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-G\"ursey transformation. Our analysis shows that either choice of the parity gives the correct results of neutron-antineutron oscillations if carefully treated.
Highlights
Motivated by the possible baryon number violation in some unification schemes, many authors have discussed neutron-antineutron oscillations in the past [1,2,3,4,5,6,7,8,9] and, in spite of the phenomenon not yet having been observed, experimental bounds have been established [12]
In the analysis of neutron-antineutron oscillations, it has recently been argued in the literature that the use of the iγ0 parity npðt; −x⃗ Þ 1⁄4 iγ0nðt; −x⃗ Þ, which is consistent with the Majorana condition, is mandatory and that the ordinary parity transformation of the neutron field npðt; −x⃗ Þ 1⁄4 γ0nðt; −x⃗ Þ has difficulties
We have shown that the use of the conventional γ0-parity for the starting neutron field gives rise to a consistent description of the emergent Majorana fermions in the oscillation process and a consistent description of neutron-antineutron oscillations
Summary
Motivated by the possible baryon number violation in some unification schemes, many authors have discussed neutron-antineutron oscillations in the past [1,2,3,4,5,6,7,8,9] (see Refs. [10,11]) and, in spite of the phenomenon not yet having been observed, experimental bounds have been established [12]. We define the charge conjugation C, which is given by the representation theory of the Clifford algebra, by nðxÞ → ncðxÞ 1⁄4 CnðxÞT; ncðxÞ → nðxÞ; ð3Þ and the parity P is defined as the mirror symmetry for a Dirac fermion by the customarily used “γ0-parity”. The parity transformation of the charge conjugated fields is ncðxÞ → ðncÞpðt; −x⃗ Þ 1⁄4 −γ0ncðt; −x⃗ Þ: ð6Þ This definition of parity amounts to assigning an intrinsic parity þ1 to the neutron and −1 to the antineutron. We will show that the use of the conventional γ0-parity for the starting neutron field gives a logically consistent description of neutron-antineutron oscillations if a proper treatment and interpretation is applied. The proposal in [26] is to characterize the emergent Majorana fermions by CP symmetry. A formal proof of the canonical equivalence of the two choices of parity operation in the analysis of neutron-antineutron oscillations will be given in Appendix A using the Pauli-Gürsey transformation
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