Coupled-cluster calculations of neutrinoless double-beta decay in $^{48}$Ca*

We use coupled-cluster theory and nuclear interactions from chiral effective field theory to compute the nuclear matrix element for the neutrinoless double-beta decay of $^{48}$Ca. Benchmarks with the no-core shell model in several light nuclei and in the traditional shell model in the $pf$ shell inform us about the accuracy of our approach. For $^{48}$Ca we find a relatively small matrix element. We also compute the nuclear matrix element for the two-neutrino double-beta decay of $^{48}$Ca and find agreement with data when using a quenching factor deduced from two-body currents in the recent ab-initio calculation of the Ikeda sum-rule in $^{48}$Ca [Gysbers {\it et al.}, Nature Physics {\bf 15}, 428-431 (2019)]. Work available as [S. J. Novario, P. Gysbers, J. Engel, G. Hagen, G. R. Jansen, T. D. Morris, P. Navrátil, T. Papenbrock, S. Quaglioni, arXiv:2008.09696].