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Register a new userNeutron-Antineutron Oscillation as a Signal of CP Violation
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Assuming the Lorentz and CPT invariances we show that neutron-antineutron oscillation implies breaking of CP along with baryon number violation -- i.e. two of Sakharov conditions for baryogenesis. The oscillation is produced by the unique operator in the effective Hamiltonian. This operator mixing neutron and antineutron preserves charge conjugation C and breaks P and T. External magnetic field always leads to suppression of oscillations. Its presence does not lead to any new operator mixing neutron and antineutron.
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We point out that if neutron--antineutron oscillation is observed in a free neutron oscillation experiment, it will put an upper limit on the strengths of Lorentz invariance violating (LIV) mass operators for neutrons at the level of $10^{-23}$ GeV or so, which would be the most stringent LIV limit for neutrons. We also study constraints on $Delta B=2$ LIV operators and find that for one particular operator degaussing is not necessary to obtain a visible signal. We also note that observation of $n-bar{n}$ oscillation signal in the nucleon decay search experiment involving nuclei does not lead to any limit on LIV operators since the nuclear potential difference between neutron and antineutrons will mask any Lorentz violating effect.
The values of the antineutron-nucleus scattering lengths, and in particular their imaginary parts, are needed to evaluate the feasibility of using neutron mirrors in laboratory experiments to search for neutron-antineutron oscillations. We analyze existing experimental and theoretical constraints on these values with emphasis on low $A$ nuclei and use the results to suggest materials for the neutron/antineutron guide and to evaluate the systematic uncertainties in estimating the neutron-antineutron oscillation time. As an example we discuss a scenario for a future neutron-antineutron oscillation experiment proposed for the European Spallation Source. We also suggest future experiments which can provide a better determination of the values of antineutron-nuclei scattering lengths.
In the analysis of neutron-antineutron oscillations, it has been recently argued in the literature that the use of the $igamma^{0}$ parity $n^{p}(t,-vec{x})=igamma^{0}n(t,-vec{x})$ 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, $igamma^{0}$ parity and $gamma^{0}$ parity, are compensated for by the Pauli-Gursey transformation. Our analysis shows that either choice of the parity gives the correct results of neutron-antineutron oscillations if carefully treated.
We consider the possibility of neutron-antineutron ($n-bar n$) conversion, in which the change of a neutron into an antineutron is mediated by an external source, as can occur in a scattering process. We develop the connections between $n-{bar n}$ conversion and $n-{bar n}$ oscillation, in which a neutron spontaneously tranforms into an antineutron, noting that if $n-{bar n}$ oscillation occurs in a theory with B-L violation, then $n-{bar n}$ conversion can occur also. We show how an experimental limit on $n-{bar n}$ conversion could connect concretely to a limit on $n-{bar n}$ oscillation, and vice versa, using effective field theory techniques and baryon matrix elements computed in the M.I.T. bag model.
We analyze status of ${bf C}$, ${bf P}$ and ${bf T}$ discrete symmetries in application to neutron-antineutron transitions breaking conservation of baryon charge ${cal B}$ by two units. At the level of free particles all these symmetries are preserved. This includes ${bf P}$ reflection in spite of the opposite internal parities usually ascribed to neutron and antineutron. Explanation, which goes back to the 1937 papers by E. Majorana and by G. Racah, is based on a definition of parity satisfying ${bf P}^{2}=-1$, instead of ${bf P}^{2}=1$, and ascribing $ {bf P}=i$ to both, neutron and antineutron. We apply this to ${bf C}$, ${bf P}$ and ${bf T}$ classification of six-quark operators with $|Delta {cal B} |=2$. It allows to specify operators contributing to neutron-antineutron oscillations. Remaining operators contribute to other $|Delta {cal B} |=2$ processes and, in particular, to nuclei instability. We also show that presence of external magnetic field does not induce any new operator mixing the neutron and antineutron provided that rotational invariance is not broken.
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