A Compact Dimensionless Reactor Readout Linking CKM and PMNS Inputs

A Reproducible Single-Observable Flavor Scaffold

抄録

We present a narrowly scoped and fully reproducible phenomenological relation connecting a composite quantity derived from the CKM matrix with the reactor-angle scale of the PMNS matrix.
The analysis is based on explicitly specified benchmark values for the CKM matrix elements, which are treated as fixed reference inputs rather than quantities determined by the present work. From these inputs, we define a dimensionless composite parameter characterizing the hierarchical structure of quark mixing and use it to construct a simple readout for the leptonic reactor mixing angle.
For the adopted benchmark values, this relation reproduces a reactor-angle scale close to the experimentally observed value. The resulting prediction follows directly from the stated readout formula and does not require any additional fitting parameters.
The benchmark inputs are selected from representative values consistent with the ranges reported by the Particle Data Group and contemporary CKM global-fit analyses. All derived quantities are obtained directly from the prescribed relation, ensuring full numerical reproducibility.
The proposed relation should be interpreted as a phenomenological candidate for a single-observable reactor-angle readout. It is not intended as evidence for a universal square-root law, a first-principles derivation of the underlying exponent, a complete prediction of the PMNS matrix, a determination of the leptonic CP phase, a derivation of the neutrino mass scale, or a selection between Dirac and Majorana neutrino scenarios.