Abstract

We develop an ab-initio normalization scheme for the strong-sector coupling in the Axis Model. The non-Abelian vacuum induces a canonical Yang–Mills kinetic term with coefficient τ (ρ0) at a matching scale Λq , and subgroup couplings are fixed by geometric projector weights ωH via gH−2 (Λq) = ωH /τ (ρ0). In the canonical product–UV background with ωC = 1 and τ (ρ0) = 0.1776, the resulting boundary value gs2(Λq ) = τ (ρ0) implies a baseline prediction αs(MZ) ≃ 2.9 × 10−2  under standard two-loop QCD running, which is far below the observed value. We therefore interpret the discrepancy as evidence that the effective color projector weight is reduced by vacuum anisotropy (tilt) in the UV. A diagnostic inversion of the two-loop flow shows that matching αs(MZ) ≃ 0.118 requires an effective color weight ωCeff ≃ 0.6368 at Λq (with the same τ (ρ0)). Finally, we demonstrate in Appendix C that such a reduced weight arises naturally from a microscopic three-leg (color-triplet) coupled-oscillator kernel: the stiff coherence axis tilts away from the pure color direction, yielding ωCeff < 1 without introducing additional IR fitting parameters.

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Keywords: Axis Model, QCD, SU(3), Strong coupling, renormalization group, two-loop running, threshold matching, vacuum anisotropy, kernel tilt, projector weights, coherent background, pre-geometric normalization, ab initio coupling