By S. Bilensky
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Additional resources for Absolute Values of Neutrino Masses - Status and Prospects
32 Let us consider three typical neutrino mass spectra in the case of three massive and mixed neutrinos13 : 1. m1 ≪ m2 ≪ m3 (hierarchy of neutrino masses). For the effective Majorana mass | m | we have the upper bound | m | ≤ sin2 ϑsol ∆m2sol + |Ue3 |2 ∆m2atm . 15) Using the best-fit values of the oscillation parameters ∆m2atm , ∆m2sol , tan2 ϑsol , and the CHOOZ bound on |Ue3 |2 (Eqs. 8 × 10−3 eV . 2 × 10−3 eV . 14) of the future (ββ)0ν -decay experiments. Thus, the observation of (ββ)0ν decay in the experiments of the next generation could pose a problem for the natural hierarchy of neutrino masses.
Has been obtained (see Ref. ). The problem of the calculation of the nuclear matrix elements of neutrinoless double-β decay is a real theoretical challenge. It is obvious that without a solution of this problem the effective Majorana neutrino mass | m | cannot be determined from the experimental data with reliable accuracy (see the discussion in Ref. [155, 148]). The authors of Ref.  proposed a method which allows to check the results of the calculations of the nuclear matrix elements of the (ββ)0ν -decay of different nuclei by confronting them with experimental data.
2. A sensitivity of a few 10−2 eV for | m | is planned to be reached in future experiments on the search for neutrinoless double-β decay of different nuclei. From Eq. 26) we have R(A, Z/A′, Z ′ ) ≡ 0ν T1/2 (A, Z) 0ν T1/2 (A′ , Z ′) = |M(A′ , Z ′ )|2 G0ν (E0′ , Z ′ ) . 28) Thus, if the neutrinoless double β -decay of different nuclei is observed, the calculated ratios of the corresponding squared nuclear matrix elements can be confronted with the experimental values. Table 2 shows the ratios of the lifetimes of (ββ)0ν -decay of several nuclei, calculated in six different models, using the values of the lifetimes given in Ref.
Absolute Values of Neutrino Masses - Status and Prospects by S. Bilensky