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Tribimaximal mixingTribimaximal mixing ^{[1]} is a specific postulated form for the PontecorvoMakiNakagawaSakata (PMNS) lepton mixing matrix U. Tribimaximal mixing is defined by a particular choice of the matrix of modulisquared of the elements of the PMNS matrix as follows: The tribimaximal mixing form is compatible with all verified neutrino oscillation experiments to date,^{[2]} and may be used as a zerothorder approximation to more general forms for the PMNS matrix e.g.^{[3]}^{[4]} which are also consistent with the data. In the standard (PDG^{[2]}) convention for the PMNS matrix, tribimaximal mixing may be specified in terms of lepton mixing angles as follows: Additional recommended knowledge
Explanation of nameThe name tribimaximal reflects the commonality of the tribimaximal mixing matrix with two previously proposed specific forms for the PMNS matrix, the trimaximal^{[5]} and bimaximal^{[6]} mixing schemes, both now ruled out by data. In tribimaximal mixing,^{[1]} the ν_{2} neutrino mass eigenstate is said to be "trimaximally mixed" in that it consists of a uniform admixture of ν_{e}, ν_{μ} and ν_{τ} flavour eigenstates, ie. maximal mixing among all three flavour states. The ν_{3} neutrino mass eigenstate, on the other hand, is "bimaximally mixed" in that it comprises a uniform admixture of only two flavour components, ie. ν_{μ} and ν_{τ} maximal mixing, with effective decoupling of the ν_{e} from the ν_{3}, just as in the original bimaximal scheme.^{[6]} PhenomenologyBy virtue of the zero (  U_{e3}  ^{2} = 0) in the tribimaximal mixing matrix, exact tribimaximal mixing would predict zero for all CPviolating asymmetries in the case of Dirac neutrinos (in the case of Majorana neutrinos, Majorana phases are still permitted, and could still lead to CPviolating effects). For solar neutrinos the large angle MSW effect in tribimaximal mixing accounts for the experimental data, predicting average suppressions in the Sudbury Neutrino Observatory (SNO) and in lower energy solar neutrino experiments (and in long baseline reactor neutrino experiments). The bimaximally mixed ν_{3} in tribimximal mixing accounts for the factor of two suppression observed for atmospheric muonneutrinos (and confirmed in longbaseline accelerator experiments). Nearzero ν_{e} appearance in a ν_{μ} beam is predicted in exact tribimaximal mixing (  U_{e3}  ^{2} = 0), and future experiments may well rule this out. Further characteristic predictions^{[1]} of tribimaxiaml mixing, eg. for very long baseline ν_{μ} and ν_{τ} (vacuum) survival probabilities , will be extremely hard to test experimentally. HistoryThe name tribimaximal first appeared in the literature in 2002^{[1]} although this specific scheme had been previously published in 1999^{[7]} as a viable alternative to the trimaximal^{[5]} scheme. Tribimaximal mixing is sometimes confused with other mixing schemes, e.g.^{[8]} which differ from tribimaximal mixing by row and/or columnwise permutations of the mixingmatrix elements. Such permuted forms are experimentally distinct however, and are now ruled out by data.^{[2]} References


This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Tribimaximal_mixing". A list of authors is available in Wikipedia. 