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

TL;DR

This paper employs a statistical approach using three effective Hamiltonians within the interacting shell model to estimate the neutrinoless double-beta decay nuclear matrix element of $^{136}$Xe, providing a quantified uncertainty range.

Contribution

It introduces a novel statistical analysis method to quantify uncertainties in the $^{136}$Xe neutrinoless double-beta decay NME using multiple Hamiltonians and existing nuclear data.

Findings

Estimated NME range: 1.55 - 2.65 at 90% confidence level

Mean NME value: 1.99 with a standard deviation of 0.37

Proposed a common probability distribution for the NME

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.