Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review

Abstract

The nuclear matrix elements that govern the rate of neutrinoless double beta decay must be accurately calculated if experiments are to reach their full potential. Theorists have been working on the problem for a long time but have recently stepped up their efforts as ton-scale experiments have begun to look feasible. Here we review past and recent work on the matrix elements in a wide variety of nuclear models and discuss work that will be done in the near future. Ab initio nuclear-structure theory, which is developing rapidly, holds out hope of more accurate matrix elements with quantifiable error bars.

35 pages, 14 figures

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Cited by in corpus (53)

• Value of the axial-vector coupling strength in $\beta$ and $\beta \beta$ decays: A review
• Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven
• Final result of CUPID-0 phase-I in the search for the ${}^{82}$Se Neutrinoless Double Beta Decay
• Neutrinoless double beta decay matrix elements in light nuclei
• Precision Analysis of the ${}^{136}$Xe Two-Neutrino $\beta \beta$ Spectrum in KamLAND-Zen and Its Impact on the Quenching of Nuclear Matrix Elements
• Impact of the quenching of $g_{\mathrm{A}}$ on the sensitivity of $0\nu \beta \beta$ experiments
• Neutrinoless double-beta decay matrix elements in large shell-model spaces with the generator-coordinate method
• Nucleosynthesis and observation of the heaviest elements
• Low background techniques in bolometers for double-beta decay search
• Shell-model calculation of ${}^{100}$Mo double-$\beta$ decay
• Study of one-proton transfer reaction for the ${}^{18}$O + ${}^{48}$Ti system at 275 MeV
• Long-distance Contributions to Neutrinoless Double Beta Decay ${\pi }^{-}\to {\pi }^{+}ee$
• Variational approach with the superposition of the symmetry-restored quasi-particle vacua for nuclear shell-model calculations
• Multi-channel experimental and theoretical constraints for the ${}^{116}$Cd(${}^{20}$Ne,${}^{20}$F)${}^{116}$In charge exchange reaction at 306 MeV
• ${}^{100}$Mo-enriched Li${}_2$MoO${}_4$ scintillating bolometers for $0\nu 2\beta$ decay search: from LUMINEU to CUPID-0/Mo projects
• Final Results of GERDA on the Two-Neutrino Double-$\beta$ Decay Half-Life of ${}^{76}$Ge
• Testing the Inverted Neutrino Mass Ordering with Neutrinoless Double-Beta Decay
• Radiopure tungstate and molybdate crystal scintillators for double beta decay experiments
• The union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double-beta decay
• Predicting the neutrinoless double-beta decay matrix element of ${}^{136}$Xe using a statistical approach
• Nuclear Structure at the Crossroads
• Probing the Mechanism of Neutrinoless Double-Beta Decay in Multiple Isotopes
• Global calculation of two-neutrino double-$\beta$ decay within the finite amplitude method in nuclear density functional theory
• Nuclear matrix elements for neutrinoless double beta decays and spin-dipole giant resonances
• One-neutron transfer reaction in the ${}^{18}$O + ${}^{48}$Ti collision at 275 MeV
• Majorana neutrino signals at Belle-II and ILC
• Correlations Between Neutrinoless Double-Beta, Double Gamow-Teller and Double-Magnetic Decays in the pnQRPA Framework
• Neutron-proton pairing and double-beta decay in the interacting boson model
• Half-life Expectations for Neutrinoless Double Beta Decay in Standard and Non-Standard Scenarios
• Present Status of Nuclear Shell-Model Calculations of Neutrinoless Double-Beta Decay Matrix Elements
• Neutrino Masses and Mixing in Models with Large Extra Dimensions and Localized Fermions
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• Microscopic description of hexadecapole collectivity in even-even rare-earth nuclei near $N=90$
• Partial restoration of spin-isospin SU(4) Symmetry and the One-QRPA method in Double Beta Decay
• Microscopic description of quadrupole-hexadecapole coupling in radium, thorium, uranium and plutonium isotopes with the Gogny energy density functional
• Quadrupole-hexadecapole correlations in neutron-rich samarium and gadolinium isotopes
• Comparative study of ${}^6$He $\beta$-decay based on different similarity-renormalization-group evolved chiral interactions
• Two-body weak currents in heavy nuclei
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• On ${}^{146}$Nd, ${}^{144}$Sm and other unexplored 2$\beta$ decay isotopes
• Flavoured Neutrinoless Double Beta Decay
• Low Energy Constraints From Absolute Neutrino Mass Observables and Lepton Flavor Violation in Left-Right Symmetric Model
• Pairing properties of the double-β emitter 116Cd
• Double Beta Decay Experiments at Canfranc Underground Laboratory
• Quadrupole-hexadecapole coupling in the rare earth region with beyond mean field correlations
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• CP violation in $B_s$ decays mediated by two nearly-degenerate Majorana neutrinos