A Built-in Horizontal Symmetry of SO(10)
Abstract
In a renormalizable SO(10) theory, all fermion mass matrices are linear combinations of three fundamental types, M10, M126, and M120 whose superscripts indicate their SO(10) transformation properties. The speaker points out that each of these fundamental mass matrices possesses a natural symmetry, which can be used to generate an unbroken horizontal symmetry, if the natural symmetry is taken to be its residual symmetry. This built-in symmetry is a Coxeter group. If it is finite, it must be one of five groups, S4, Z2 x S4, Z2 x A5, plus two ‘rank-4’ groups. These symmetries reduce the number of parameters in an SO(10) fit in a way to be discussed. Since they are built-in and can be derived theoretically, it is hoped that they place better constraints than those without a theoretical basis.
About the program
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