Geometric Origin of the Proton Spin Crisis in the Zhang Effective Metric
The EMC experiment revealed that the intrinsic spins of quarks contribute only about 30% of the proton's total spin, the famous proton spin crisis. Within the rotational-order geometric unification framework of the Zhang Effective Metric, we treat the proton as a baryonic Skyrmion soliton living on the internal S³ fibre. Canonical quantization of collective rotational coordinates, together with the WZW term whose coefficient is fixed by N_c=3, generates the proton half-integer spin. We keep the original Jaffe-Manohar spin sum rule unchanged. The high-dimensional topological holonomy of the S³ fibre supplies an extra geometric orbital angular momentum L_geo, nested within the partonic orbital term but distinct from standard 4D partonic orbital angular momentum. This topological channel complements the existing QCD description. The magnitude of L_geo is anchored to the internal scale r₁≈0.4 fm from Paper 72, naturally matching the ~70% missing spin fraction. We also clearly separate this colored baryon Skyrmion from the gauge-singlet dark matter knots of Paper 71, which carry no WZW coupling and do not gain fermionic spin.
Authors
- Xiangdong Zhang
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-10-30
- DOI
- https://doi.org/10.5281/zenodo.23804709
- Primary Topic
- Quantum Chromodynamics and Particle Interactions
- Type
- preprint