Neutrinoless <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi><mml:mi>β</mml:mi></mml:mrow></mml:math> -decay nuclear matrix elements from two-neutrino <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi><mml:mi>β</mml:mi></mml:mrow></mml:math> -decay data

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