Neutrinoless $\beta\beta$ decay mediated by the exchange of light and heavy neutrinos: The role of nuclear structure correlations

TL;DR

This paper compares nuclear matrix elements for neutrinoless double beta decay mediated by light and heavy neutrinos, highlighting how nuclear structure correlations influence the uncertainties and discrepancies in theoretical calculations.

Contribution

It provides a detailed comparison of matrix elements for light and heavy neutrino exchange, emphasizing the role of nuclear correlations and their impact on calculation uncertainties.

Findings

Heavy-neutrino exchange matrix elements are less sensitive to nuclear correlations.

Discrepancies in matrix elements mainly stem from treatment of long-range correlations.

Shorter-range heavy-neutrino exchange shows reduced theoretical uncertainty.

Abstract

Neutrinoless $\beta\beta$ decay nuclear matrix elements calculated with the shell model and energy-density functional theory typically disagree by more than a factor of two in the standard scenario of light-neutrino exchange. In contrast, for a decay mediated by sterile heavy neutrinos the deviations are reduced to about 50\%, an uncertainty similar to the one due to short-range effects. We compare matrix elements in the light- and heavy-neutrino-exchange channels, exploring the radial, momentum transfer and angular momentum-parity matrix element distributions, and considering transitions that involve correlated and uncorrelated nuclear states. We argue that the shorter-range heavy-neutrino exchange is less sensitive to collective nuclear correlations, and that discrepancies in matrix elements are mostly due to the treatment of long-range correlations in many-body calculations. Our analysis supports previous studies suggesting that isoscalar pairing correlations, which affect mostly the longer-range part of the neutrinoless $\beta\beta$ decay operator, are partially responsible for the differences between nuclear matrix elements in the standard light-neutrino-exchange mechanism.