We consider the seesaw model with two right-handed neutrinos, $N_1$ and $N_2$, the masses of which are hierarchical, and investigate their contribution to the neutrinoless double beta ($0 \nu \beta \beta$) decay. Although the lepton number is broken by the Majorana masses of right-handed neutrinos, such decay processes can be absent in some cases. We present a possibility where the lighter $N_1$ gives a destructive contribution to the decay of active neutrinos by choosing the specific mixing elements of $N_1$, while $N_2$ is sufficiently heavy not to contribute to the $0 \nu \beta \beta$ decay. In this case the mixing elements of $N_1$ in the charged current interaction are determined by its mass and the Majorana phase of active neutrinos. We then study the impacts of such a possibility on the direct search for $N_1$. In addition, we discuss the consequence of the case when the $0 \nu \beta \beta$ decay in one specific nucleus is absent.

中文翻译：

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如果没有特定的无中微子双β衰变怎么办？

我们考虑具有两个右手中微子 $N_1$ 和 $N_2$ 的跷跷板模型，它们的质量是分层的，并研究它们对无中微子双 beta ($0 \nu \beta \beta$) 衰变的贡献。尽管轻子数被右旋中微子的马约拉纳质量所打破，但在某些情况下可能不存在这种衰变过程。我们提出了一种可能性，即较轻的 $N_1$ 通过选择 $N_1$ 的特定混合元素对活跃中微子的衰变产生破坏性贡献，而 $N_2$ 足够重，不会对 $0 \nu \beta \beta 做出贡献$衰减。在这种情况下，$N_1$ 在充电电流相互作用中的混合元素由其质量和活跃中微子的马约拉纳相决定。然后我们研究这种可能性对直接搜索 $N_1$ 的影响。此外，