Predicting the neutrinoless double-beta decay matrix element of ${}^{136}$Xe using a statistical approach

Abstract

Calculation of the nuclear matrix elements (NMEs) for double-beta decay is of paramount importance for guiding experiments and for analyzing and interpreting the experimental data, especially for the search of the neutrinoless double beta decay mode ($0\nu \beta \beta$). However, there are currently still large differences between the NME values calculated by different methods, hence a quantification of their uncertainties is very much required. In this paper we propose a statistical analysis of $0\nu \beta \beta$ NME for the ${}^{136}Xe$ isotope, based on the interacting shell model, but using three independent effective Hamiltonians, emphasizing the range of the NMEs' most probable values and its correlations with observables that can be obtained from the existing nuclear data. Consequently, we propose a common probability distribution function for the $0\nu \beta \beta$ NME, which has a range of (1.55 - 2.65) at 90\% confidence level, with a mean value of 1.99 and a standard deviation of 0.37.

arXiv comment13 pages, 4 figures, and one table. arXiv admin note: text overlap with arXiv:2203.10577

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Cited by in corpus (8)

• Neutrinoless $\beta \beta$ decay nuclear matrix elements complete up to N${}^2$LO in heavy nuclei
• Interplay between non-interfering neutrino exchange mechanisms and nuclear matrix elements in $0\nu \beta \beta$ decay
• Impact of shell model interactions on nuclear responses to WIMP elastic scattering
• Subspace-projected multireference covariant density functional theory
• Benchmarking nuclear matrix elements of $0\nu \beta \beta$ decay with high-energy nuclear collisions
• Two-neutrino $\beta \beta$ decay to excited states at next-to-leading order
• Ab initio short-range nuclear matrix elements for neutrinoless double-beta decay
• The study of $0\nu \beta \beta$ decay of ${}^{136}$Xe using nonclosure approach in nuclear shell model