Constraints on Neutrino Mass Ordering and Degeneracy from Planck and Neutrino-less Double Beta Decay

We investigate constraints on neutrino mass ordering and degeneracy by considering the first cosmological result based on the Planck measurements of the cosmic microwave background. It is shown that the result at 95\%~C.L. rejects a neutrino mass degeneracy larger than 85\% (82.5\%) for the normal (inverted) hierarchical case. We can also find some regions where the neutrino mass ordering will be able to be distinguished by combining a value of sum of the neutrino masses with an effective neutrino mass determined by neutrino-less double beta decay experiments. The results are obtained from the latest data of neutrino oscillation, cosmic microwave background, and the neutrino-less double beta decay experiments. These have significance in the discrimination of the neutrino mass ordering