The golden ratio prediction for the solar angle from a natural model with A 5 flavour symmetry

Abstract

We formulate a consistent model predicting, in the leading order approximation, maximal atmospheric mixing angle, vanishing reactor angle and tan θ 12 = 1/φ where φ = (1 + √ 5)/2 is the Golden Ratio. The model is based on the flavour symmetry A 5 ×Z 5 ×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.

Repressing anarchy in neutrino mass textures

“…The observed sin 2 θ 12 , the best measured mixing angle, is very close, from below, to the so called Tri-Bimaximal (TB) value [13][14][15][16][17] of sin 2 θ 12 = 1/3. Alternatively, it is also very close, from above, to the Golden Ratio (GR) value [18][19][20][21] sin 2 θ 12 = 1/ √ 5 φ ∼ 0.276, where φ = (1 + √ 5)/2 is the GR (for a different connection to the GR, see refs. [22,23]).…”

Testing solar lepton mixing sum rules in neutrino oscillation experiments

“…Therefore, we can enumerate the viable models of this type by deriving the values of θ ν 12 associated with those leading-order mixing patterns with θ ν 13 = 0 which are derivable from considerations of symmetry. In this article, we shall show that this leads us to four well-motivated solar sum rules: one based on TBM mixing [6] where s ν 12 = 1/ √ 3, one based on bimaximal (BM) mixing [25][26][27] where s ν 12 = 1/ √ 2 and two patterns based on versions of golden ratio mixing including GR1 with t ν 12 = 1/ϕ [28][29][30] and GR3 with c ν 12 = ϕ/ √ 3 [31,32], where ϕ =…”

“…Therefore the linearized expressions well describe the correlation to the precision of the first phases of the next-generation of superbeams, which expect a sensitivity of [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] • [50,51]; however, the full expressions will be necessary in the subsequent phases, where precisions are expected to be 8-18…”

“…The first is the original golden ratio mixing pattern (GR1) [28][29][30], related to the flavour symmetry A 5 . It predicts t ν 12 = 1/ϕ, i.e.…”

Spontaneous breaking of gauge groups to discrete symmetries

“…Another subgroup of interest, which has been used in a number of recent models [32][33][34][35], is A 5 . From table 19 we see that the 13 is the lowest dimensional irrep that contains a trivial A 5 singlet.…”