Three flavor neutrino oscillations, LSND, SNP and ANP

The recently reanalysed LSND data is investigated in the context of three flavor oscillations, with an emphasis on mass hierarchies and $s_{13}$. The resultant mass hierarchies and oscillation angles are tested with regard to "key" features of solar neutrinos and atmospheric neutrinos, e.g., "average" survival probability in the case of solar neutrinos, and zenith angle dependence and up-down asymmetry in the case of high energy atmospheric neutrinos. We find there are three distinct mass hierarchies, e.g., $\Delta m << \Delta M, \Delta m < \Delta M$ and $\Delta m \simeq \Delta M$. In the first and second case, the calculated range of $s_{13}$ is in agreement with the "LMA" solution of Akhmedov {\it et al.}, the lower limit on $s_{13}$ in these cases is also in agreement with the recent analysis of Garcia {\it et al.} based on the constraints of SNP, ANP and CHOOZ, therefore, strongly supporting the neutrino oscillations observed at LSND. Further, the solutions of $s_{13}$ found in the third case correspond to the value of $s_{13}$ found by Akhmedov {\it et al.} in the case of "SMA" and "LOW" solutions. A rough estimate of the possibility of the existence of CP violation in the leptonic sector is also carried out for different possible ranges of $s_{13}$, indicating that the CP asymmetries may be measureable even in the case of LSND.