Possibility of measuring the $CP$ Majorana phases in $0\nu \beta \beta$ decay

In view of recent measurements of the mixing angle ${\theta }_{13}$, we investigate the possibility to determine the difference of two $CP$ Majorana phases of the neutrino mixing matrix from the study of neutrinoless double-beta decay. We show that if cosmological measurements will reach the sensitivity of 0.1 eV for the sum of neutrino masses, i.e., the mass value of the lightest neutrino will be strongly constrained, the long-baseline neutrino oscillation experiments will determine inverted hierarchy of neutrino masses and if neutrinoless double-beta decay will be observed, this determination might be possible. The required experimental accuracies and the uncertainties in the calculated nuclear matrix elements of the process are discussed in this context.

Figure 1

The $CP$ phase ${\alpha }_2$ (left panels) and difference of phases ${\alpha }_{21}$ (right panels) are plotted, respectively, as function of the absolute value of the effective Majorana mass for the IH and NH of neutrino masses and the chosen value of $m_0$.

Figure 2

The difference of $CP$ phases ${\alpha }_{21}={\alpha }_2-{\alpha }_1$ plotted as a function of $|m_{\beta \beta }{|}^{\mathrm{obs}}$ for the inverted hierarchy of neutrino masses. The current experimental errors of neutrino mixing parameters and mass squared differences are taken into account; $m_0$ is taken to be in the range of 0 to 10 meV. The blue, red, and orange regions correspond to $|m_{\beta \beta }{|}^{\mathrm{obs}}$ with errors (${\sigma }_{\beta \beta }/|m_{\beta \beta }{|}^{\mathrm{obs}}$) of 0%, 15%, and 25%, respectively.