Neutrinoless double-$\beta$-decay $\left(0\nu \beta \beta \right)$ 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 ${}^{48}\mathrm{Ca}$ $0\nu \beta \beta$ NME using the interacting shell model, emphasizing the range of the NME probable values and their 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, and a mean value of 0.68.

• Received 13 May 2022
• Revised 25 August 2022
• Accepted 28 September 2022

DOI:https://doi.org/10.1103/PhysRevC.106.054302