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Marni D. Sheppeard

Wednesday, January 21, 2009

M Theory Lesson 254

Dave at Carl's blog has pointed out that

cos(θ)=229

where θ is the sum of row (or column) entries in the circulant decomposition of the tribimaximal mixing matrix. In M Theory, we are used to coming across this number 2/9. For example, it appears as a determinant,

29=1-(13+23i)(13-23i)

in the 2D component of the transform of the tribimaximal mixing matrix. The number

13+23

also appears in the 2D component of R3R2, a MUB analogue of the (absolute value of) the tribimaximal matrix. That is, this number is a normalised form of (1+iω2), where ω is the usual cubed root of unity.

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