Statistical analysis for the neutrinoless double- β -decay matrix element of Ca48

Neutrinoless double beta decay ($0\nu\beta\beta$) nuclear matrix elements (NME) are the object of many theoretical calculation methods, and are very important for analysis and guidance of a large number of experimental efforts. However, there are large discrepancies between the NME values provided by different methods. In this paper we propose a statistical analysis of the $^{48}$Ca $0\nu\beta\beta$ NME using the interacting shell model, emphasizing the range of the NME probable values and its correlations with observables that can be obtained from the existing nuclear data. Based on this statistical analysis with three independent effective Hamiltonians we propose a common probability distribution function for the $0\nu\beta\beta$ NME, which has a range of (0.45 - 0.95) at 90\% confidence level of, and a mean value of 0.68.