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Neutrinoless $\beta\beta$ decay nuclear matrix elements calculated with theshell model and energy-density functional theory typically disagree by morethan a factor of two in the standard scenario of light-neutrino exchange. Incontrast, for a decay mediated by sterile heavy neutrinos the deviations arereduced to about 50\%, an uncertainty similar to the one due to short-rangeeffects. We compare matrix elements in the light- and heavy-neutrino-exchangechannels, exploring the radial, momentum transfer and angular momentum-paritymatrix element distributions, and considering transitions that involvecorrelated and uncorrelated nuclear states. We argue that the shorter-rangeheavy-neutrino exchange is less sensitive to collective nuclear correlations,and that discrepancies in matrix elements are mostly due to the treatment oflong-range correlations in many-body calculations. Our analysis supportsprevious studies suggesting that isoscalar pairing correlations, which affectmostly the longer-range part of the neutrinoless $\beta\beta$ decay operator,are partially responsible for the differences between nuclear matrix elementsin the standard light-neutrino-exchange mechanism.

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