Neutrinoless double-beta decay interpretation

For light Majorana-neutrino exchange between two ordinary left-handed charged currents, the amplitude is proportional to $m_{\beta\beta}=|\sum_iU_{ei}^2m_i|$. The two electron-flavor vertices supply two unconjugated mixing entries, unlike the ordinary oscillation product that cancels each column phase. Consequently relative Majorana phases can affect this coherent sum. The Dirac-phase placement within U depends on the parameterization; the full squared-entry expression avoids assigning a physical meaning to an isolated convention-dependent phase. All masses here are nonnegative physical mass eigenvalues.

Different complex contributions can interfere destructively even when every neutrino has a nonzero mass. The effective double-beta mass therefore differs from the positive kinematic combination m beta and from the cosmological mass sum. A null search cannot generally prove that neutrinos are Dirac: the effective sum may be small, the mass scale low, or the detector insufficiently sensitive. Conversely, an observed lepton-number-violating decay would not automatically determine the lightest mass or both relative phases. One magnitude supplies less information than the several unknown parameters inside it.

The phase-space factor is calculable, but the nuclear matrix element depends on a many-body treatment and its operator conventions. Effective axial coupling and additional nuclear contributions also matter. Different acceptable calculations can map the same half-life bound into a range of effective-mass bounds. If another lepton-number-violating mechanism contributes, such as a short-distance operator, even this light-exchange translation can fail. Comparing isotopes, electron distributions, complementary processes, and theoretical calculations can help distinguish explanations, but the total rate in one nucleus is not a mechanism fingerprint.

Under the usual local weak-interaction assumptions, the Schechter-Valle argument connects an actual neutrinoless double-beta amplitude to a radiatively induced Majorana mass term. It does not show that this tiny induced term dominates the observed neutrino masses or mediates the measured decay rate. Explicit calculations demonstrate that distinction. Thus evidence for lepton-number violation would support a Majorana mass component, while numerical extraction of m beta beta still requires dominance by the particular light-neutrino-exchange mechanism in the displayed formula. The theorem and the quantitative interpretation answer different questions.

The complete-dataset KamLAND-Zen report, in its March 2026 manuscript version, gives a xenon-136 half-life lower bound of $3.8\times10^{26}$ years at ninety percent confidence. Assuming light exchange, its selected phenomenological nuclear calculations translate this into upper limits between 28 and 122 meV on the effective Majorana mass. The interval reflects model-dependent translations of one bound, not a measured allowed mass band. The paper also reports a median sensitivity different from its observed limit; expected sensitivity is not an additional observed exclusion.

A credible candidate must be separated from radioactive backgrounds, the ordinary two-neutrino spectrum, detector response effects, and other energy deposits. The idealized signal places nearly all decay energy in the two electrons, but finite resolution broadens that feature. Efficiency and exposure determine event yield only after those selection assumptions are specified. Reporting the isotope, statistical confidence convention, background treatment, nuclear inputs, and assumed mechanism makes the inference reproducible. The current cited null result establishes neither Dirac nature nor a nonzero Majorana mass measurement; it constrains a specified class of lepton-number-violating explanations.