1207.2545 (Zhen-hua Zhao)

Bi-maximal neutrino mixing model revisited with a new ansatz for mass
matrices    [PDF]

Zhen-hua Zhao

In this paper, we would like to propose a new ansatz for mass matrices of charged leptons and neutrinos which will help us understand both mass hierarchy and flavor mixing in the lepton sector. In this approach, electron and muon are massless and the mixing matrix turns out to be Bi-maximal, at the leading order(LO). Only after taking into account the effect of next-to-leading order(NLO), can electron and muon obtain masses and then the mass hierarchy among electron, muon and tau can get an understanding. Furthermore, NLO contributions which is about $2 \frac{m_\mu}{m_\tau}$ suppressed compared to the LO contributions can make the mixing angles consistent with experimental results. Remarkably, there is a numerical relation between the mixing angles $\theta_{12}$ and $\theta_{13}$ i.e. $\sin{\theta_{13}}\approx \frac{1}{\sqrt 2}\displaystyle \frac{1-\tan{\theta_{12}}}{1+\tan{\theta_{12}}}$ which can be tested by precision measurements. Because the NLO corrections to $\tan{\theta_{23}}$ is of order $\frac{m_\mu}{m_\tau} \sqrt{\frac{\Delta m_{12}^2}{\Delta m_{13}^2}}$, $\theta_{23}$ remains very close to $45^\circ$. A model which can reproduce this ansatz from the underlying physics is also given.

View original: http://arxiv.org/abs/1207.2545