Processes that break baryon number by two units and the Majorana nature of the neutrino

We employ the simplest possible models of scalar-fermion interactions that are consistent with the gauge symmetries of the Standard Model and permit no proton decay to analyze the connections possible among processes that break baryon number by two units. In this context we show how the observation of $n$-${\bar n}$ oscillations and of a pattern of particular nucleon-antinucleon conversion processes --- all accessible through e-d scattering --- namely, selecting from $e^- p \to e^+ {\bar p}$, $e^- p \to {\bar n} {\bar \nu}$, $e^- n \to {\bar p} {\bar \nu}$, and $e^- n \to e^- {\bar n} $ would reveal that the decay $\pi^- \pi^- \to e^- e^-$ must occur also. This latter process is the leading contribution to neutrinoless double beta decay in nuclei mediated by new short-distance physics, in contrast to that mediated by light Majorana neutrino exchange. The inferred existence of $\pi^- \pi^- \to e^- e^-$ would also reveal the Majorana nature of the neutrino, though the absence of this inference would not preclude it.