Neutrino Mass Induced $n$-$\overline{n}$ Oscillation

Abstract: The Georgi-Glashow model is the simplest possible attempt at grand unification. However, due to its particle content, it preserves a global $U(1)_{B-L}$ symmetry, where $B$ and $L$ are baryon and lepton numbers, respectively. It thus leaves neutrinos massless just as in the Standard Model. Extensions of the Georgi-Glashow model that break lepton number by two units, i.e., scenarios with $|\Delta L|=2$ operator(s), naturally generate potentially viable Majorana neutrino masses. Consequently, $B-L$ breaking via the same dynamics that yields $|\Delta L| = 2$ interactions unavoidably induces $|\Delta B| = 2$ transitions, leading to intriguing processes such as neutron-antineutron ($n$-$\overline{n}$) oscillation. We demonstrate this intrinsic connection between neutrino mass generation and $n$-$\overline{n}$ oscillation within tree-level seesaw mechanisms of the Type I, II, and III varieties, as well as in the one-loop and two-loop radiative neutrino mass models. Our study exhausts the simplest possible extensions of the Georgi-Glashow model that yield realistic neutrino masses and mixing parameters and, in the process, induce $n$-$\overline{n}$ oscillation.