Large-scale shell-model analysis of the neutrinoless $\beta\beta$ decay of $^{48}$Ca

TL;DR

This paper uses large-scale shell-model calculations including $sd$ and $pf$ shells to analyze the neutrinoless double-beta decay of $^{48}$Ca, finding a significant enhancement in the nuclear matrix element that impacts decay lifetime estimates.

Contribution

It provides a comprehensive shell-model analysis including cross-shell excitations, improving the accuracy of nuclear matrix elements for $^{48}$Ca neutrinoless double-beta decay.

Findings

Nuclear matrix element is increased by about 30% with cross-shell excitations.

Decay lifetime is reduced by nearly a factor of two.

Good agreement with experimental spectra and two-neutrino decay data.

Abstract

We present the nuclear matrix element for the neutrinoless double-beta decay of $^{48}$Ca based on large-scale shell-model calculations including two harmonic oscillator shells ($sd$ and $pf$ shells). The excitation spectra of $^{48}$Ca and $^{48}$Ti, and the two-neutrino double-beta decay of $^{48}$Ca are reproduced in good agreement to experiment. We find that the neutrinoless double-beta decay nuclear matrix element is enhanced by about 30\% compared to $pf$-shell calculations. This reduces the decay lifetime by almost a factor of two. The matrix-element increase is mostly due to pairing correlations associated with cross-shell $sd$-$pf$ excitations. We also investigate possible implications for heavier neutrinoless double-beta decay candidates.