Nonperturbative renormalization of the neutrinoless double-beta operator in p-shell nuclei

TL;DR

This paper develops effective two-body operators for neutrinoless double-beta decay in p-shell nuclei using Lee-Suzuki mappings, enabling accurate approximations of large no-core-shell-model calculations and highlighting the potential need for three-body corrections.

Contribution

It introduces a nonperturbative method to construct effective decay operators that replicate large-scale no-core calculations in p-shell nuclei, with implications for heavier nuclei.

Findings

Effective two-body operators reproduce no-core results well in p-shell nuclei.

Some discrepancies suggest the importance of three-body corrections in heavier nuclei.

Method can be extended to fp-shell nuclei like 76Ge within coupled-cluster theory.

Abstract

We use Lee-Suzuki mappings and related techniques to construct effective two-body p-shell interactions and neutrinoless double-beta operators that exactly reproduce the results of large no-core-shell-model calculations of double-beta decay in nuclei with mass number A=6. We then apply the effective operators to the decay of nuclei with A=7, 8, and 10, again comparing with no-core calculations in much larger spaces. The results with the effective two-body operators are generally good. In some cases, however, they differ non-negligibly from the full no-core results, suggesting that three-body corrections to the decay operator in heavier nuclei may be important. An application of our procedure and related ideas to fp-shell nuclei such as 76Ge should be feasible within coupled-cluster theory.