Prediction of LSND effect as a "sterile" perturbation of the bimaximal texture for three active neutrinos

Abstract

As a contribution to the hypothesis of mixing of three active neutrinos with, at least, one sterile neutrino, we report on a simple $4\times 4$ texture whose $3\times 3$ part arises from the popular bimaximal texture for three active neutrinos ${\nu }_e,{\nu }_{\mu },{\nu }_{\tau }$, where $c_{12}=1/\sqrt{2}=s_{12}$, $c_{23}=1/\sqrt{2}=s_{23}$ and $s_{13}=0$. Such a $3\times 3$ bimaximal texture is perturbed through a rotation in the 14 plane, where ${\nu }_4$ is the extra neutrino mass state induced by the sterile neutrino ${\nu }_s$ which becomes responsible for the LSND effect. Then, with $m_1^2\simeq m_2^2$ we predict that ${\sin }^{2}2{\theta }_{\mathrm{atm}}=1/2(1+c_{14}^2)\sim 0.95$ and ${\sin }^{2}2{\theta }_{\mathrm{LSND}}=1/2s_{14}^4\sim 5\times 10^{-3}$, and in addition $\Delta m_{\mathrm{atm}}^2=\Delta m_{32}^2$ and $\Delta m_{\mathrm{LSND}}^2=|\Delta m_{41}^2|$, where $c_{14}^2={\sin }^{2}2{\theta }_{\mathrm{sol}}\sim 0.9$ and $\Delta m_{21}^2=\Delta m_{\mathrm{sol}}^2\sim 10^{-7}{\mathrm{eV}}^2$ if e.g. the LOW solar solution is applied.

Comments: Reference [9] lost in the original submission added