Trimaximal Mixing

Trimaximal mixing (also known as threefold maximal mixing) refers to the highly symmetric, maximally CP-violating, fermion mixing configuration, characterised by a unitary matrix having all its elements equal in modulus (, ) as may be written, e.g.:

U= \begin{bmatrix} \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \\ \frac{\omega}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{\bar{\omega}}{\sqrt{3}} \\ \frac{\bar{\omega}}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{\omega}{\sqrt{3}} \end{bmatrix} \Rightarrow (|U_{i\alpha}|^2)= \begin{bmatrix} \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \end{bmatrix}

where and are the complex cube roots of unity. In the standard PDG convention, trimaximal mixing corresponds to:, and . The Jarlskog -violating parameter takes its extremal value .

Originally proposed as a candidate lepton mixing matrix, and actively studied as such (and even as a candidate quark mixing matrix), trimaximal mixing is now definitively ruled-out as a phenomenologically viable lepton mixing scheme by neutrino oscillation experiments, especially the CHOOZ reactor experiment, in favour of the (related) tribimaximal mixing scheme.

Famous quotes containing the word mixing:

    “It was not till the middle of the second dance, when, from some pauses in the movement wherein they all seemed to look up, I fancied I could distinguish an elevation of spirit different from that which is the cause or the effect of simple jollity.—In a word, I thought I beheld Religion mixing in the dance.”
    —Laurence Sterne (1713–1768)