Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism

Nuclear weak decays provide important probes to fundamental symmetries in nature. A precise description of these processes in atomic nuclei requires comprehensive knowledge on both the strong and weak interactions in the nuclear medium and on the dynamics of quantum many-body systems. In particular, an observation of the hypothetical double beta decay without emission of neutrinos (0v beta beta) would unambiguously demonstrate the Majorana nature of neutrinos and the existence of the lepton-number violation process. It would also provide unique information on the ordering and absolute scale of neutrino masses. The next-generation tonne-scale experiments with sensitivity up to 10(28) years after a few years of running will probably provide a definite answer to these fundamental questions based on our current knowledge on the nuclear matrix element (NME), the precise determination of which is a challenge to nuclear theory. Beyond-mean-field approaches have been frequently adapted for the study of nuclear structure and decay throughout the nuclear chart for several decades. In this review, we summarize the status of beyond-mean-field calculations of the NMEs of 0v beta beta decay assuming the standard mechanism of an exchange of light Majorana neutrinos. The challenges and prospects in the extension and application of beyond-mean-field approaches for 0v beta beta decay are discussed. (C) 2022 Elsevier B.V. All rights reserved.