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Register a new userAb Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of $^{48}$Ca
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Working with Hamiltonians from chiral effective field theory, we develop a novel framework for describing arbitrary deformed medium-mass nuclei by combining the in-medium similarity renormalization group with the generator coordinate method. The approach leverages the ability of the first method to capture dynamic correlations and the second to include collective correlations without violating symmetries. We use our scheme to compute the matrix element that governs the neutrinoless double beta decay of $^{48}$Ca to $^{48}$Ti, and find it to have the value $0.61$, near or below the predictions of most phenomenological methods. The result opens the door to ab initio calculations of the matrix elements for the decay of heavier nuclei such as $^{76}$Ge, $^{130}$Te, and $^{136}$Xe.
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We calculate basis-space converged neutrinoless $beta beta$ decay nuclear matrix elements for the lightest candidates: 48Ca, 76Ge and 82Se. Starting from initial two- and three-nucleon forces, we apply the ab initio in-medium similarity renormalization group to construct valence-space Hamiltonians and consistently transformed $beta beta$-decay operators. We find that the tensor component is non-negligible in 76Ge and 82Se, and resulting nuclear matrix elements are overall 25-45% smaller than those obtained from the phenomenological shell model. While a final matrix element with uncertainties still requires substantial developments, this work nevertheless opens a path toward a true first-principles calculation of neutrinoless $beta beta$ decay in all nuclei relevant for ongoing large-scale searches.
We use coupled-cluster theory and nuclear interactions from chiral effective field theory to compute the nuclear matrix element for the neutrinoless double-beta decay of $^{48}$Ca. Benchmarks with the no-core shell model in several light nuclei inform us about the accuracy of our approach. For $^{48}$Ca we find a relatively small matrix element. We also compute the nuclear matrix element for the two-neutrino double-beta decay of $^{48}$Ca with a quenching factor deduced from two-body currents in recent ab-initio calculation of the Ikeda sum-rule in $^{48}$Ca [Gysbers et al., Nature Physics 15, 428-431 (2019)].
$^{48}$Ca, the lightest double beta decay candidate, is the only one simple enough to be treated exactly in the nuclear shell model. Thus, the $betabeta(2 u)$ half-life measurement, reported here, provides a unique test of the nuclear physics involved in the $betabeta$ matrix element calculation. Enriched $^{48}$Ca sources of two different thicknesses have been exposed in a time projection chamber, and yield T$_{1/2}^{2 u} = (4.3^{+2.4}_{-1.1} [{rm stat.}] pm 1.4 [{rm syst.}]) times 10^{19}$ years, compatible with the shell model calculations.
We report ab initio benchmark calculations of nuclear matrix elements (NMEs) for neutrinoless double-beta ($0 ubetabeta$) decays in light nuclei with mass number ranging from $A=6$ to $A=22$. We use the transition operator derived from light-Majorana neutrino exchange and evaluate the NME with three different methods: two variants of in-medium similarity renormalization group (IMSRG) and importance-truncated no-core shell model (IT-NCSM). The same two-plus-three-nucleon interaction from chiral effective field theory is employed, and both isospin-conserving ($Delta T=0$) and isospin-changing ($Delta T=2$) transitions are studied. We compare our resulting ground-state energies and NMEs to those of recent ab initio no-core shell model and coupled-cluster calculations, also with the same inputs. We show that the NMEs of $Delta T=0$ transitions are in good agreement among all calculations, at the level of 10%. For $Delta T=2$, relative deviations are more significant in some nuclei. The comparison with the exact IT-NCSM result allows us to analyze these cases in detail, and indicates the next steps towards improving the IMSRG-based approaches. The present study clearly demonstrates the power of consistent cross-checks that are made possible by ab initio methodology. This capability is crucial for providing meaningful many-body uncertainties in the NMEs for the $0 ubetabeta$ decays in heavier candidate nuclei, where quasi-exact benchmarks are not available.
We show that chiral effective field theory (EFT) two-body currents provide important contributions to the quenching of low-momentum-transfer Gamow-Teller transitions, and use chiral EFT to predict the momentum-transfer dependence that is probed in neutrinoless double-beta decay. We then calculate for the first time the neutrinoless double-beta decay operator based on chiral EFT currents and study the nuclear matrix elements at successive orders. The contributions from chiral two-body currents are significant and should be included in all calculations.
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