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

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
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Geometric Origin of the Proton Spin Crisis in the Zhang Effective Metric

Xiangdong Zhang
3 links
Zenodo (CERN European Organization for Nuclear Research)
Quantum Chromodynamics and Particle Interactions
preprint

Geometric Origin of the Proton Spin Crisis in the Zhang Effective Metric

Xiangdong Zhang
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Quantum Chromodynamics and Particle Interactions
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