Parity of the neutron consistent with neutron-antineutron oscillations

Abstract

In the analysis of neutron-antineutron oscillations, it has been recently argued in the literature that the use of the $i{\gamma }^0$ parity $n^p(t,-\vec{x})=i{\gamma }^{0}n(t,-\vec{x})$ which is consistent with the Majorana condition is mandatory and that the ordinary parity transformation of the neutron field $n^p(t,-\vec{x})={\gamma }^{0}n(t,-\vec{x})$ has a difficulty. We show that a careful treatment of the ordinary parity transformation of the neutron works in the analysis of neutron-antineutron oscillations. Technically, the CP symmetry in the mass diagonalization procedure is important and the two parity transformations, $i{\gamma }^0$ parity and ${\gamma }^0$ parity, are compensated for by the Pauli-Gürsey transformation. Our analysis shows that either choice of the parity gives the correct results of neutron-antineutron oscillations if carefully treated.

Comments: 19 pages. Some modifications in Appendix B were made. This version is going to be published in Phys. Rev. D