Model independent constraints of the averaged neutrino masses revisited

Averaged neutrino masses defined by $\la m_\nu\ra_{ab} \equiv\left| \sum_{j=1}^{3}U_{aj}U_{bj}m_j\right|$ ($a,b=e,\mu,\tau$) are reanalyzed using up-to-date observed MNS parameters and neutrino masses by the neutrino oscillation experiments together with the cosmological constraint on neutrino masses. The values of $\la m_\nu\ra_{ab}$ are model-independently evaluated in terms of effective neutrino mass defined by $\overline{m_\nu}\equiv\left(\sum |U_{ej}|^2m_j^2\right)^{1/2}$ which is observable in the single beta decay. We obtain lower bound for $\langle m_\nu \rangle_{ee}$ in the inverted hierarchy(IH) case, $17~\mbox{meV} \leq \langle m_\nu \rangle_{ee}$ and one for $\langle m_\nu \rangle_{\tau \mu}$ in the normal hierarchy(NH) case, $5~\mbox{meV}\leq \langle m_\nu \rangle_{\tau \mu}$. We also obtain that all the averaged masses $\la m_\nu\ra_{ab}$ have upper bounds which are at most $80~\mbox{meV}$.