On the simplicity of numbers

TL;DR

This paper explores the algebraic properties of a hypothetical neutrino mixing angle of 9 degrees, relating it to symmetry groups of Platonic solids and discussing potential implications for neutrino flavor dynamics.

Contribution

It introduces a novel perspective linking a specific neutrino mixing angle to discrete symmetry groups of Platonic solids, suggesting new algebraic structures in neutrino physics.

Findings

The angle 9° has special algebraic properties in its periodic functions.

Connections are proposed between symmetry groups and neutrino mixing.

Open questions remain about the role of these symmetries in neutrino dynamics.

Abstract

The recent measurements of reactor antinu_{e} disappearance and its interpretation in terms of the three light neutrino mixing angle {theta}_13 by the DAYA BAY \rightarrow {theta}_13 = (8.83 + 0.81 - 0.88) \circ and RENO \rightarrow {theta}_{13} = (9.36 + 0.88 - 0.96) \circ collaborations, gave rise to this treatise, upon the hypothetical substitution {theta}_13 \rightarrow \vartheta_9 = 9 \circ. The latter angle (\vartheta_9 = 9\circ) is related to interesting algebraic properties of its periodic functions, which in turn have their origin in the discrete symmetry groups S5 = Z2 \times A5 and A5, the point groups associated with the regular d = 3 'Platonic bodies' : dodecahedron and icosahedron. How these discrete groups may be related to dynamical symmetries of mass and mixing of light neutrino flavors is left open.