Multi-Isotope Fingerprints of Long- and Short-Range Mechanisms in Neutrinoless Double Beta Decay

Neutrinoless double beta decay ($0\nu\beta\beta$) is a key probe of leptonnumber violation and the Majorana nature of neutrinos, but identifyingthe microscopic origin of the decay remains a major theoreticalchallenge.In realistic extensions of the Standard Model, long-range lightneutrino exchange and short-range contributions from heavy particleexchange can coexist and interfere, rendering interpretations based onsingle-isotope decay rates ambiguous. In this work we demonstrate that ratios of half-lives measured inmultiple isotopes provide a robust discriminator of the underlying$0\nu\beta\beta$ mechanism.Focusing on a left--right symmetric model, we construct a unifiedeffective-field-theory framework that consistently incorporates bothlong- and short-range contributions from the ultraviolet scale down tothe low-energy nuclear description.We introduce a multi-isotope fingerprint plane and quantify deviationsfrom the universal isotope scaling expected for long-range dominatedscenarios using a geometric distance measure. We find that long-range dominated scenarios collapse onto anexceptionally thin one-dimensional manifold in the fingerprint space,while mixed scenarios populate regions that are separated by one to twoorders of magnitude in the distance measure.Although different nuclear matrix element schemes significantly modifythe absolute location of the fingerprint, the relative separationbetween long-range dominated and mixed mechanisms remains largelyunchanged.This demonstrates that the multi-isotope fingerprint constitutes astable, nuclear-model-insensitive diagnostic of the underlying decaymechanism. Our results highlight the potential of coordinated multi-isotope$0\nu\beta\beta$ searches to go beyond discovery and performmechanism-level tests of lepton number violation, complementary toabsolute half-life measurements.