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

Abstract

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

Comments: 9 pages, 3 figures, 2 tables; Fixed sign error in Eq. (5)