Possibilities of Future Double Beta Decay Experiments to Investigate Inverted and Normal Ordering Region of Neutrino Mass

An overview of modern experiments on the search for neutrinoless double decay is presented. The obtained limits on the effective mass of the Majorana neutrino < m(nu)> are discussed taking into account the uncertainties in the value of the nuclearmatrix elements (NMEs) and the value of the axial-vector constant g(A). Predictions for the values of < m(nu)> from the results of oscillation experiments and modern cosmological data are presented. The possibilities of the next generation experiments with sensitivity to < m(nu)> at the level of similar to 10-50 meV (studying mainly the inverted ordering (IO) region) are discussed. The prospects for studying the normal ordering (NO) region are discussed too. It is shown that the possibilities of studying the NO depend on the mass of the lightest neutrino m(0). In the limiting case of small mass (m(0) <= 0.1 meV), the values of < m(nu)> approximate to 1-4 meV are predicted, which makes the study of this region inaccessible by the next generation experiments. But there is an allowed region of m(0) (7-30 meV) in the framework of NO, where the predicted values for < m(nu)> could be similar to 10-30 meV and that is quite achievable for the next generation experiments. The possibility to rich in the future sensitivity to < m(nu)> at the level of similar to 1-10 meV is also discussed.