High Energy Particle Physics |
Authors: Belkacem Lichani
We document a set of empirical relations linking the three mixing angles of the CKM matrix to quark mass ratios in the form sin θij = pmi/mj, extending the historical Gatto-Sartori-Tonin (1968) relation. Evaluated within the space of possiblecombinatorial configurations (C(15, 3) = 455 triplets of pairs), this structure stands out with a statistical significance of p = 0.0022 in reproducing the experimental hierarchy to better than 5%, and displays internal consistency at 0.90σ upon cross-extraction of the up quark mass. By algebraic construction, such a texture defined on positive real mass ratios is structurally incapable of generating a complex phase. The CP-violating phase is therefore treated separately via the conjecture |sin δCP | = mW /mZ, a testable numerical observation providing a sharp predictivetarget for the DUNE experiment (δCP ≈ 298◦). We emphasize that this work does not constitute a complete dynamical theory and presents an open anomaly: the paradoxical use of family 1—2 masses in the expression of the mixing angle θ23 (generations 2—3) contradicts standard texture models. These results are presented as afactual mapping of numerical regularities, laying down rigorous constraints for thedevelopment of future flavor symmetry models.
Comments: 7 Pages. Intéressant
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