Trimaximal mixing[1] (also known as threefold maximal mixing[2]) 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.:

where and are the complex cube roots of unity. In the standard PDG[3] convention, trimaximal mixing corresponds to: , and . The Jarlskog -violating parameter [4] takes its extremal value .

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

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  1. ^ a b 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): 79–92. arXiv:hep-ph/9904297. Bibcode:1999PhLB..458...79H. doi:10.1016/S0370-2693(99)00438-4. S2CID 16800198.
  2. ^ a b P.F. Harrison, D. H. Perkins and W. G. Scott (1995). "Threefold Maximal Lepton Mixing and the Solar and Atmospheric Neutrino Deficits" (PDF). Physics Letters B. 349 (1–2): 137–144. 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" (PDF). Journal of Physics G. 33 (1): 1. arXiv:astro-ph/0601168. Bibcode:2006JPhG...33....1Y. doi:10.1088/0954-3899/33/1/001. S2CID 117958297.
  4. ^ C. Jarlskog (1985). "Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal   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): 958–960. 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): 333–335. 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): 357–364. arXiv:hep-ph/9411219. Bibcode:1995PhLB..352..357G. CiteSeerX 10.1.1.347.269. doi:10.1016/0370-2693(95)00424-J. S2CID 15430104.
  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): 186–196. arXiv:hep-ph/9702243. Bibcode:1997PhLB..396..186H. doi:10.1016/S0370-2693(97)00105-6. S2CID 14447907.
  9. ^ P.F. Harrison & W. G. Scott (1994). "Generation Permutation Symmetry and the Quark Mixing Matrix". Physics Letters B. 333 (3–4): 471–475. arXiv:hep-ph/9406351. Bibcode:1994PhLB..333..471H. doi:10.1016/0370-2693(94)90170-8. S2CID 15792208.
  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): 331–374. arXiv:hep-ex/0301017. Bibcode:2003EPJC...27..331A. doi:10.1140/epjc/s2002-01127-9. S2CID 14226312.
  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): 167–173. arXiv:hep-ph/0202074. Bibcode:2002PhLB..530..167H. doi:10.1016/S0370-2693(02)01336-9. S2CID 16751525.