Correlations in oscillation data and their impact on neutrino mixing models

With increasing precision of neutrino experiments, complete correlation among the oscillation parameters will scrutinize theoretical neutrino mass and mixing models. Using available 1D–3D global-fit datasets, we construct a multidimensional ${\tilde{\chi }}^2$ function that provides a conservative estimate of the full six-dimensional parameter correlations. In our approach, we delineate the model-constrained parameter space by combining the interpolated experimental data with the analytical relations implied by a given mixing scheme. We identify ${\tilde{\chi }}_{\text{min}}^2$, corresponding to the optimal agreement attainable for parameter points satisfying the model. Applying this framework to several schemes (${\text{TM}}_{1,2}$, $\mu 1,2$–$\tau 1,2$) yields generally better fits for IO than for NO, with the $\mu 1$–$\tau 1$ scheme under IO providing the best overall fit. While $\mu 1,2$–$\tau 1,2$ and ${\text{TM}}_1$ schemes perform significantly better than ${\text{TM}}_2$, the latter is excluded at $>3\sigma$ C.L. using NuFIT~v6.1 data. We further evaluate the implications of these correlation-respecting constraints on the effective neutrino mass observables relevant to tritium $\beta$-decay ($m_{\beta }$) and neutrinoless double $\beta$-decay ($m_{\beta \beta }$). The proposed approach can be readily extended to test any theoretical framework that predicts algebraic relations among neutrino oscillation parameters, and we provide a GitHub starter kit.