The golden ratio prediction for the solar neutrino mixing

TL;DR

This paper proposes a neutrino mixing model based on the golden ratio, predicting specific mixing angles and symmetries, which can be tested with current and future neutrino experiments.

Contribution

It introduces a novel texture for the neutrino mass matrix linked to the golden ratio and explores its implications for neutrino and quark mixing angles.

Findings

Predicts cotangent of solar mixing angle equals the golden ratio

Suggests the model can be distinguished from tri-bi-maximal mixing with data

Proposes a geometric symmetry interpretation of the neutrino mass matrix

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}.