Beyond Half-Life Limits: Robust Operator-Level Interpretation of Multi-Isotope Neutrinoless Double-Beta Decay

Abstract

Current and future neutrinoless double-beta decay ($0\nu\beta\beta$) searches are usually characterized by half-life limits or projected sensitivities. For operator-level interpretation, however, the relevant question is not only the strength of the limit, but also the stability of the inferred constraints on low-energy lepton-number-violating (LNV) coefficients under changes of isotope and nuclear matrix-element (NME) method. Using $\nu$DoBe, we convert half-life limits or projected sensitivities into limits on low-energy LNV coefficients for several choices of isotope, operator class, and NME method. We then compare the resulting limits across isotopes and NME methods. We quantify the stability by the spread of coefficient limits in non-observation scenarios and, for single-operator post-discovery benchmarks, by the spread of isotope-to-isotope half-life ratios. For the operator examples considered in this paper, the light-Majorana exchange mechanism gives the most stable interpretation. The selected dimension-six operators remain reasonably robust, while the short-range dimension-nine examples show a stronger dependence on isotope and NME-method choices. The same hierarchy appears in post-discovery benchmarks based on isotope-to-isotope half-life ratios: the reliability of such tests depends on whether the predicted half-life pattern remains stable across NME methods. A multi-isotope $0\nu\beta\beta$ program therefore provides information beyond half-life reach by testing the stability of the operator interpretation. This spread-based analysis provides a practical way to identify which low-energy operator scenarios are suitable for isotope-ratio tests after a possible discovery, and which require more care before being connected to ultraviolet models of lepton-number violation.