On the neutrino mass spectrum and neutrinoless double-beta decay

Assuming 3-ν mixing, neutrino oscillation explanation of the solar and atmospheric neutrino data and of the first KamLAND results, massive Majorana neutrinos and neutrinoless double-beta ((ββ)0ν-) decay generated only by the (V–A) charged current weak interaction via the exchange of the three Majorana neutrinos, we analyze in detail the possibility of determining the type of the neutrino mass spectrum by measuring of the effective Majorana mass |〈m〉| in (ββ)0ν-decay. The three possible types of neutrino mass spectrum are considered: (i) normal hierarchical (NH) m1⪡m2⪡m3, (ii) inverted hierarchical (IH), m1⪡m2≅m3, and (iii) quasi-degenerate (QD), m1≅m2≅m3, m1,2,3≳0.20 eV. The uncertainty in the measured value of |〈m〉| due to the imprecise knowledge of the relevant nuclear matrix elements is taken into account in the analysis. We derive the ranges of values of tan2θ⊙, θ⊙ being the mixing angle which controls the solar neutrino oscillations, and of the nuclear matrix element uncertainty factor, for which the measurement of |〈m〉| would allow one to discriminate between the NH and IH, NH and QD, and IH and QD spectra.