Projected Yukawa Operator and Chiral Polar Factor
Year: 2026
Type: preprint
Abstract: The companion line note types the Yukawa line as L_Y = ∧²(E_weak) under [H-Weak] of Q14 ([H-Spin] for the fermion sectors) and reads levels on the model operator of ℂ³_gen. Four premises, supplied by no source: [H-Res], the model operator is E_Π² restricted to ℂ³_gen; [H-Sq], H_Π = (Y^gen_Π)† Y^gen_Π = λ_Y² E_Π² restricted to ℂ³_gen; [H-Fac], a weak linking carrier whose invariant couplings have multiplicity at most one, so that the results on the generation block Y^gen_Π reach Y_Π; [H-Grad], the J_3 grading of each generation carrier. The polar decomposition Y^gen_Π = U_Π H_Π^½ is linear algebra; under [H-Res] and [H-Sq], the eigenvalues of H_Π are λ_Y² times each of 1, ½ + u, ½ − u, and the unitary U_Π, the chiral orientation and mixing, is invisible to the squared residue. Under [H-Grad], [U_Π] is non-trivial at first order iff its polar generator Ω has a transverse part. The projection A_Π^odd of the sl_2 lift onto its J_Π-odd anti-hermitian part vanishes, a selection no source justifies, and is not the polar generator. The polar factor of Sym²g (real cascade step g, not a Yukawa morphism) has a non-zero external entry. Whether Yukawa morphisms with polar factor U_Π exist is open. On the orientation-compatible branch of Q14, an input, the real diagonal split is a Lorentz-chirality imbalance, not the V−A structure. Under [H-Res], [H-Sq] and the dictionary gate u = 1/10, the levels split at order one, not as the charged-fermion hierarchy.
Author: Beau, Jérôme
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165378223
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