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arXiv · 0705.4559

The golden ratio prediction for the solar neutrino mixing

Yuji Kajiyama·Martti Raidal·Alessandro Strumia
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Abstract

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}.

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Yuji Kajiyama, Martti Raidal, Alessandro Strumia. 2007-11-28. The golden ratio prediction for the solar neutrino mixing. https://doi.org/10.1103/physrevd.76.117301

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