Neutrinoless $\beta \beta$-decay nuclear matrix elements from two-neutrino $\beta \beta$-decay data

Abstract

We study two-neutrino ($2\nu \beta \beta$) and neutrinoless double-$\beta$ ($0\nu \beta \beta$) decays in the nuclear shell model and proton-neutron quasiparticle random-phase approximation (pnQRPA) frameworks. Calculating the decay half-life of several dozens of nuclei ranging from calcium to xenon with the shell model, and of $\beta \beta$ emitters with a wide range of proton-neutron pairing strengths in the pnQRPA, we observe good linear correlations between $2\nu \beta \beta$- and $0\nu \beta \beta$-decay nuclear matrix elements for both methods. We then combine the correlations with measured $2\nu \beta \beta$-decay half-lives to predict $0\nu \beta \beta$-decay matrix elements with theoretical uncertainties based on our systematic calculations. Our results include two-body currents and the short-range $0\nu \beta \beta$-decay operator.

12 pages, 8 figures, 4 tables; corresponds to the published version

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• Search for Majorana Neutrinos with the Complete KamLAND-Zen Dataset
• Final Results of GERDA on the Two-Neutrino Double-$\beta$ Decay Half-Life of ${}^{76}$Ge
• Predicting the neutrinoless double-beta decay matrix element of ${}^{136}$Xe using a statistical approach
• Neutrinoless double beta decay rates in the presence of light sterile neutrinos
• Correlations Between Neutrinoless Double-Beta, Double Gamow-Teller and Double-Magnetic Decays in the pnQRPA Framework
• Neutrinoless $\beta \beta$ decay nuclear matrix elements complete up to N${}^2$LO in heavy nuclei
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• Muon Capture on ${}^6$Li, ${}^{12}$C, and ${}^{16}$O from $AbInitio$ Nuclear Theory
• ${}^{138}\mathrm{Ba}(d,\alpha )$ study of states in ${}^{136}\mathrm{Cs}$: Implications for new physics searches with xenon detectors
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