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:
:$\begin , U_, ^2 & , U_, ^2 & , U_, ^2 \\ , U_, ^2 & , U_, ^2 & , U_, ^2 \\ , U_, ^2 & , U_, ^2 & , U_, ^2 \end = \begin \frac & \frac & 0 \\ \frac & \frac & \frac \\ \frac & \frac & \frac \end$.

According to PDG convention, bimaximal mixing corresponds to $\theta_=\theta_=45^\circ$ and $\theta_=\delta_=0$, which produces following matrix:
:$\begin U_ & U_ & U_ \\ U_ & U_ & U_ \\ U_ & U_ & U_ \end = \begin \frac & \frac & 0 \\ -\frac & \frac & \frac \\ \frac & -\frac & \frac \end$.
Alternatively, $\theta_=\theta_=-45^\circ$ and $\theta_=\delta_=0$ can be used, which corresponds to:
:$\begin U_ & U_ & U_ \\ U_ & U_ & U_ \\ U_ & U_ & U_ \end = \begin \frac & -\frac & 0 \\ \frac & \frac & -\frac \\ \frac & \frac & \frac \end$.

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:
:$U= \begin \cos\theta & \sin\theta & 0 \\ -\sin\theta/\sqrt & \cos\theta/\sqrt & \frac \\ \sin\theta/\sqrt & -\cos\theta/\sqrt & \frac \end.$
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 $\theta_$.

See also

* Trimaximal mixing
* Tribimaximal mixing
* Neutrino oscillation
* Double Chooz

References

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Leptons
Standard Model
Neutrinos