Saturday, July 3, 2010

M Theory Lesson 337

If we take three particle states called $\nu_{\alpha}$, $\nu_{\beta}$ and $\nu_{\gamma}$, and use the $R_2$ parameters as coefficients for two (in this case neutrino) mixed states, given by then the tribimaximal transformed states take the form Note that the zero element of the tribimaximal mixing matrix results in a final state that only depends upon two of the three input states. For instance, if $\alpha$, $\beta$ and $\gamma$ denote mass states, then there exists a flavor state that mixes only two mass states. This may be true for a particular flavor neutrino but not the corresponding antineutrino, since antineutrinos might use a transposed mixing matrix. In any case, the inverse of a tribimaximal matrix in $R_2$ form is also tribimaximal. The general tribimaximal form (with two $R_2$ factors) is only broken when CP violation is present.

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