Determining Majorana nature of neutrino from nucleon decays and $n-\overline{n}$ oscillations

We show that the discovery of baryon number violation in two processes, with at least one obeying the selection rule $\mathrm{\Delta }(B-L)=\pm 2$, can determine the Majorana character of neutrinos. Thus, observing $p\to e^{+}{\pi }^0$ and $n\to e^{-}{\pi }^{+}$ decays, or $p\to e^{+}{\pi }^0$ and $n-\overline{n}$ oscillations, or $n\to e^{-}{\pi }^{+}$ and $n-\overline{n}$ oscillations would establish that neutrinos are Majorana particles. We discuss this in a model-independent effective operator approach.

Figure 1

Diagrams responsible for (a) $p\to e^{+}{\pi }^0$ decay; (b) $n\to e^{-}{\pi }^{+}$ decay; and (c) $n-\overline{n}$ oscillations.

Figure 2

Neutrinoless double beta decay diagrams resulting from combining (a) $p\to e^{+}{\pi }^0$ and $n\to e^{-}{\pi }^{+}$ decays; (b) $p\to e^{+}{\pi }^0$ decay and $n-\overline{n}$ oscillation; and (c) $n\to e^{-}{\pi }^{+}$ decay and $n-\overline{n}$ oscillation.

Figure 3

Neutrino Majorana mass induced through any diagram that causes neutrinoless double beta decay.

Figure 4

Diagrams inducing neutrinoless double beta decay in $SO(10)$ models by combining $p\to e^{+}{\pi }^0$ and $n\to e^{-}{\pi }^{+}$ decays. (a) Exchange of vector bosons of $SO(10)$. (b) Exchange of vector bosons and scalars belonging to 120 of $SO(10)$. The quantum numbers of these fields are $X(3,2,-5/6)$, $V_Q(3,2,1/6)$, $V_{u^c}(3^{*},1,-2/3)$, $\overline{\eta }(3^{*},1,-2/3)$ and $\overline{\chi }(3^{*},2,-7/6)$ under Standard Model gauge symmetry. Here $H(1,2,1/2)$ is the SM Higgs field, and ${\mathrm{\Delta }}^c$ is the Higgs field responsible for $B-L$ breaking [8].

Figure 5

Leading diagram for neutrinoless double beta decay in a model with observable $n\to e^{-}{\pi }^{+}$ decay and $n-\overline{n}$ oscillations. Here ${\mathrm{\Delta }}_{ud}$ and ${\mathrm{\Delta }}_{dd}$ are color sextet scalars.

Figure 6

The “$B-L$ triangle” explains how discovering $n-\overline{n}$ oscillations and proton decay would imply that neutrinos are Majorana fermions.