Nuclear matrix elements for neutrinoless double-beta decay in covariant density functional theory

We review the first fully relativistic description for the neutrinoless double-beta decay by the beyond-mean-field covariant density functional theory. The calculations of the nuclear transition matrix elements are based on a full relativistic transition operator and nuclear wave functions in which the dynamic effects of particle-number, angular-momentum, and parity conservations as well as shape fluctuations are incorporated. We find that the commonly used nonrelativistic approximation for the transition operator is justified within the mechanism of light-Majorana-neutrino exchange. We stress that reducing the discrepancies in the predicted nuclear matrix elements by different nuclear models is a major challenge in nuclear physics.