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Tribimaximal mixing

Tribimaximal mixing ^[1] 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:

$\begin{bmatrix} |U_{e 1}|^2 & |U_{e 2}|^2 & |U_{e 3}|^2 \\ |U_{\mu 1}|^2 & |U_{\mu 2}|^2 & |U_{\mu 3}|^2 \\ |U_{\tau 1}|^2 & |U_{\tau 2}|^2 & |U_{\tau 3}|^2 \end{bmatrix} = \begin{bmatrix} \frac{2}{3} & \frac{1}{3} & 0 \\ \frac{1}{6} & \frac{1}{3} & \frac{1}{2} \\ \frac{1}{6} & \frac{1}{3} & \frac{1}{2} \end{bmatrix}.$

The tribimaximal mixing form is compatible with all verified neutrino oscillation experiments to date,^[2] and may be used as a zeroth-order 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:

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

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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 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]

Phenomenology

By virtue of the zero ( $| U e 3 | 2 = 0$ ) 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 $<P_{ee}> \simeq 1/3$ in the Sudbury Neutrino Observatory (SNO) and $<P_{ee}> \simeq 5/9$ 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 $<P_{\mu \mu}> \simeq 1/2$ observed for atmospheric muon-neutrinos (and confirmed in long-baseline accelerator experiments). Near-zero $ν e$ appearance in a $ν μ$ beam is predicted in exact tribimaximal mixing ( $| U e 3 | 2 = 0$ ), 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 $(P_{\mu \mu}=P_{\tau \tau} \simeq 7/18)$ , will be extremely hard to test experimentally.

History

The 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 column-wise permutations of the mixing-matrix elements. Such permuted forms are experimentally distinct however, and are now ruled out by data.^[2]

References

^ ^a ^b ^c ^d P.F. Harrison, D. H. Perkins and W. G. Scott (2002). "Tribimaximal mixing and the neutrino oscillation data". Physics Letters B 530: 167.
^ ^a ^b ^c W.M. Yao et al. (2006). "Particle Data Group - 2006 Review of Particle Physics". Journal of Physics G 33 (1). Neutrino mass, mixing, and flavor change.
^ G. Altarelli and F. Feruglio (1998). "Models of neutrino masses from oscillations with maximal mixing". Journal of High Energy Physics 9811: 021.
^ J.D. Bjorken, P.F. Harrison and W. G. Scott (2006). "Simplified unitarity triangles for the lepton sector". Physical Review D 74: 073012.
^ ^a ^b P.F. Harrison, D. H. Perkins and W. G. Scott (1995). "Threefold maximal lepton mixing and the solar and atmospheric neutrino deficits". Physics Letters B 349: 137.
^ ^a ^b V.D. Barger, S. Pakvasa, T.J. Weiler and K. Whisnant (1998). "Bimaximal mixing of three neutrinos". Physics Letters B 437: 107.
^ P.F. Harrison, D. H. Perkins and W. G. Scott (1999). "A Redetermination of the neutrino mass squared difference in tri-maximal mixing with terrestrial matter effects". Physics Letters B 458: 79.
^ L. Wolfenstein (1978). "Oscillations Among Three Neutrino Types and CP Violation". Physical Review D 18: 958.

Category: Leptons

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.

Tribimaximal mixing

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Contents

Explanation of name

Phenomenology

History

References

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