Bimaximal mixing

Bimaximal mixing refers to a proposed form of the lepton mixing matrix. It is characterized by the $$\nu_3$$ neutrino being a bimaximal mixture of $$\nu_\mu$$ and $$\nu_\tau$$ and being completely decoupled from the $$\nu_e$$, i.e. a uniform mixture of $$\nu_\mu$$ and $$\nu_\tau$$. The $$\nu_e$$ is consequently a uniform mixture of $$\nu_1$$ and $$\nu_2$$. Other notable properties are the symmetries between the $$\nu_\mu$$ and $$\nu_\tau$$ flavours and $$\nu_1$$ and $$\nu_2$$ mass eigenstates and an absence of CP violation. The moduli squared of the matrix elements have to be:
 * $$\begin{bmatrix}

\end{bmatrix} = \begin{bmatrix} \frac{1}{2} & \frac{1}{2} & 0 \\ \frac{1}{4} & \frac{1}{4} & \frac{1}{2} \\ \frac{1}{4} & \frac{1}{4} & \frac{1}{2} \end{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

According to PDG convention, bimaximal mixing corresponds to $$\theta_{12}=\theta_{23}=45^\circ$$ and $$\theta_{13}=\delta_{13}=0$$, which produces following matrix:
 * $$\begin{bmatrix}

U_{e 1} & U_{e 2} & U_{e 3} \\ U_{\mu 1} & U_{\mu 2} & U_{\mu 3} \\ U_{\tau 1} & U_{\tau 2} & U_{\tau 3} \end{bmatrix} = \begin{bmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\ -\frac{1}{2} & \frac{1}{2} & \frac{1}{\sqrt{2}} \\ \frac{1}{2} & -\frac{1}{2} & \frac{1}{\sqrt{2}} \end{bmatrix}$$. Alternatively, $$\theta_{12}=\theta_{23}=-45^\circ$$ and $$\theta_{13}=\delta_{13}=0$$ can be used, which corresponds to:
 * $$\begin{bmatrix}

U_{e 1} & U_{e 2} & U_{e 3} \\ U_{\mu 1} & U_{\mu 2} & U_{\mu 3} \\ U_{\tau 1} & U_{\tau 2} & U_{\tau 3} \end{bmatrix} = \begin{bmatrix} \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} & 0 \\ \frac{1}{2} & \frac{1}{2} & -\frac{1}{\sqrt{2}} \\ \frac{1}{2} & \frac{1}{2} & \frac{1}{\sqrt{2}} \end{bmatrix}$$.

Phenomenology
The L/E flatness of the electron-like event ratio at Super-Kamiokande severely restricts the CP-conserving neutrino mixing matrices to the form:

U= \begin{bmatrix} \cos\theta & \sin\theta & 0 \\ -\sin\theta/\sqrt{2} & \cos\theta/\sqrt{2} & \frac{1}{\sqrt{2}} \\ \sin\theta/\sqrt{2} & -\cos\theta/\sqrt{2} & \frac{1}{\sqrt{2}} \end{bmatrix}. $$ Bimaximal mixing corresponds to $$\theta=45^\circ$$. Tribimaximal mixing and golden-ratio mixing also correspond to an angle in the above parametrization. Bimaximal mixing, along with these other mixing schemes, have been falsified by a non-zero $$\theta_{13}$$.