Nuclear matrix element of neutrinoless double-beta decay: relativity and short-range correlations

Abstract

Background:The discovery of neutrinoless double-Î_s10 (0νÎ_s10Î_s10) 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 M0ν of 0νÎ_s10Î_s10 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 M0ν by assuming the mechanism of exchanging light or heavy neutrinos for the 0νÎ_s10Î_s10 decay. Methods:The nuclear matrix elements M0ν 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 M0ν are obtained for ten 0νÎ_s10Î_s10-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 M0ν with the observed lower limits on the 0νÎ_s10Î_s10-decay half-lives, the predicted strongest limits on the effective masses are |mν| < 0.06 eV for light neutrinos and |m−1νh|−1 > 3.065 × 1E8 GeV for heavy neutrinos