Baryon Observables as Projections of a Single Heat Kernel
Abstract
The heat kernel K(τ) = Tr(e−τ 𝒟2) of the Dirac operator in a topological soliton background is a single mathematical object from which baryon observables emerge as different functionals. The chiral quark-soliton model is recovered as the mean-field (Hartree-Fock) evaluation of K(τ) in a self-consistent hedgehog soliton background. The constituent quark mass Mq is not an external input but an emergent fixed point: the instanton liquid parametrization of the QCD vacuum (ρ = 0.33 fm, n = 1 fm−4) predicts Mq = 362 MeV, and the self-consistent Hartree-Fock iteration converges to a stable nucleon mass MN = 923 MeV (−1.7%) with Fπ = 91.5 MeV (−1.6%), with no adjustable parameter beyond ΛQCD (*Note.* Fπ = 91.5 MeV uses the normalization Fπexp ≈ 92.2 MeV; some references use fπ = √2 Fπ ≈ 130 MeV (chiral convention); our convention follows Christov et al. [12]). At this point, the full proper-time integral also yields the N-Δ splitting Δ = 295 MeV (+0.7%), and the axial coupling gA = 1.174 (−7.3%). At this emergence point, the isovector form factor GM(1) = 2.815 yields μp = 1.740 n.m. (−37.7%) and μn = −1.075 n.m. (−43.8%). For comparison, matching Fπ = 93.0 MeV (Mq = 375 MeV) gives GM(1) = 2.79 and μp = 1.73 n.m. The proper-time decomposition of K(τ) reveals a systematic spectral anatomy: the nucleon mass is UV-dominated (66% from |ε| > 500 MeV) and well-captured by the gradient expansion, while gA (97% IR) and the magnetic moments (99% IR) require the full Dirac sea. The hierarchy of deviations — 0.1% (MN/Fπ), 0.7% (Δ), 1.7% (MN, Fπ), 7.3% (gA), 37.7% (μp) (at the zero-parameter point Mq = 362 MeV) — correlates with the infrared spectral weight of each observable, identifying the two-body meson exchange current as the dominant missing mechanism. The Skyrme model is the UV sector of K(τ); its structural blindness to IR-dominated observables is a consequence, not a deficiency. This is Emergence Paper III of the emergence programme. Together with Emergence Paper I (gauge structure from moduli) and Emergence Paper II (chirality from the UV topological sector), these papers demonstrate that gauge symmetry, chirality, and baryon masses are projections of a single spectral object determined by ΛQCD.
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BibTeX
@misc{dechery2026baryon,
title = {{Baryon Observables as Projections of a Single Heat Kernel}},
author = {Fabien Déchery},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05751221v4},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Baryon Observables as Projections of a Single Heat Kernel
AU - Fabien Déchery
PY - 2026
DA - 2026/09/15
PB - HAL
UR - https://hal.science/hal-05751221v4
AB - The heat kernel K(τ) = Tr(e^−τ 𝒟^2) of the Dirac operator in a topological soliton background is a single mathematical object from which baryon observables emerge as different functionals. The chiral quark-soliton model is recovered as the mean-field (Hartree-Fock) evaluation of K(τ) in a self-consistent hedgehog soliton background. The constituent quark mass M_q is not an external input but an emergent fixed point: the instanton liquid parametrization of the QCD vacuum (ρ = 0.33 fm, n = 1 fm^−4) predicts M_q = 362 MeV, and the self-consistent Hartree-Fock iteration converges to a stable nucleon mass M_N = 923 MeV (−1.7%) with F_π = 91.5 MeV (−1.6%), with no adjustable parameter beyond Λ_QCD (*Note.* F_π = 91.5 MeV uses the normalization F_π^exp ≈ 92.2 MeV; some references use f_π = √2 F_π ≈ 130 MeV (chiral convention); our convention follows Christov et al. [12]). At this point, the full proper-time integral also yields the N-Δ splitting Δ = 295 MeV (+0.7%), and the axial coupling g_A = 1.174 (−7.3%). At this emergence point, the isovector form factor G_M^(1) = 2.815 yields μ_p = 1.740 n.m. (−37.7%) and μ_n = −1.075 n.m. (−43.8%). For comparison, matching F_π = 93.0 MeV (M_q = 375 MeV) gives G_M^(1) = 2.79 and μ_p = 1.73 n.m. The proper-time decomposition of K(τ) reveals a systematic spectral anatomy: the nucleon mass is UV-dominated (66% from |ε| > 500 MeV) and well-captured by the gradient expansion, while g_A (97% IR) and the magnetic moments (99% IR) require the full Dirac sea. The hierarchy of deviations — 0.1% (M_N/F_π), 0.7% (Δ), 1.7% (M_N, F_π), 7.3% (g_A), 37.7% (μ_p) (at the zero-parameter point M_q = 362 MeV) — correlates with the infrared spectral weight of each observable, identifying the two-body meson exchange current as the dominant missing mechanism. The Skyrme model is the UV sector of K(τ); its structural blindness to IR-dominated observables is a consequence, not a deficiency. This is Emergence Paper III of the emergence programme. Together with Emergence Paper I (gauge structure from moduli) and Emergence Paper II (chirality from the UV topological sector), these papers demonstrate that gauge symmetry, chirality, and baryon masses are projections of a single spectral object determined by Λ_QCD.
ER -