Trimaximal mixing

Trimaximal mixing cite journal | author = P.F. Harrison, D. H. Perkins and W. G. Scott | title = A Redetermination of the Neutrino Mass-Squared Difference in Tri-Maximal Mixing with Terrestrial Matter Effects | journal = Physics Letters B | volume = 458 | year = 1999 | pages = 79 | url = http://arxiv.org/pdf/hep-ph/9904297 | doi = 10.1016/S0370-2693(99)00438-4 ] (also known as threefold maximal mixing cite journal | author = P.F. Harrison, D. H. Perkins and W. G. Scott | title = Threefold Maximal Lepton Mixing and the Solar and Atmospheric Neutrino Deficits | journal = Physics Letters B | volume = 349 | year = 1995 | pages = 137 | url = http://www-lib.kek.jp/cgi-bin/img_index?9503190 | doi = 10.1016/0370-2693(95)00213-5 ] ) refers to the highly symmetric, maximally CP-violating, $3\; imes\; 3$ 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.:

:

where $omega=exp(i2pi/3)$ and are the complex cube roots of unity. In the standard PDG cite journal | author = W.M. Yao et al. | title = Particle Data Group - 2006 Review of Particle Physics | journal = Journal of Physics G | volume = 33 | issue = 1 | year = 2006 | url = http://pdg.lbl.gov " [http://pdg.lbl.gov/2006/reviews/numixrpp.pdf Neutrino mass, mixing, and flavor change] ".] convention, trimaximal mixing corresponds to: $heta\_\{12\}=\; heta\_\{23\}=pi/4$, $heta\_\{13\}=sin^\{-1\}(1/sqrt\{3\})$ and $delta=pi/2$. The Jarlskog $CP$-violating parameter $J$ cite journal | author = C. Jarlskog | title = Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal $CP$ Non-Conservation | journal = Physical Review Letters | volume = 55 | year = 1985 | pages = 1039 | doi = 10.1103/PhysRevLett.55.1039 ] takes its extremal value $|J|=1/(6sqrt\{3\})$.

Originally proposed as a candidate lepton mixing matrix cite journal | author = L. Wolfenstein | title = Oscillations Among Three Neutrino Types and CP Violation | journal = Physical Review D | volume = 18 | year = 1978 | pages = 958 | url = http://link.aps.org/abstract/PRD/V18/P958 | doi = 10.1103/PhysRevD.18.958] cite journal | author = N. Cabibbo | title = Time Reversal Violation in Neutrino Oscillation | journal = Physics Letters B | volume = 32 | year = 1978 | pages = 333 | doi = 10.1016/0370-2693(78)90132-6] , and actively studied HPS1999] HPS1995] cite journal | author = C. Giunti, C. W. Kim and J. D. Kim, | title = Atmospheric Neutrino Problem in Maximally Mixed Three Generations of Neutrinos | journal = Physics Letters B | volume = 352 | year = 1995 | pages = 357 | doi = 10.1016/0370-2693(95)00424-J] cite journal | author = P.F. Harrison, D. H. Perkins and W. G. Scott | title = Further Evidence for Threefold Maximal Lepton Mixing and a Hierarchical Spectrum of Neutrino Mass-Squared Differences | journal = Physics Letters B | volume = 396 | year = 1997 | pages = 186 | url = http://arxiv.org/pdf/hep-ph/9702243 ] as such (and even as a candidate quark mixing matrix cite journal | author = P.F. Harrison and W. G. Scott | title = Generation Permutation Symmetry and the Quark Mixing Matrix | journal = Physics Letters B | volume = 333 | year = 1994 | pages = 471 | url = http://arxiv.org/pdf/hep-ph/9406351 | doi = 10.1016/0370-2693(94)90170-8 ] ), trimaximal mixing is now definitively ruled-out as a phenomenologically viable lepton mixing scheme by neutrino oscillation experiments, especially the CHOOZ reactor experiment cite journal | author = M. Apollonio et al. | title = Search for Neutrino Oscillations on a Long Baseline at the CHOOZ Nuclear Power Station | journal = European Journal of Physics J | volume = C27 | year = 2003 | pages = 331 | url = http://arxiv.org/pdf/hep-ex/0301017 ] , in favour of the (related) tribimaximal mixing cite journal | author = P.F. Harrison, D. H. Perkins and W. G. Scott | title = Tri-Bimaximal Mixing and the Neutrino Oscillation Data | journal = Physics Letters B | volume = 530 | year = 2002 | pages = 167 | url = http://arxiv.org/pdf/hep-ph/0202074 | doi = 10.1016/S0370-2693(02)01336-9 ] scheme.

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