Trimaximal mixing (also known as threefold maximal mixing ) refers to the highly

symmetric Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...

, maximally CP-violating,

3 \times 3

fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...

mixing configuration, characterised by a

unitary matrix In linear algebra, a Complex number, complex Matrix (mathematics), square matrix is unitary if its conjugate transpose is also its Invertible matrix, inverse, that is, if U^* U = UU^* = UU^ = I, where is the identity matrix. In physics, esp ...

(

U

) having all its elements equal in modulus (

, U_, =1/\sqrt

a,i=1,2,3

) as may be written, e.g.: :

U= 
\begin
\frac & \frac & \frac \\
\frac & \frac & \frac \\ 
\frac & \frac & \frac 
\end
\Rightarrow (, U_, ^2)=
\begin
\frac & \frac & \frac \\
\frac & \frac & \frac \\ 
\frac & \frac & \frac 
\end

where

\omega=\exp(i2\pi/3)

and

\bar=\exp(-i2\pi/3)

are the complex

cube roots In mathematics, a cube root of a number is a number such that . All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. F ...

of unity. In the standard PDG convention, trimaximal mixing corresponds to:

\theta_=\theta_=\pi/4

\theta_=\sin^(1/\sqrt)

and

\delta=\pi/2

. The Jarlskog

CP

-violating parameter

J

takes its extremal value

, J, =1/(6\sqrt)

. 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 Tribimaximal mixing is a specific postulated form for the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) lepton mixing matrix ''U''. Tribimaximal mixing is defined by a particular choice of the matrix of moduli-squared of the elements of the PMNS ma ...

scheme.

References

{{reflist, 2 Leptons Standard Model Particle physics Neutrinos