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Golden ratio prediction for solar neutrino mixing

Yuji Kajiyama¹, Martti Raidal¹, and Alessandro Strumia²

¹National Institute of Chemical Physics and Biophysics, Ravala 10, Tallinn 10143, Estonia
²Dipartimento di Fisica dell’Universit`a di Pisa and INFN, Pisa, Italy

Phys. Rev. D 76, 117301 – Published 6 December, 2007

DOI: https://doi.org/10.1103/PhysRevD.76.117301

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 $1.4 σ$ below the present best-fit value and final SNO and KamLAND data could discriminate it from tri-bimaximal mixing. The neutrino mass matrix is invariant under a $Z_{2} \otimes Z_{2}^{'}$ 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, $θ_{C} = π / 4 - θ_{12} \approx 13.3 °$ , up to the uncertainties comparable to $V_{u b}$ .

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References (12)

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Golden ratio prediction for solar neutrino mixing

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