Model independent constraints of the averaged neutrino masses revisited

Abstract

Averaged neutrino masses defined by $\text{la}{m}_{\nu }{\text{ra}}_{ab}\equiv \left|{\sum }_{j=1}^3{U}_{aj}{U}_{bj}{m}_j\right|$ ($a,b=e,\mu ,\tau$) 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 $\text{la}{m}_{\nu }{\text{ra}}_{ab}$ are model-independently evaluated in terms of effective neutrino mass defined by $\overline{m_{\nu }}\equiv {\left(\sum |U_{ej}{|}^2{m}_j^2\right)}^{1/2}$ which is observable in the single beta decay. We obtain lower bound for $⟨m_{\nu }{⟩}_{ee}$ in the inverted hierarchy(IH) case, $17\text{mbox}meV\le ⟨m_{\nu }{⟩}_{ee}$ and one for $⟨m_{\nu }{⟩}_{\tau \mu }$ in the normal hierarchy(NH) case, $5\text{mbox}meV\le ⟨m_{\nu }{⟩}_{\tau \mu }$. We also obtain that all the averaged masses $\text{la}{m}_{\nu }{\text{ra}}_{ab}$ have upper bounds which are at most $80\text{mbox}meV$.

Comments: 8 pages, 7 figures, to appear in MPLA