  We discuss the possibilities of distinguishing among different mechanisms of
neutrinoless double beta decay arising in the effective field theory framework.
Following the review and detailed investigation of the particular ways of
discrimination, we conclude that the 32 different low-energy effective
operators can be split into multiple groups that are in principle
distinguishable from each other by measurements of the phase-space observables
and by comparison of the decay rates obtained using different isotopes. This
would require not only a substantial experimental precision but necessarily
also a considerable improvement of the current theoretical knowledge of the
underlying nuclear physics. Specifically, the limiting aspect in our approach
turns out to be the currently unknown or uncertain values of low-energy
constants. Besides the study adopting the effective field theory language we
also look into several typical UV models.
