Tribimaximal mixing

Tribimaximal mixing

Tribimaximal mixing cite journal | author = P.F. Harrison, D. H. Perkins and W. G. Scott | title = Tribimaximal 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 ] is a specific postulated form for the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) lepton mixing matrix "U". Tribimaximal mixing is defined by a particular choice of the matrix of moduli-squared of the elements of the PMNS matrix as follows:

:egin{bmatrix}
U_{e 1}|^2 & |U_{e 2}|^2 & |U_{e 3}|^2 \
U_{mu 1}|^2 & |U_{mu 2}|^2 & |U_{mu 3}|^2 \
U_{ au 1}|^2 & |U_{ au 2}|^2 & |U_{ au 3}|^2 end{bmatrix}= egin{bmatrix}frac{2}{3} & frac{1}{3} & 0 \frac{1}{6} & frac{1}{3} & frac{1}{2} \ frac{1}{6} & frac{1}{3} & frac{1}{2} end{bmatrix}.

The tribimaximal mixing form is compatible with all verified neutrino oscillation experiments to date,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] ".] and may be used as a zeroth-order approximation to more general forms for the PMNS matrix e.g.cite journal | author = G. Altarelli and F. Feruglio | title = Models of neutrino masses from oscillations with maximal mixing | journal = Journal of High Energy Physics | volume = 9811 | year = 1998 | pages = 021 | url = http://arxiv.org/pdf/hep-ph/9809596 | doi = 10.1088/1126-6708/1998/11/021 ] cite journal | author = J.D. Bjorken, P.F. Harrison and W. G. Scott | title = Simplified unitarity triangles for the lepton sector | journal = Physical Review D | volume = 74 | year = 2006 | pages = 073012 | url = http://arxiv.org/pdf/hep-ph/0511201 | doi = 10.1103/PhysRevD.74.073012 ] which are also consistent with the data. In the standard (PDGPDG] ) convention for the PMNS matrix, tribimaximal mixing may be specified in terms of lepton mixing angles as follows:

:egin{matrix} heta_{12}=sin^{-1} ({frac{1}{sqrt{3})simeq 35.3^{circ} & heta_{23}=45^{circ}\ heta_{13}=0 & delta=0.end{matrix}

Explanation of name

The name "tribimaximal" reflects the commonality of the tribimaximal mixing matrix with two previously proposed specific forms for the PMNS matrix, the trimaximalcite 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] and bimaximalcite journal | author = V.D. Barger, S. Pakvasa, T.J. Weiler and K. Whisnant | title = Bimaximal mixing of three neutrinos | journal = Physics Letters B | volume = 437 | year = 1998 | pages = 107 | url = http://arxiv.org/pdf/hep-ph/9806387 | doi = 10.1016/S0370-2693(98)00880-6] mixing schemes, both now ruled out by data. In tribimaximal mixing,TBM2002] the u_2 neutrino mass eigenstate is said to be "trimaximally mixed" in that it consists of a uniform admixture of u_e, u_{mu} and u_{ au} flavour eigenstates, ie. maximal mixing among all three flavour states. The u_3 neutrino mass eigenstate, on the other hand, is "bimaximally mixed" in that it comprises a uniform admixture of only two flavour components, ie. u_{mu} and u_{ au} maximal mixing, with effective decoupling of the u_e from the u_3, just as in the original bimaximal scheme.BIMAX]

Phenomenology

By virtue of the zero (|U_{e3}|^2=0) in the tribimaximal mixing matrix, exact tribimaximal mixing would predict zero for all CP-violating asymmetries in the case of Dirac neutrinos (in the case of Majorana neutrinos, Majorana phases are still permitted, and could still lead to CP-violating effects).

For solar neutrinos the large angle MSW effect in tribimaximal mixing accounts for the experimental data, predicting average suppressions simeq 1/3 in the Sudbury Neutrino Observatory (SNO) and simeq 5/9 in lower energy solar neutrino experiments (and in long baseline reactor neutrino experiments). The bimaximally mixed u_3 in tribimaximal mixing accounts for the factor of two suppression simeq 1/2 observed for atmospheric muon-neutrinos (and confirmed in long-baseline accelerator experiments). Near-zero u_e appearance in a u_{mu} beam is predicted in exact tribimaximal mixing (|U_{e3}|^2 = 0), and future experiments may well rule this out. Further characteristic predictionsTBM2002] of tribimaximal mixing, eg. for very long baseline u_{mu} and u_{ au} (vacuum) survival probabilities (P_{mu mu}=P_{ au au} simeq 7/18), will be extremely hard to test experimentally.

History

The name "tribimaximal" first appeared in the literature in 2002TBM2002] although this specific scheme had been previously published in 1999cite 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 ] as a viable alternative to the trimaximalTRIMAX] scheme. Tribimaximal mixing is sometimes confused with other mixing schemes, e.g.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] which differ from tribimaximal mixing by row- and/or column-wise permutations of the mixing-matrix elements. Such permuted forms are experimentally distinct however, and are now ruled out by data.PDG]

References


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