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We evaluate the leading-order short-range nuclear matrix element for theneutrinoless double-beta ($0\nu\beta\beta$) decay of the nuclei most relevantfor experiments, including $^{76}$Ge, $^{100}$Mo, $^{130}$Te and $^{136}$Xe. Inour calculations, performed with the nuclear shell model and proton-neutronquasiparticle random-phase approximation (pnQRPA) methods, we estimate thecoupling of this term by the contact charge-independence-breaking coupling ofvarious nuclear Hamiltonians. Our results suggest a significant impact of theshort-range matrix element, which is about $15\%-50\%$ and $30\%-80\%$ of thestandard $0\nu\beta\beta$-decay long-range matrix element for the shell modeland pnQRPA, respectively. Combining the full matrix elements with the resultsfrom current $0\nu\beta\beta$-decay experiments we find that, if both matrixelements carry the same sign, these searches move notably toward probing theinverted mass ordering of neutrino masses.

Impact of the leading-order short-range nuclear matrix element on the neutrinoless double-beta decay of medium-mass and heavy nuclei