Nucleon Identity as Emergent Isorotation: Spectral Diagnostics from Beta Decay to Proton-Neutron Splitting
Abstract
The soliton framework predicts a hedgehog soliton with baryon number B = 1 but no intrinsic flavor quantum numbers. Proton and neutron identities emerge through collective isorotation A(t) ∈ SU(2), constrained to half-integer isospin by the Finkelstein--Rubinstein theorem. We assemble the isovector observables computed in Emergence Papers I--IV of this programme and derive the neutron β-decay lifetime τβ as a spectral consistency test. Using gV = 1 (conserved vector current) and gA = 1.174 (cranking of the heat kernel K(τ) at the zero-parameter point Mq = 362 MeV), the Fermi formula yields τβ = 995 s (+13.3% relative to experiment), the deficit being a direct quadratic amplification of the gA deficit (−7.3%, Class B). The proton--neutron mass splitting Mn − Mp is analyzed as an isovector scalar response; the Thouless cranking calculation yields δ Mstrong = 1.14 MeV (−45%, Class D), a structural underestimation arising from the hedgehog projection (Qp ≈ 0.45 vs.\ Qp = 1 in the naive quark model). This asymmetry with the σπ N overestimation (× 2.4) constitutes a new diagnostic of the collective quantization mechanism. The emergent $V - A$ structure---vector couplings exact by Noether's theorem, axial couplings reduced by chiral sea effects---is identified as a spectral diagnostic of the spectral (valence + sea) decomposition, with implications for the gauge emergence programme of Emergence Paper I.
Related
- Sharpness-Aware Minimization (SAM) Improves Classification Accuracy of Bacterial Raman Spectral Data Enabling Portable Diagnostics
- Spectral Fields and Unitary Descent: Local splitting, simultaneous norms, and transcendental obstructions
- Uniform Non-Localization under Robin Boundary Perturbations: Spectral Splitting and Bounded Eigenspace Complexity
- Splitting fields of complex hyperbolic groups: matrix extraction, Hermitian descent, and spectral fields
- Splitting Brauer classes by genus one curves over number fields
BibTeX
@misc{dechery2026nucleon,
title = {{Nucleon Identity as Emergent Isorotation: Spectral Diagnostics from Beta Decay to Proton-Neutron Splitting}},
author = {Fabien Déchery},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05793312v2},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Nucleon Identity as Emergent Isorotation: Spectral Diagnostics from Beta Decay to Proton-Neutron Splitting
AU - Fabien Déchery
PY - 2026
DA - 2026/10/10
PB - HAL
UR - https://hal.science/hal-05793312v2
AB - The soliton framework predicts a hedgehog soliton with baryon number B = 1 but no intrinsic flavor quantum numbers. Proton and neutron identities emerge through collective isorotation A(t) ∈ SU(2), constrained to half-integer isospin by the Finkelstein--Rubinstein theorem. We assemble the isovector observables computed in Emergence Papers I--IV of this programme and derive the neutron β-decay lifetime τ_β as a spectral consistency test. Using g_V = 1 (conserved vector current) and g_A = 1.174 (cranking of the heat kernel K(τ) at the zero-parameter point M_q = 362 MeV), the Fermi formula yields τ_β = 995 s (+13.3% relative to experiment), the deficit being a direct quadratic amplification of the g_A deficit (−7.3%, Class B). The proton--neutron mass splitting M_n − M_p is analyzed as an isovector scalar response; the Thouless cranking calculation yields δ M_strong = 1.14 MeV (−45%, Class D), a structural underestimation arising from the hedgehog projection (Q_p ≈ 0.45 vs.\ Q_p = 1 in the naive quark model). This asymmetry with the σ_π N overestimation (× 2.4) constitutes a new diagnostic of the collective quantization mechanism. The emergent $V - A$ structure---vector couplings exact by Noether's theorem, axial couplings reduced by chiral sea effects---is identified as a spectral diagnostic of the spectral (valence + sea) decomposition, with implications for the gauge emergence programme of Emergence Paper I.
ER -