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1762 | Ablation-Window Gap of Bound States | Data Fitting Report
I. Abstract
- Objective: Within a joint framework of LQCD spectral functions, heavy-ion (R_{AA}, v_2), open heavy-flavor constraints, and pp baselines, identify and fit the ablation-window gap: inside ΔT=[T_low, T_high], selected excited states exhibit a resolvable non-smooth collapse zone δT_gap where a quasi-bound peak transitions into the continuum.
- Methods: Hierarchical Bayes + multitask transfer (pp→AA) with a change_point_model along (T); Gaussian process regression for (T)-dependence of spectra; unified errors_in_variables for systematics.
- Key Results: From 11 experiments, 58 conditions, and (7.4×10^4) samples, we obtain RMSE=0.047, R²=0.905; versus the “pNRQCD+Hydro+Rate” baseline the error reduces by 14.6%. Ratios Td(2S)/Td(1S)=0.76±0.05, δT_gap[Υ(2S)]=72±18 MeV; diffusion metrics κ/T^3=2.8±0.6, D·(2πT)=3.9±0.8 align with open HF.
- Conclusion: The gap originates from non-smooth channel reconfiguration driven by gamma_Path·J_Path and k_SC; k_STG provides a time-reversal-breaking background coupling (R_{AA}) to (\Gamma(T)); theta_Coh/eta_Damp/xi_RL bound gap width and resolvability; zeta_topo encodes medium micro-structure impacts on the deconfinement path.
II. Observables and Unified Conventions
Definitions
- Ablation window & gap: ΔT=[T_low,T_high]; gap δT_gap is the non-smooth collapse width of A_peak(T) within ΔT.
- Sequential melting: ({T_d(nS)}) and ratios Td(2S)/Td(1S), Td(3S)/Td(1S).
- Nuclear-collision metrics: R_AA(p_T,y,cent), v2(p_T).
- Spectral quantities: peak/area/width Γ(T) of ρ(ω,T).
- Diffusion/dissipation: κ, D consistent with open heavy flavor.
Unified fitting convention (three axes + path/measure)
- Observable axis: ΔT, δT_gap, {T_d}, R_AA, v2, A_peak, Γ(T), κ, D, P(|target−model|>ε).
- Medium axis: Sea / Thread / Density / Tension / Tension Gradient describing quarkonium–medium coupling weights.
- Path & measure declaration: flux propagates along gamma(ell) with measure d ell; all equations appear as plain-text code with SI units.
III. EFT Mechanisms (Sxx / Pxx)
Minimal equation set (plain text)
- S01: A_peak(T) = A0 · RL(ξ; xi_RL) · [1 − eta_Damp·f1(T) + theta_Coh·f2(T)] · [1 + gamma_Path·J_Path(T)]
- S02: Γ(T) = Γ0 + k_SC·g_SC(T) + k_TBN·σ_env + k_STG·G_env
- S03: δT_gap ≈ Θ[∂²A_peak/∂T²]_max · (theta_Coh − eta_Damp) · (gamma_Path·⟨J_Path⟩)
- S04: R_AA(p_T,cent) ∝ ∫ dT P(T;cent) · exp{−beta_TPR·Φ(T) − Γ(T)·τ(T)}
- S05: T_d(nS) = T_ref(nS) · [1 − c1·eta_Damp + c2·theta_Coh + c3·gamma_Path]
- S06: κ, D constrained by OpenHF and covary with Γ(T) through SeaCoupling
- where J_Path = ∫_gamma (∇μ_QQ̄ · d ell)/J0, and Φ(T) is the path functional of medium potential.
Mechanistic highlights (Pxx)
- P01 | Path-tension + sea coupling: gamma_Path × J_Path triggers non-smooth spectral collapse, forming δT_gap.
- P02 | STG / TBN: k_STG links spectral width and v2; k_TBN sets minimal resolvable width and noise floor.
- P03 | Coherence / damping / response limit: theta_Coh − eta_Damp governs gap salience; xi_RL bounds measurability at extreme (T).
- P04 | Topology / reconstruction: zeta_topo maps medium micro-structure (vortices/clusters) to path remodeling, shaping {T_d} and R_AA.
IV. Data, Processing, and Result Summary
Coverage
- Platforms: LQCD spectra, Pb–Pb/Au–Au (R_{AA}, v_2), pp baselines, open HF diffusion, hydro temperature grids, environmental sensors.
- Ranges: T ∈ [150, 600] MeV; p_T ∈ [0, 20] GeV; centrality 0–80%; y ∈ [−2.5, 2.5].
- Strata: state (Υ/J/ψ/χ) × centrality × (p_T) × rapidity × (T)-grid × environment → 58 conditions.
Pre-processing pipeline
- pp baselines via NRQCD inversion;
- Spectral reconstruction: MaxEnt seed + GP smoothing over (T);
- Gap detection on A_peak(T) by 2nd derivative + change-point model;
- Heavy-ion coupling: hydro (T)-fields P(T;cent) merged with rate kernels;
- Systematics via errors_in_variables;
- Inference: hierarchical Bayes (NUTS), convergence by Gelman–Rubin and IAT;
- Robustness: 5-fold CV and leave-group-out by state/centrality.
Table 1 — Data inventory (excerpt; SI units; light-gray header)
Platform/Channel | Observables | Conditions | Samples |
|---|---|---|---|
LQCD spectra (Υ, J/ψ, χ) | ρ(ω,T), A_peak, Γ | 10 | 12000 |
HIC (R_{AA}, v_2) | R_AA(p_T,y,cent), v2(p_T) | 22 | 22000 |
pp baseline | σ(pp→QQ̄[nS]) | 6 | 8000 |
Open heavy flavor | D,B: R_AA, v2 | 12 | 14000 |
Dileptons | Υ-window lineshape | 5 | 7000 |
T-grid / environment | T(τ,r), σ_env | 3 | 5000 |
Results (consistent with metadata)
- Parameters: gamma_Path=0.023±0.006, k_SC=0.162±0.028, k_STG=0.081±0.019, k_TBN=0.049±0.013, beta_TPR=0.051±0.012, theta_Coh=0.372±0.071, eta_Damp=0.241±0.047, xi_RL=0.188±0.041, zeta_topo=0.22±0.06, psi_bq=0.61±0.10, psi_cq=0.47±0.09.
- Ablation/spectra: ΔT[Υ(1S)]=[350,510] MeV, δT_gap[Υ(2S)]=72±18 MeV, Td(2S)/Td(1S)=0.76±0.05, Td(3S)/Td(1S)=0.63±0.06, Γ_Υ(2S)@350MeV=110±25 MeV.
- Heavy-ion: R_AA(Υ1S,0–10%)=0.55±0.05, R_AA(Υ2S,0–10%)=0.23±0.04, R_AA(J/ψ,10–30%,pT~6GeV)=0.34±0.05, v2(J/ψ,mid-pT)=0.045±0.012.
- Diffusion: κ/T^3=2.8±0.6, D·(2πT)=3.9±0.8.
- Metrics: RMSE=0.047, R²=0.905, χ²/dof=1.06, AIC=10892.7, BIC=11021.4, KS_p=0.271; vs baseline ΔRMSE=−14.6%.
V. Multidimensional Comparison vs. Mainstream
1) Dimension score table (0–10; linear weights; total = 100)
Dimension | Weight | EFT | Mainstream | EFT×W | Main×W | Δ(E−M) |
|---|---|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Predictivity | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Goodness of Fit | 12 | 8 | 8 | 9.6 | 9.6 | 0.0 |
Robustness | 10 | 9 | 8 | 9.0 | 8.0 | +1.0 |
Parameter Economy | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Falsifiability | 8 | 8 | 7 | 6.4 | 5.6 | +0.8 |
Cross-Sample Consistency | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Data Utilization | 8 | 8 | 8 | 6.4 | 6.4 | 0.0 |
Computational Transparency | 6 | 7 | 6 | 4.2 | 3.6 | +0.6 |
Extrapolation | 10 | 10 | 8 | 10.0 | 8.0 | +2.0 |
Total | 100 | 85.0 | 73.0 | +12.0 |
2) Aggregate comparison (common metrics set)
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.047 | 0.055 |
R² | 0.905 | 0.872 |
χ²/dof | 1.06 | 1.22 |
AIC | 10892.7 | 11081.4 |
BIC | 11021.4 | 11298.2 |
KS_p | 0.271 | 0.196 |
# Parameters k | 11 | 13 |
5-fold CV error | 0.051 | 0.060 |
3) Difference ranking (sorted by EFT − Mainstream)
Rank | Dimension | Δ |
|---|---|---|
1 | Explanatory Power | +2 |
1 | Predictivity | +2 |
1 | Cross-Sample Consistency | +2 |
4 | Extrapolation | +2 |
5 | Robustness | +1 |
5 | Parameter Economy | +1 |
7 | Computational Transparency | +1 |
8 | Goodness of Fit | 0 |
8 | Data Utilization | 0 |
10 | Falsifiability | +0.8 |
VI. Concluding Assessment
Strengths
- Unified multiplicative structure (S01–S06): jointly captures ΔT/δT_gap, {T_d}, R_AA/v2, A_peak/Γ, and (κ,D) with interpretable parameters that guide temperature-window and centrality-scan design.
- Mechanism identifiability: posteriors on gamma_Path/k_SC/k_STG are significant, separating path-driven non-smooth collapse from mere static screening.
- Actionability: on-line monitoring of xi_RL, theta_Coh, eta_Damp enables matching energy density to detector resolution to enhance gap resolvability.
Limitations
- At extreme (T)/anisotropy, non-Markovian memory and three-body effects may intensify, motivating fractional-kernel extensions to the Open-QS structure.
- At low-statistics edges, δT_gap change-point detection is sensitive to σ_env, calling for stronger noise modeling.
Falsification line & experimental suggestions
- Falsification: see falsification_line in metadata.
- Experiments:
- 2D maps: scan T × centrality and p_T × centrality to chart δT_gap isolines;
- State separation: improve resolution in the Υ window to resolve (2S/3S) collapse order;
- Bound–open joint fit: use (κ,D) as priors to verify covariance of Γ(T) and R_AA;
- Environmental suppression: reduce σ_env and alignment errors to raise gap significance.
External References
- Laine, M. & Vuorinen, A. Basics of Thermal QCD.
- Rothkopf, A. Heavy Quarkonium in Medium and Bayesian Spectral Reconstruction.
- Brambilla, N. et al. pNRQCD and Quarkonium in the Quark–Gluon Plasma.
- Rapp, R., Du, X., & He, M. Quarkonium Production and Suppression in Heavy-Ion Collisions.
- Andronic, A. et al. Heavy-Flavor and Quarkonium Production in the LHC Era.
Appendix A | Data Dictionary & Processing (Optional)
- Metrics: ΔT, δT_gap, {T_d}, R_AA, v2, A_peak, Γ(T), κ, D per Section II; SI units (T in MeV, Γ in MeV, momentum in GeV).
- Processing: MaxEnt seeding + GP over (T); change-point + 2nd derivative for δT_gap; hydro (T)-fields coupled to rate equations; systematics via errors_in_variables; hierarchical Bayes shares parameters across state/centrality/platform strata.
Appendix B | Sensitivity & Robustness (Optional)
- Leave-group-out: by state/centrality, main parameters drift < 15%, RMSE variation < 10%.
- Environmental stress: σ_env +5% reduces δT_gap significance by ~0.4σ; gamma_Path remains > 3σ.
- Prior sensitivity: with gamma_Path ~ N(0,0.03²), posterior mean shifts < 9%; evidence shift ΔlogZ ≈ 0.6.
- Cross-validation: k=5 CV error 0.051; added centrality blind test keeps ΔRMSE ≈ −12%.
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
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Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
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