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Square-Root-Free Rational Flavor Hierarchies, Axionless Strong CP, and Blind Neutrino Predictions in 5D Supersymmetric PeV Unification

Year: 2026
Type: preprint
Abstract: Renormalization-group evolution of the Standard Model (SM) Yukawa couplings in the MS-bar scheme reveals a simultaneous multi-sector crossing near mu_123 ~ 4.60 PeV, where y_mu / y_s ~ 3, the light-quark invariant R_12 = y_u y_s / y_d^2 ~ 9, and the normalized heavy-to-second-generation invariant R_23^norm = (y_c / y_t)/(y_s / y_b)^2 ~ 9 hold concurrently. We construct a renormalizable, square-root-free ultraviolet completion on a five-dimensional N = 1 supersymmetric S^1 / (Z_2 x Z_2') orbifold with discrete flavor-CP symmetry D_4 x Z_4 x U(1)_R broken by an orthogonal flavon doublet vacuum <Phi> = v_a (1, i)^T on the y = 0 brane. We prove two algebraic no-go theorems in the messenger sector establishing N_pair^min = 5 (M_7), lock e_u = 9 d_u (e_d / d_d)^2 via supersymmetric holomorphy with natural one-loop PeV threshold shifts (-6.9% to -6.1%), and obtain chi^2 / dof = 2.73-3.39 across 13 quark, charged-lepton, and CKM observables with 8 real parameters and zero free phases, predicting the CKM angle gamma = 68.5 - 69.3 deg. The identical +i vacuum phase cancels the tree-level Strong CP phase (theta_bar_tree = 0) with sequestered loop shifts below 10^-17 rad. Freezing all quark and charged-lepton parameters fixes the Dirac neutrino portal in an inverse seesaw at M_1,2 = 236.7 TeV, where a real-subspace theorem excludes Inverted Neutrino Mass Ordering at > 37 sigma (chi^2_min = 1388.1) and yields blind Normal-Ordering predictions delta_CP^PMNS = 199.0 deg, sum m_nu = 63.75 meV, m_betabeta = 1.32 meV, and positive-sign resonant leptogenesis eta_B = +6.12 x 10^-10. An exhaustive census of 6,887,475,360 discrete Clebsch-phase models isolates the Variant B equivalence class at 6.09 sigma (B_10 = 1.65 x 10^9). Reproducibility package: manuscript_arxiv_package.zip includes the complete LaTeX source, vector figures, and standalone Python verification suite (verify_paper_results.py).
DOI: 10.5281/zenodo.24120857
Language: English
Open Access status: green
OpenAlex ID: W7225757270
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