Trimaximal mixing

Trimaximal mixing[1] (also known as threefold maximal mixing[2]) refers to the highly symmetric, maximally CP-violating, 3 \times 3 fermion mixing configuration, characterised by a unitary matrix (U) having all its elements equal in modulus ( |U_{ai}|=1/\sqrt{3}, a,i=1,2,3) 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 \omega=\exp(i2\pi/3) and \bar{\omega}=\exp(-i2\pi/3) are the complex cube roots of unity. In the standard PDG[3] convention, trimaximal mixing corresponds to: \theta_{12}=\theta_{23}=\pi/4, \theta_{13}=\sin^{-1}(1/\sqrt{3}) and \delta=\pi/2. The Jarlskog CP-violating parameter J[4] takes its extremal value |J|=1/(6\sqrt{3}).

Originally proposed as a candidate lepton mixing matrix,[5][6] and actively studied[1][2][7][8] as such (and even as a candidate quark mixing matrix[9]), trimaximal mixing is now definitively ruled-out as a phenomenologically viable lepton mixing scheme by neutrino oscillation experiments, especially the CHOOZ reactor experiment,[10] in favour of the no longer tenable (related) tribimaximal mixing[11] scheme.

References

  1. ↑ 1.0 1.1 P.F. Harrison, D. H. Perkins and W. G. Scott (1999). "A Redetermination of the Neutrino Mass-Squared Difference in Tri-Maximal Mixing with Terrestrial Matter Effects". Physics Letters B 458 (1): 79. arXiv:hep-ph/9904297. Bibcode:1999PhLB..458...79H. doi:10.1016/S0370-2693(99)00438-4.
  2. ↑ 2.0 2.1 P.F. Harrison, D. H. Perkins and W. G. Scott (1995). "Threefold Maximal Lepton Mixing and the Solar and Atmospheric Neutrino Deficits". Physics Letters B 349 (1–2): 137. Bibcode:1995PhLB..349..137H. doi:10.1016/0370-2693(95)00213-5.
  3. ↑ W.M. Yao et al. (2006). "Review of Particle Physics: Neutrino mass, mixing, and flavor change". Journal of Physics G 33: 1. arXiv:astro-ph/0601168. Bibcode:2006JPhG...33....1Y. doi:10.1088/0954-3899/33/1/001.
  4. ↑ C. Jarlskog (1985). "Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal CP Non-Conservation". Physical Review Letters 55 (10): 1039–1042. Bibcode:1985PhRvL..55.1039J. doi:10.1103/PhysRevLett.55.1039. PMID 10031712.
  5. ↑ L. Wolfenstein (1978). "Oscillations Among Three Neutrino Types and CP Violation". Physical Review D 18 (3): 958. Bibcode:1978PhRvD..18..958W. doi:10.1103/PhysRevD.18.958.
  6. ↑ N. Cabibbo (1978). "Time Reversal Violation in Neutrino Oscillation". Physics Letters B 32 (3): 333. Bibcode:1978PhLB...72..333C. doi:10.1016/0370-2693(78)90132-6.
  7. ↑ C. Giunti, C. W. Kim and J. D. Kim, (1995). "Atmospheric Neutrino Problem in Maximally Mixed Three Generations of Neutrinos". Physics Letters B 352 (3–4): 357. arXiv:hep-ph/9411219. Bibcode:1995PhLB..352..357G. doi:10.1016/0370-2693(95)00424-J.
  8. ↑ P.F. Harrison, D. H. Perkins and W. G. Scott (1997). "Further Evidence for Threefold Maximal Lepton Mixing and a Hierarchical Spectrum of Neutrino Mass-Squared Differences". Physics Letters B 396 (1–4): 186. arXiv:hep-ph/9702243. Bibcode:1997PhLB..396..186H. doi:10.1016/S0370-2693(97)00105-6.
  9. ↑ P.F. Harrison and W. G. Scott (1994). "Generation Permutation Symmetry and the Quark Mixing Matrix". Physics Letters B 333 (3–4): 471. arXiv:hep-ph/9406351. Bibcode:1994PhLB..333..471H. doi:10.1016/0370-2693(94)90170-8.
  10. ↑ M. Apollonio et al. (2003). "Search for Neutrino Oscillations on a Long Baseline at the CHOOZ Nuclear Power Station". European Physical Journal C 27 (3): 331. arXiv:hep-ex/0301017. Bibcode:2003EPJC...27..331A. doi:10.1140/epjc/s2002-01127-9.
  11. ↑ P.F. Harrison, D. H. Perkins and W. G. Scott (2002). "Tri-Bimaximal Mixing and the Neutrino Oscillation Data". Physics Letters B 530 (1–4): 167. arXiv:hep-ph/0202074. Bibcode:2002PhLB..530..167H. doi:10.1016/S0370-2693(02)01336-9.