Predicting neutrinoless double beta decay

We give predictions for the neutrinoless double beta decay rate in a simple variant of the $A_4$ family symmetry model. We show that there is a lower bound for the $\beta {\beta }_{0\nu }$ amplitude even in the case of normal hierarchical neutrino masses, corresponding to an effective mass parameter $|m_{ee}|\ge 0.17\sqrt{\Delta m_{\mathrm{ATM}}^2}$. This result holds both for the $CP$ conserving and $CP$ violating cases. In the latter case we show explicitly that the lower bound on $|m_{ee}|$ is sensitive to the value of the Majorana phase. We conclude therefore that in our scheme, $\beta {\beta }_{0\nu }$ may be accessible to the next generation of high sensitivity experiments.

Figure 1

Solar mixing angle, ${tan}^2{\theta }_{12}$, vs $b/d$.

Figure 2

$|m_{ee}/\sqrt{\Delta m_{\mathrm{ATM}}^2}|$ vs $|t_{2S}|$ according to Eq. (17). The bound depends slightly on the value of $\alpha$: the left panel corresponds to $\alpha =0.022$ and the right one to $\alpha =0.065$. The dark (red) lines correspond to normal hierarchy, while the gray (green) line is for the inverse hierarchy case. The vertical line corresponds to the horizontal line in Fig. 1 at ${tan}^2{\theta }_{12}=1/2$.

Figure 3

$|m_{ee}/\sqrt{\Delta m_{\mathrm{ATM}}^2}|$ vs $|t_{2S}|$ for $\alpha =0.065$ when complex parameters are allowed.

Figure 4

Lower bound on $|m_{ee}/\sqrt{\Delta m_{\mathrm{ATM}}^2}|$ vs $|\cos ({\varphi }_1)|$, given current $t_{2S}$ uncertainty. The lines in dark (red) and gray (green) correspond to normal and inverse hierarchy, respectively.