The neutrinoless double $\beta$ decay and the neutrino mass hierarchy
  Recently the evidence of the neutrinoless double $\beta$   ($0\nu \beta\beta$) decay has been announced. This means that neutrinos are Majorana particles and their mass hierarchy is forced to certain patterns in the diagonal basis of charged lepton mass matrix. We estimate the magnitude of $0\nu \beta\beta$ decay in the classification of the neutrino mass hierarchy patterns as Type A, $m_{1,2} \ll m_{3}$, Type B,   $m_1 \sim m_2 \gg m_3$, and Type C, $m_1 \sim m_2 \sim m_3$, where $m_{i}$ is the $i$-th generation neutrino absolute mass. The data of $0\nu \beta\beta$ decay experiment suggests the neutrino mass hierarchy pattern should be Type B or C. Type B predicts a small magnitude of $0\nu \beta\beta$ decay which is just edge of the allowed region of experimental value in $95% \mathrm{c.l.}$, where Majorana CP phases should be in a certain parameter region. Type C can induce the suitably large amount of $0\nu \beta\beta$ decay which is consistent with the experimental data, where overall scale of degenerate neutrino mass plays a crucial role, and its large value can induce the large $0\nu \beta\beta$ decay in any parameter regions of Majorana CP phases. 
Naoyuki Haba and Tomoharu Suzuki