Nuclear matrix element of neutrinoless double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math>decay: Relativity and short-range correlations

Background:The discovery of neutrinoless double-$\ensuremath{\beta}$ ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decay would demonstrate the nature of neutrinos, have profound implications for our understanding of matter-antimatter mystery, and solve the mass hierarchy problem of neutrinos. The calculations for the nuclear matrix elements ${M}^{0\ensuremath{\nu}}$ of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay are crucial for the interpretation of this process.Purpose: We study the effects of relativity and nucleon-nucleon short-range correlations on the nuclear matrix elements ${M}^{0\ensuremath{\nu}}$ by assuming the mechanism of exchanging light or heavy neutrinos for the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay.Methods:The nuclear matrix elements ${M}^{0\ensuremath{\nu}}$ are calculated within the framework of covariant density functional theory, where the beyond-mean-field correlations are included in the nuclear wave functions by configuration mixing of both angular-momentum and particle-number projected quadrupole deformed mean-field states.Results: The nuclear matrix elements ${M}^{0\ensuremath{\nu}}$ are obtained for ten $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay candidate nuclei. The impact of relativity is illustrated by adopting relativistic or nonrelativistic decay operators. The effects of short-range correlations are evaluated.Conclusions: The effects of relativity and short-range correlations play an important role in the mechanism of exchanging heavy neutrinos though the influences are marginal for light neutrinos. Combining the nuclear matrix elements ${M}^{0\ensuremath{\nu}}$ with the observed lower limits on the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay half-lives, the predicted strongest limits on the effective masses are $|\ensuremath{\langle}{m}_{\ensuremath{\nu}}\ensuremath{\rangle}|&lt;0.06\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ for light neutrinos and $|\ensuremath{\langle}{m}_{{\ensuremath{\nu}}_{h}}^{\ensuremath{-}1}\ensuremath{\rangle}{|}^{\ensuremath{-}1}&gt;3.065\ifmmode\times\else\texttimes\fi{}{10}^{8}\phantom{\rule{0.28em}{0ex}}\mathrm{GeV}$ for heavy neutrinos.