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

TL;DR

This paper assesses the impact of the leading-order short-range nuclear matrix element on neutrinoless double-beta decay in medium-mass and heavy nuclei, revealing its significant contribution and implications for neutrino mass hierarchy experiments.

Contribution

It provides the first detailed evaluation of the short-range matrix element's magnitude using shell model and pnQRPA methods, highlighting its substantial influence on decay rate predictions.

Findings

Short-range matrix element constitutes 15%-50% (shell model) and 30%-80% (pnQRPA) of the long-range matrix element.

Including the short-range term shifts experimental sensitivity toward the inverted neutrino mass hierarchy.

Results suggest the importance of considering short-range effects in neutrinoless double-beta decay analyses.

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.