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Register a new userPerturbative Renormalization of Neutron-Antineutron Operators
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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 $< 7%$.
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We study the off-shell mixing and renormalization of flavor-diagonal dimension-5 T- and P-odd operators involving quarks, gluons, and photons, including quark electric dipole and chromo-electric dipole operators. We present the renormalization matrix to one-loop in the $bar{rm MS}$ scheme. We also provide a definition of the quark chromo-electric dipole operator in a regularization-independent momentum-subtraction scheme suitable for non-perturbative lattice calculations and present the matching coefficients with the $bar{rm MS}$ scheme to one-loop in perturbation theory, using both the naive dimensional regularization and t Hooft-Veltman prescriptions for $gamma_5$.
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.
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.
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.
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.
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