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Register a new userNeutron--Antineutron Oscillations: Discrete Symmetries and Quark Operators
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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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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.
Two-loop anomalous dimensions and one-loop renormalization scheme matching factors are calculated for six-quark operators responsible for neutron-antineutron transitions. When combined with lattice QCD determinations of the matrix elements of these operators, our results can be used to reliably predict the neutron-antineutron vacuum transition time, $tau_{nbar{n}}$, in terms of basic parameters of baryon-number violating beyond-the-Standard-Model theories. The operators are classified by their chiral transformation properties, and a basis in which there is no operator mixing due to strong interactions is identified. Operator projectors that are required for non-perturbative renormalization of the corresponding lattice QCD six-quark operator matrix elements are constructed. A complete calculation of $delta m = 1/tau_{nbar{n}}$ in a particular beyond-the-Standard-Model theory is presented as an example to demonstrate how operator renormalization and results from lattice QCD are combined with experimental bounds on $delta m$ to constrain the scale of new baryon-number violating physics. At the present computationally accessible lattice QCD matching scale of $sim$ 2 GeV, the next-to-next-to-leading-order effects calculated in this work correct the leading-order plus next-to-leading-order $delta m$ predictions of beyond-the-Standard-Model theories by $< 26%$. Next-to-next-to-next-to-leading-order effects provide additional unknown corrections to predictions of $delta m$ that are estimated to be $< 7%$.
Experimental observation of nucleon instability is one of the missing key components required for the explanation of baryon asymmetry of the universe. Proton decays with the modes and rates predicted by(B-L)-conserving schemes of Grand Unification are not observed experimentally. There are reasons to believe that (B-L) might not be conserved in nature, thus leading to the nucleon decay into lepton+(X) and to phenomena such as Majorana masses of neutrinos, neutrinoless double-beta decays, and most spectacularly to the transitions of neutron to anti-neutron. The energy scale where (B-L) violation takes place cannot be predicted by theory and therefore has to be explored by experiments. Different experimental approaches to searching for (B-L)-violating transition of neutron to antineutron are discussed in this paper. Most powerful search for neutron to antineutron transitions can be performed in a new reactor-based experiment at HFIR reactor (ORNL) where sensitivity can be >1,000 times higher than in the previous experiments.
Fundamental symmetry tests of baryon number violation in low-energy experiments can probe beyond the Standard Model (BSM) explanations of the matter-antimatter asymmetry of the universe. Neutron-antineutron oscillations are predicted to be a signature of many baryogenesis mechanisms involving low-scale baryon number violation. This work presents first-principles calculations of neutron-antineutron matrix elements needed to accurately connect measurements of the neutron-antineutron oscillation rate to constraints on $|Delta B|=2$ baryon number violation in BSM theories. Several important systematic uncertainties are controlled by using a state-of-the-art lattice gauge field ensemble with physical quark masses and approximate chiral symmetry, performing nonperturbative renormalization with perturbative matching to the $overline{text{MS}}$ scheme, and studying excited state effects in two-state fits. Phenomenological implications are highlighted by comparing expected bounds from proposed neutron-antineutron oscillation experiments to predictions of a specific model of post-sphaleron baryogenesis. Quantum chromodynamics is found to predict at least an order of magnitude more events in neutron-antineutron oscillation experiments than previous estimates based on the MIT bag model for fixed BSM parameters. Lattice artifacts and other systematic uncertainties that are not controlled in this pioneering calculation are not expected to significantly change this conclusion.
This paper summarizes the relevant theoretical developments, outlines some ideas to improve experimental searches for free neutron-antineutron oscillations, and suggests avenues for future improvement in the experimental sensitivity.
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