work this paper cites.

Similar

M. Raidal, Phys. Rev. Lett. 93 (2004) 161801 [arXiv:hep-ph/0404046]
2004
Cited alongside, same era.
F. Feruglio, Nucl. Phys. Proc. Suppl. 143 (2005) 184 [arXiv:hep-ph/0410131]
2005
Cited alongside, same era.
For recent works and references, see: S. Antusch, J. Kersten, M. Lindner, M. Ratz and M. A. Schmidt, JHEP 0503 (2005) 024 [arXiv:hep-ph/0501272]. J. R. Ellis, A. Hektor, M. Kadastik, K. Kannike and M. Raidal, Phys. Lett. B 631 (2005) 32 [arXiv:hep-ph/0506122]
2005
Cited alongside, same era.
For reviews and references see A. Strumia and F. Vissani,
Original
Cited in the paper.

Then

A. Bandyopadhyay, S. Choubey, S. Goswami and S. T. Petcov, Phys. Rev. D 72 (2005) 033013 [arXiv:hep-ph/0410283]
Original
2005
Later among the works it cites.
For a summary and references see E. Ma,
Original
2006
Later among the works it cites.
The Particle Data Group,
2007
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