Precision-Era Reassessment of Modified Quark--Lepton Complementarity: NuFIT 6.1, Phase-Convention Covariance and Lepton-Number Violation

Abstract

Quark-lepton complementarity (QLC) provides a phenomenological framework for comparing quark and lepton flavour structures. We reassess a modified QLC correlation-matrix construction using the 2026 Particle Data Group quark-mixing inputs and the NuFIT 6.1 oscillation likelihoods. The historical prediction $\sin^2θ_{23}=0.4235$ is strongly disfavoured, with $Δχ^2=17.99$ for normal ordering and 20.43 for inverted ordering, whereas later ordering-dependent estimates remain compatible with present preferred regions. Reconstructed ensembles of the complex correlation matrix show that the first row is comparatively stable, while about 99\% of the squared mean-texture evolution occurs in the lower two rows; roughly 72\% of the present ensemble remains closer to the tribimaximal than to the bimaximal reference texture. We further formulate the lepton sector in the symmetric Schechter-Valle parametrization. The oscillation phase appears as the invariant combination $δ=ϕ_{13}-ϕ_{12}-ϕ_{23}$, while independent phase directions remain relevant to lepton-number-violating (LNV) amplitudes. We prove that, for unrestricted diagonal quark-lepton mismatch phases, changing from the standard PDG convention to the symmetric parametrization leaves the full ensemble of $|V_{c,ij}|$ invariant: additional left phases are absorbed into the mismatch matrix and right phases only rephase columns. Consequently, the QLC magnitude texture does not constrain the independent Majorana/LNV phases. The historical $S_1$ and $S_2$ limits are also found to lie close to their phase-agnostic kinematic ceilings.