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| '''Trimaximal mixing'''<ref name="HPS1999">
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| {{cite journal
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| | author=P.F. Harrison, D. H. Perkins and W. G. Scott
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| | year=1999
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| | title=A Redetermination of the Neutrino Mass-Squared Difference in Tri-Maximal Mixing with Terrestrial Matter Effects
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| | journal=[[Physics Letters B]]
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| | volume=458 |issue=1 | pages=79
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| | arxiv=hep-ph/9904297
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| | bibcode=1999PhLB..458...79H
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| | doi=10.1016/S0370-2693(99)00438-4
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| }}</ref> (also known as threefold maximal mixing<ref name="HPS1995">
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| {{cite journal
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| | author=P.F. Harrison, D. H. Perkins and W. G. Scott
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| | year=1995
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| | title=Threefold Maximal Lepton Mixing and the Solar and Atmospheric Neutrino Deficits
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| | url=http://www-lib.kek.jp/cgi-bin/img_index?9503190
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| | journal=[[Physics Letters B]]
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| | volume=349 |issue=1–2 | pages=137
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| | bibcode=1995PhLB..349..137H
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| | doi=10.1016/0370-2693(95)00213-5
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| }}</ref>) refers to the highly symmetric, maximally CP-violating, <math>3 \times 3</math> [[fermion]] mixing configuration, characterised by a [[unitary matrix]] (<math>U</math>) having all its elements equal in modulus
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| (<math> |U_{ai}|=1/\sqrt{3}</math>, <math>a,i=1,2,3</math>) as may be written, e.g.:
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| | |
| :<math>
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| U=
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| \begin{bmatrix}
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| \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{1}{\sqrt{3}} \\
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| \frac{\omega}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{\bar{\omega}}{\sqrt{3}} \\
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| \frac{\bar{\omega}}{\sqrt{3}} & \frac{1}{\sqrt{3}} & \frac{\omega}{\sqrt{3}}
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| \end{bmatrix}
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| \Rightarrow (|U_{i\alpha}|^2)=
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| \begin{bmatrix}
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| \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\
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| \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\
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| \frac{1}{3} & \frac{1}{3} & \frac{1}{3}
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| \end{bmatrix}
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| </math>
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| | |
| where <math>\omega=\exp(i2\pi/3)</math> and <math>\bar{\omega}=\exp(-i2\pi/3)</math>
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| are the complex [[cube roots]] of unity. In the standard PDG<ref name="PDG">
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| {{cite journal
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| | author=W.M. Yao ''et al.''
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| | year=2006
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| | title=Review of Particle Physics: Neutrino mass, mixing, and flavor change
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| | url=http://pdg.lbl.gov/2006/reviews/numixrpp.pdf
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| | journal=[[Journal of Physics G]]
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| | volume=33 |page=1
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| |arxiv = astro-ph/0601168 |bibcode = 2006JPhG...33....1Y |doi = 10.1088/0954-3899/33/1/001 }}</ref> convention, trimaximal mixing corresponds to: <math>\theta_{12}=\theta_{23}=\pi/4</math>, <math>\theta_{13}=\sin^{-1}(1/\sqrt{3})</math> and <math>\delta=\pi/2</math>. The Jarlskog <math>CP</math>-violating parameter <math>J</math><ref name="JCP">
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| {{cite journal
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| | author=C. Jarlskog
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| | year=1985
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| | title=Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal <math>CP</math> Non-Conservation
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| | journal=[[Physical Review Letters]]
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| | volume=55 | issue=10 | pages=1039
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| | bibcode=1985PhRvL..55.1039J
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| | doi=10.1103/PhysRevLett.55.1039
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| | pmid=10031712
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| }}</ref> takes its extremal value <math>|J|=1/(6\sqrt{3})</math>.
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| | |
| Originally proposed as a candidate [[neutrino oscillation|lepton mixing]] matrix,<ref name="WOLF78">
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| {{cite journal
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| | author=L. Wolfenstein
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| | year=1978
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| | title=Oscillations Among Three Neutrino Types and CP Violation
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| | journal=[[Physical Review D]]
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| | volume=18 |issue=3 | pages=958
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| | bibcode=1978PhRvD..18..958W
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| | doi=10.1103/PhysRevD.18.958
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| }}</ref><ref name="CAB78">
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| {{cite journal
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| | author=N. Cabibbo
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| | year=1978
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| | title=Time Reversal Violation in Neutrino Oscillation
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| | journal=[[Physics Letters B]]
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| | volume=32 |issue=3 | pages=333
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| | bibcode=1978PhLB...72..333C
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| | doi=10.1016/0370-2693(78)90132-6
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| }}</ref> and actively studied<ref name="HPS1999"/><ref name="HPS1995"/><ref name="GIUNTI1995">
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| {{cite journal
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| | author=C. Giunti, C. W. Kim and J. D. Kim,
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| | year=1995
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| | title=Atmospheric Neutrino Problem in Maximally Mixed Three Generations of Neutrinos
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| | journal=[[Physics Letters B]]
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| | volume=352 |issue=3–4 | pages=357
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| | arxiv=hep-ph/9411219
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| | bibcode=1995PhLB..352..357G
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| | doi=10.1016/0370-2693(95)00424-J
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| }}</ref><ref name="HPS1997">
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| {{cite journal
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| | author=P.F. Harrison, D. H. Perkins and W. G. Scott
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| | year=1997
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| | title=Further Evidence for Threefold Maximal Lepton Mixing and a Hierarchical Spectrum of Neutrino Mass-Squared Differences
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| | journal=[[Physics Letters B]]
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| | volume=396 |issue=1–4 | pages=186
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| | arxiv=hep-ph/9702243
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| | bibcode=1997PhLB..396..186H
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| | doi=10.1016/S0370-2693(97)00105-6
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| }}</ref> as such (and even as a candidate quark mixing matrix<ref name="HS1994">
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| {{cite journal
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| | author=P.F. Harrison and W. G. Scott
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| | year=1994
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| | title=Generation Permutation Symmetry and the Quark Mixing Matrix
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| | journal=[[Physics Letters B]]
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| | volume=333 |issue=3–4 | pages=471
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| | arxiv=hep-ph/9406351
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| | bibcode=1994PhLB..333..471H
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| | doi=10.1016/0370-2693(94)90170-8
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| }}</ref>), trimaximal mixing is now definitively ruled-out as a phenomenologically viable lepton mixing scheme by [[neutrino oscillation]] experiments, especially the [[CHOOZ]] reactor experiment,<ref name="CHOOZ">
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| {{cite journal
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| | author=M. Apollonio et al.
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| | year=2003
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| | title=Search for Neutrino Oscillations on a Long Baseline at the CHOOZ Nuclear Power Station
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| | journal=[[European Physical Journal C]]
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| | volume=27 |issue=3 | pages=331
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| | arxiv=hep-ex/0301017
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| | bibcode=2003EPJC...27..331A
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| | doi=10.1140/epjc/s2002-01127-9
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| }}</ref> in favour of the no longer tenable (related) [[tribimaximal mixing]]<ref name="HPS2002">
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| {{cite journal
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| | author=P.F. Harrison, D. H. Perkins and W. G. Scott
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| | year=2002
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| | title=Tri-Bimaximal Mixing and the Neutrino Oscillation Data
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| | journal=[[Physics Letters B]]
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| | volume=530 |issue=1–4 | pages=167
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| | arxiv=hep-ph/0202074
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| | bibcode=2002PhLB..530..167H
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| | doi=10.1016/S0370-2693(02)01336-9
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| }}</ref> scheme.
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| | |
| ==References== | |
| {{reflist|2}}
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| | |
| [[Category:Leptons]]
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| [[Category:Standard Model]]
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| [[Category:Particle physics]]
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Andrew Simcox is the name his mothers and fathers gave him and he totally enjoys this name. My spouse doesn't like it the way I do but what I really like doing is caving but I don't have the time lately. He works as a bookkeeper. My wife and I reside in Mississippi but now I'm contemplating other choices.
My web site: phone psychic