Tribimaximal Mixing

Tribimaximal mixing 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 was compatible with all verified neutrino oscillation experiments until recently, and may be used as a zeroth-order approximation to more general forms for the PMNS matrix e.g. which are also consistent with the data. In the standard (PDG) convention for the PMNS matrix, tribimaximal mixing may be specified in terms of lepton mixing angles as follows:

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

The tribimaximal mixing is now ruled out because θ13 is large. This possibility was foreseen in certain theoretical schemes, that were put forward before tribimaximal mixing and that supported a large solar mixing before it was confirmed experimentally (these schemes do not have a special name, but for the reasons explained above, they could be called pre-tribimaximal or also non-tribimaximal). This situation is not new: also in nineties, the solar mixing angle was supposed to be small by most theorists, till when KamLAND proved that the contrary is true.

Read more about Tribimaximal Mixing:  Explanation of Name, Phenomenology, History

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