Sterile neutrino creating a reduced LSND effect

Abstract

Although the hypothetic sterile neutrino $ν_s$ is probably not involved significantly in the deficits of solar $ν_e$'s and atmospheric $ν_μ$'s, it may cause the possible LSND effect. In fact, we face such a situation, when the popular nearly bimaximal texture of active neutrinos $ν_e$, $ν_μ$, $ν_τ$ is perturbed through a small rotation in the 14 plane, where $ν_4$ is the extra neutrino mass state induced by the sterile neutrino $ν_s$. Then, with $m^2_1\simeq m^2_2$ we predict in the simplest case of $s_{13}\to0$ that $\sin^22θ_{\rm LSND}=s^4_{14}/2$ and $Δm^2_{\rm LSND} = |Δm^2_{41}|$. However, the negative CHOOZ experiment imposes on $s^4_{14}/2$ the upper bound $1.3\times10^{-3}$, suggesting a reduction of the amplitude of possible LSND effect.