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The golden ratio prediction for the solar angle from a natural model with \(A_{5}\) flavour symmetry. (English) Zbl 1301.81339

Summary: We formulate a consistent model predicting, in the leading order approximation, maximal atmospheric mixing angle, vanishing reactor angle and tan \(\theta_{12} = 1/\phi\) where \(\phi = {{{\left( {1 + \sqrt {5} } \right)}} \left/ {2} \right.}\) is the Golden Ratio. The model is based on the flavour symmetry \(A_{5}\) {\(\times\)} \(Z_{5}\) {\(\times\)} \(Z_{3}\), spontaneously broken by a set of flavon fields. By minimizing the scalar potential of the theory up to the next-to-leading order in the symmetry breaking parameter, we demonstrate that this mixing pattern is naturally achieved in a finite portion of the parameter space, through the vacuum alignment of the flavon fields. The leading order approximation is stable against higher-order corrections. We also compare our construction to other models based on discrete symmetry groups.

MSC:

81V22 Unified quantum theories
81V15 Weak interaction in quantum theory
81R40 Symmetry breaking in quantum theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
86A10 Meteorology and atmospheric physics
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