Baryon number violation accompanied by CP-violation as a quantum tunneling effect induced by superfluid pairing interactions

In this work, we explore a new picture of baryon number ($\mathcal{B}$) violation inspired by the formal analogies between the Brout-Englert-Higgs model and the Ginzburg-Landau model. A possible manifestation of this new picture could be the transition between a pair of neutrons and a pair of antineutrons (i.e. $nn \rightarrow \bar{n}\bar{n}$), which violates $\mathcal{B}$ by 4 units. In the presence of the superfluid pairing interactions, two neutrons can form a Cooper pair and can be modeled by a semi-classical complex scalar field, which carries two units of $\mathcal{B}$. In the presence of the $\mathcal{B}$-violating terms, the system does not possess a continuous $U(1)$ symmetry but instead it respect a discrete $Z_2$ symmetry. Before the spontaneous breaking of the $Z_2$ symmetry, the ground state (vacuum) of the neutron Cooper field and that of the antineutron Cooper field should have degenerate energy levels. After the spontaneous breaking of the $Z_2$ symmetry, the degeneracy of the ground states would be removed and a domain wall that interpolates between the two inequavalent ground states can emerge. If the vacuum energy of the neutron Cooper field is higher than that of the antineutron Cooper field, the false vacuum ($nn$) would decay into the true vacuum ($\bar{n}\bar{n}$) through a quantum tunneling process across the domain wall. Therefore, The $nn \rightarrow \bar{n}\bar{n}$ transition process can be considered as a false vacuum decay through a quantum tunneling process induced by the superfluid pairing interactions. Both the $\mathcal{B}$-violating and CP-violating effects can be quite naturally accommodated in the $nn \rightarrow \bar{n}\bar{n}$ transition process. The $\mathcal{B}$-violating process accompanied by CP-violation would open a promising avenue for exploring new physics beyond the Standard Model.