Trimaximal mixing (also known as threefold maximal mixing) refers to the highly symmetric, maximally CP-violating, 3 × 3 fermion mixing configuration, characterised by a unitary matrix ( U ) having all its elements equal in modulus ( | U a i | = 1 / 3 , a , i = 1 , 2 , 3 ) as may be written, e.g.:
U = [ 1 3 1 3 1 3 ω 3 1 3 ω ¯ 3 ω ¯ 3 1 3 ω 3 ] ⇒ ( | U i α | 2 ) = [ 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 ] where ω = exp ( i 2 π / 3 ) and ω ¯ = exp ( − i 2 π / 3 ) are the complex cube roots of unity. In the standard PDG convention, trimaximal mixing corresponds to: θ 12 = θ 23 = π / 4 , θ 13 = sin − 1 ( 1 / 3 ) and δ = π / 2 . The Jarlskog C P -violating parameter J takes its extremal value | J | = 1 / ( 6 3 ) .
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 no longer tenable (related) tribimaximal mixing scheme.
