Neutrinoless $ββ$-decay nuclear matrix elements from two-neutrino $ββ$-decay data

We study two-neutrino ($2νββ$) and neutrinoless double-$β$ ($0νββ$) decays in the nuclear shell model and proton-neutron quasiparticle random-phase approximation (pnQRPA) frameworks. Calculating the decay half-life of several dozens of nuclei ranging from calcium to xenon with the shell model, and of $ββ$ emitters with a wide range of proton-neutron pairing strengths in the pnQRPA, we observe good linear correlations between $2νββ$- and $0νββ$-decay nuclear matrix elements for both methods. We then combine the correlations with measured $2νββ$-decay half-lives to predict $0νββ$-decay matrix elements with theoretical uncertainties based on our systematic calculations. Our results include two-body currents and the short-range $0νββ$-decay operator.