Benchmark neutrinoless double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> decay matrix elements in a light nucleus

Abstract

We compute nuclear matrix elements of neutrinoless double-$\ensuremath{\beta}$ decay mediated by light Majorana-neutrino exchange in the $A=6$ system. The goal is to benchmark two many-body approaches, the no-core shell model and the multireference in-medium similarity renormalization group (SRG). We use a SRG-evolved next-to-next-to-next-to-leading chiral order two-body potential for the nuclear interaction, and make the approximation that the isospin is conserved. We compare the results of the two approaches as a function of the cutoff on the many-body basis space. Although differences are seen in the predicted nuclear radii, the ground-state energies and neutrinoless double-$\ensuremath{\beta}$ decay matrix elements produced by the two approaches show significant agreement. We discuss the implications for calculations in heavier nuclei.