Statistical predictions for the neutrinoless double-beta decay nuclear matrix element of ¹³⁶Xe

Neutrinoless double beta decay (0νββ) nuclear matrix elements (NME) are investigated by many theoretical methods, and they are important for analysing and guiding a large number of experimental efforts. In particular, the ¹³⁶Xe isotope has one of the largest 0νββ half-life limit observed, and it is at the forefront of the next generation of experimental investigations. However, there are still large discrepancies between the ¹³⁶Xe 0νββ NME values provided by different theoretical methods. In this contribution we propose a statistical analysis of the ¹³⁶Xe 0νββ NME for the light Majorana neutrino exchange mechanism (a.k.a. the mass mechanism) using the interacting shell model, and emphasizing the range of the NME probable values and its correlations with observables that can be obtained from the existing nuclear data. Based on a statistical analysis with three independent effective Hamiltonians, we propose a Bayesian Model Averaging approach for providing a common probability distribution function for the ¹³⁶Xe 0νββ NME. Using this distribution function we report predictions for an optimal value of the ¹³⁶Xe 0νββ NME, its variance, and its more probable range.