Predicting the neutrinoless double-β-decay matrix element of 136 Xe using a statistical approach
Calculation of the nuclear matrix elements (NMEs) for double-β decay is of paramount importance for guiding experiments and for analyzing and interpreting the experimental data, especially for the search of the neutrinoless double β decay mode (0vββ). 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. Here, in this paper, we propose a statistical analysis of 0vββ 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 0vββ 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.