So for the neutrino mixing matrix, the one circulant piece goes to 
the norm of a Koide matrix for leptons. Now the nondegenerate mass triplets just require the addition of the appropriate complex phase.
14 years ago
Wednesday, August 18, 2010
M Theory Lesson 343
Recall that the circulant sum form of the neutrino mixing matrix may be expressed as a product $X \cdot Y$ of two $R_2$ factors. This product is a sum of a real $1$-circulant and an imaginary $2$-circulant. If we turn the ordinary matrix product into a Jordan algebra product $X \circ Y$ (much beloved by kneemo) then the $1$-circulant piece will be symmetrised, and the $2$-circulant piece remains unaltered. 
So for the neutrino mixing matrix, the one circulant piece goes to 
the norm of a Koide matrix for leptons. Now the nondegenerate mass triplets just require the addition of the appropriate complex phase.
So for the neutrino mixing matrix, the one circulant piece goes to the norm of a Koide matrix for leptons. Now the nondegenerate mass triplets just require the addition of the appropriate complex phase.
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Hmm, so it may have been more correct to start with $(1, 1/\sqrt2)$ for the R2 parameters. That is, the choice where both parameters have norm less than or equal $1$.
ReplyDeleteOh, hi Carl. Yeah, actually I thought of it after a really interesting chat with kneemo about the Riofrio cosmology (and entropic mass generation). Things are slowly getting clearer, I hope.
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