If future neutrino oscillation experiments show that the neutrino mass spectrum is with normal ordering, $m_1<m_2<m_3$, and the searches for neutrinoless double beta [$(\beta \beta {)}_{0\nu }$] decay with sensitivity to values of the effective Majorana mass $|⟨m⟩|\gtrsim {10}^{-2}\mathrm{eV}$ give negative results, the next frontier in the quest for $(\beta \beta {)}_{0\nu }$-decay will correspond to $|⟨m⟩|\sim {10}^{-3}\mathrm{eV}$. By assuming that massive neutrinos are Majorana particles and their exchange is the dominant mechanism generating $(\beta \beta {)}_{0\nu }$-decay, we analyze the conditions under which $|⟨m⟩|$, in the case of three-neutrino mixing and a neutrino mass spectrum with normal ordering, would satisfy $|⟨m⟩|\ge 0.001\mathrm{eV}$. We consider the specific cases of (i) a normal hierarchical neutrino mass spectrum, (ii) a relatively small value of the CHOOZ angle ${\theta }_{13}$, as well as (iii) the general case of a spectrum with normal ordering, a partial hierarchy, and a value of ${\theta }_{13}$ close to the existing upper limit. We study the ranges of the lightest neutrino mass $m_1$ and/or of ${sin}^2{\theta }_{13}$ for which $|⟨m⟩|\ge 0.001\mathrm{eV}$ and discuss the phenomenological implications of such scenarios. We provide also an estimate of $|⟨m⟩|$ when the three-neutrino masses and the neutrino mixing originate from a neutrino mass term of the Majorana type for the (left-handed) flavor neutrinos and $\sum _j^3{m}_j{U}_{ej}^2=0$, but there does not exist a symmetry which forbids the $(\beta \beta {)}_{0\nu }$-decay.

Close

PrevNext

View figure in article

• 
• 
• 
• 
• 
•