Plato's fire and the neutrino mass matrix

With the accumulation of many years of solar and atmospheric neutrino oscillation data, the approximate form of the 3 X 3 neutrino mixing matrix is now known. The theoretical challenge is to understand where this mixing matrix comes from. Recently, a remarkable fact was discovered that for a specific pattern of the neutrino mass matrix at a high scale, any flavor-changing radiative correction will automatically lead to the desired mixing matrix. It was also discovered that the required specific pattern at the high scale can be maintained by the non-Abelian discrete symmetry A_4 which is also the symmetry group of the regular tetrahedron, one of five perfect geometric solids known to Plato who associated it with the element ``fire''. I discuss this recent development and add to it a new and very simple mechanism for the implementation of the flavor-changing radiative correction.

review
neutrino: mass
neutrino: oscillation
neutrino: solar
neutrino: cosmic radiation
neutrino: mixing angle
radiative correction
flavor: violation
symmetry: discrete
nonabelian

References(24)

Figures(0)

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