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

{{reflist, 2, refs=

{{cite arXiv
, author = F. Vissani
, year = 1997
, title = A study of the scenario with nearly degenerate Majorana neutrinos
, eprint = hep-ph/9708483

{{cite journal
, author = V. D. Barger , author2 = S. Pakvasa , author3 = T. J. Weiler , author4 = K. Whisnant
, year = 1998
, title = Bimaximal mixing of three neutrinos
, journal = Physics Letters B
, volume = 437 , issue = 1–2
, pages = 107–116
, arxiv = hep-ph/9806387
, bibcode = 1998PhLB..437..107B
, doi = 10.1016/S0370-2693(98)00880-6
, citeseerx = 10.1.1.345.3379
, s2cid = 14622000
{{cite web, url=https://indico.cern.ch/event/300715/contributions/686782/attachments/566732/780663/king_lecture1.pdf, title=Neutrino Mass Models - Lecture 1: Lepton Mixing, first=Steve, last=King, date=August 2014, access-date=16 June 2021
{{cite web, url=https://pdg.lbl.gov/2021/reviews/rpp2020-rev-neutrino-mixing.pdf, title=14. Neutrino Masses, Mixing, and Oscillations, first1= M.C., last1=Gonzalez-Garcia, first2=M., last2=Yokoyama, date=August 2019, access-date=16 June 2021
{{cite journal
, author1=I. Stancu , author2=D. V. Ahluwalia
, name-list-style=amp , year = 1999
, title = L/E-Flatness of the Electron-Like Event Ratio in Super-Kamiokande and a Degeneracy in Neutrino Masses
, journal = Physics Letters B
, volume = 460 , issue = 3–4 , pages = 431–436
, arxiv = hep-ph/9903408
, bibcode = 1999PhLB..460..431S
, doi = 10.1016/S0370-2693(99)00811-4
, s2cid=14787873

{{cite journal
, last1=Abe , first1=Y.
, display-authors=etal.
, collaboration=Double Chooz Collaboration
, year=2014
, title=Improved measurements of the neutrino mixing angle θ₁₃ with the Double Chooz detector
, journal=Journal of High Energy Physics
, volume=2014 , issue=10
, page=86
, arxiv= 1406.7763
, bibcode= 2014JHEP...10..086A
, doi=10.1007/JHEP10(2014)086
, s2cid=53849018

{{cite journal
, doi=10.1007/JHEP09(2016)167
, arxiv=1606.09591
, title=Viability of exact tri-bimaximal, golden-ratio and bimaximal mixing patterns and renormalization-group running effects
, first1=Jue
, last1=Zhang
, first2=Shun
, last2=Zhou
, date=July 25, 2016
, journal=Journal of High Energy Physics
, volume=2016
, number=167, page=167
, bibcode=2016JHEP...09..167Z
, s2cid=119208235

Leptons
Standard Model
Neutrinos