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| '''Trimaximal mixing'''<ref name="HPS1999"> | | Jayson Berryhill is how I'm called and my spouse doesn't like it at all. The favorite pastime for him and his children is to perform lacross and he would by no means give it up. For many years she's been residing in Kentucky but her spouse wants them to move. He is an information officer.<br><br>My homepage ... free online tarot card readings ([http://m-card.co.kr/xe/mcard_2013_promote01/29877 m-card.co.kr]) |
| {{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==
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| {{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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Jayson Berryhill is how I'm called and my spouse doesn't like it at all. The favorite pastime for him and his children is to perform lacross and he would by no means give it up. For many years she's been residing in Kentucky but her spouse wants them to move. He is an information officer.
My homepage ... free online tarot card readings (m-card.co.kr)