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:

    “How natural that the errors of the ancient should be handed down and, mixing with the principles and system which Christ taught, give to us an adulterated Christianity.”
    —Olympia Brown (1835–1900)