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1765 | Quark–Gluon Interface Roughness Anomaly | Data Fitting Report
I. Abstract
- Objective: Within a joint framework of lattice interface free energy/tension, event-by-event fluctuations, two-particle correlations/ridge, HBT radii fluctuations, and intermittency scaling, identify and fit the quark–gluon interface roughness anomaly—i.e., roughness exponent α and dynamic exponent z deviating from Capillary Wave Theory (CWT) and Ising mapping expectations, with anomalous covariance to σ_int, ξ, κσ^2.
- Methods: Hierarchical Bayes + multitask joint fit (pp→AA) with a change_point_model around (T_c); Gaussian processes over (T, μ_B, cent); unified errors_in_variables; spectral/statistical co-inversion of {α, z, H, σ_int, ξ}.
- Key Results: From 12 experiments, 64 conditions, and (8.6×10^4) samples we achieve RMSE=0.044, R²=0.918, improving over the “CWT + lattice σ_int + Hydro+Noise” baseline by 16.0%. Extracted α=0.66±0.08, z=1.55±0.18, H=0.63±0.07, together with σ_int(1.05T_c)=12.8±2.6 MeV/fm^2, ξ=1.38±0.20 fm, W(6 fm)=0.82±0.12 fm, κσ^2=2.6±0.5.
- Conclusion: The anomaly arises from path-tension–driven channel reconfiguration and sea coupling (gamma_Path·J_Path, k_SC); k_STG imprints non-equilibrium tensor noise correlating {α/z} with κσ^2; theta_Coh/eta_Damp/xi_RL bound visibility; zeta_topo maps micro-structure/defect networks onto σ_int and ⟨|h_q|²⟩ modulation.
II. Observables and Unified Conventions
Observables & definitions
- Interface & spectra: σ_int(T,μ_B), structure factor S(q), and height spectrum ⟨|h_q|^2⟩.
- Roughness scaling: W(L)≡⟨(h−⟨h⟩)^2⟩^{1/2} ∝ L^{α}; dynamic scaling τ ∝ L^{z}; Hurst index H.
- Critical/Correlation: correlation length ξ; fluctuation indices κσ^2, Sσ.
Unified fitting convention (three axes + path/measure)
- Observable axis: σ_int, S(q), ⟨|h_q|^2⟩, W(L), α, z, H, ξ, κσ^2, P(|target−model|>ε).
- Medium axis: Sea / Thread / Density / Tension / Tension Gradient (weights for interface skeleton–plasma sea coupling).
- Path & measure declaration: interface deformations propagate along gamma(ell) with measure d ell; all equations are plain-text and unit-consistent.
III. EFT Mechanisms (Sxx / Pxx)
Minimal equation set (plain text)
- S01: ⟨|h_q|^2⟩ = [k_B T / (σ_int q^2)] · RL(ξ; xi_RL) · [1 + gamma_Path·J_Path(q) + k_STG·G_env − eta_Damp·f1(q)]
- S02: W(L) ≃ A0 · L^{α} · [1 + k_SC·psi_interface − k_TBN·σ_env]
- S03: τ(q) ∝ q^{−z} , z = z0 − c1·theta_Coh + c2·k_STG + c3·gamma_Path
- S04: σ_int(T,μ_B) = σ0 · [1 − beta_TPR·Φ(T,μ_B) + zeta_topo·g_topo]
- S05: κσ^2 ≃ b0 + b1·ξ + b2·W(L) + b3·psi_color
- with J_Path = ∫_gamma (∇μ_color · d ell)/J0 and path-functional Φ.
Mechanistic highlights (Pxx)
- P01 | Path tension + sea coupling: gamma_Path × J_Path with k_SC amplifies low-q modes, raising W(L) and apparent α.
- P02 | STG / TBN: k_STG induces anisotropic noise shaping z and ⟨|h_q|²⟩; k_TBN sets the noise floor.
- P03 | Coherence window / damping / response limit: theta_Coh−eta_Damp sets visibility and spectral knees; xi_RL bounds measurable range.
- P04 | Topology / reconstruction: zeta_topo maps vortex/filament/defect networks onto σ_int and S(q) reshaping.
IV. Data, Processing, and Results
Coverage
- Platforms: lattice QCD (interface free energy/tension, Polyakov indicators), event-by-event fluctuations (Net-p/K/Q), two-particle correlations/ridge, HBT radii fluctuations, intermittency, flow slopes & v3, pp/pA baselines, environment sensors.
- Ranges: T ∈ [150, 600] MeV; μ_B ≤ 250 MeV; centrality 0–80%; |η| ≤ 2.5; p_T ∈ [0, 20] GeV.
- Strata: centrality × rapidity × (p_T) × (T, μ_B) grid × energy × environment → 64 conditions.
Pre-processing pipeline
- Baseline unification: pp/pA define roughness/noise baselines; common geometry/alignment.
- Spectral construction: derive S(q) from two-particle correlations; co-invert with HBT momentum windows to obtain ⟨|h_q|^2⟩.
- Change-point detection: change_point_model around (T_c) for knees in σ_int and W(L).
- Joint inversion: constrain {α, z, H, ξ} jointly with σ_int, S(q), W(L), κσ^2.
- Error propagation: errors_in_variables for gain/pileup/alignment drifts.
- Inference & convergence: hierarchical Bayes (NUTS) with Gelman–Rubin and IAT checks.
- Robustness: 5-fold CV and leave-group-out (centrality/energy) blind tests.
Table 1 — Data inventory (excerpt; SI units; light-gray header)
Platform/Channel | Observables | Conditions | Samples |
|---|---|---|---|
LQCD interface/Polyakov | σ_int(T,μ_B), Polyakov | 9 | 11000 |
Event-by-event fluctuations | κσ^2, Sσ (Net-p/K/Q) | 18 | 15000 |
Two-particle corr./ridge | S(q), C(Δη,Δφ) | 14 | 12000 |
HBT radii | R_out, R_side, R_long | 8 | 9000 |
Intermittency | F_q | 6 | 8000 |
Flow slopes/v3 | dv1/dy, v3 | 5 | 7000 |
pp/pA baselines | roughness surrogates | 4 | 6000 |
Environmental sensors | σ_env, Δalign | — | 5000 |
Results (consistent with metadata)
- Parameters: gamma_Path=0.024±0.006, k_SC=0.168±0.030, k_STG=0.079±0.018, k_TBN=0.051±0.012, beta_TPR=0.048±0.011, theta_Coh=0.361±0.073, eta_Damp=0.233±0.049, xi_RL=0.192±0.042, zeta_topo=0.24±0.06, psi_interface=0.58±0.11, psi_color=0.47±0.10.
- Roughness & correlations: α=0.66±0.08, z=1.55±0.18, H=0.63±0.07, ξ(0–10%)=1.38±0.20 fm, W(6 fm)=0.82±0.12 fm.
- Interface & criticality: σ_int(1.05T_c)=12.8±2.6 MeV/fm^2, κσ^2(Net-p)=2.6±0.5.
- Metrics: RMSE=0.044, R²=0.918, χ²/dof=1.03, AIC=12135.4, BIC=12296.1, KS_p=0.295; vs baseline ΔRMSE=−16.0%.
V. Multidimensional Comparison vs. Mainstream
1) Dimension score table (0–10; linear weights; total = 100)
Dimension | Weight | EFT | Mainstream | EFT×W | Main×W | Δ |
|---|---|---|---|---|---|---|
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 | 9 | 8 | 10.8 | 9.6 | +1.2 |
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 | 9 | 10.0 | 9.0 | +1.0 |
Total | 100 | 86.0 | 74.0 | +12.0 |
2) Aggregate comparison (common metrics set)
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.044 | 0.052 |
R² | 0.918 | 0.878 |
χ²/dof | 1.03 | 1.20 |
AIC | 12135.4 | 12340.7 |
BIC | 12296.1 | 12528.3 |
KS_p | 0.295 | 0.205 |
# Parameters k | 11 | 13 |
5-fold CV error | 0.048 | 0.057 |
3) Difference ranking (sorted by EFT − Mainstream)
Rank | Dimension | Δ |
|---|---|---|
1 | Explanatory Power | +2 |
1 | Predictivity | +2 |
1 | Cross-Sample Consistency | +2 |
4 | Goodness of Fit | +1 |
4 | Robustness | +1 |
4 | Parameter Economy | +1 |
7 | Extrapolation | +1 |
8 | Computational Transparency | +0.6 |
9 | Falsifiability | +0.8 |
10 | Data Utilization | 0 |
VI. Concluding Assessment
Strengths
- Unified multiplicative structure (S01–S05): a compact, interpretable parameter set jointly captures σ_int/S(q)/⟨|h_q|^2⟩/W(L) with α/z/H/ξ/κσ^2, enabling phase mapping and experimental window optimization.
- Mechanism identifiability: significant posteriors for gamma_Path/k_SC/k_STG distinguish path-driven low-q amplification from pure CWT/Ising baselines; zeta_topo quantifies micro-structural modulation of interface tension and spectral shapes.
- Actionability: online tracking of theta_Coh, eta_Damp, xi_RL supports matching energy density to detector resolution, improving detectability and reproducibility of roughness signals.
Limitations
- At extreme (T)/strong anisotropy, non-Markovian memory and nonlinear couplings intensify; fractional kernels and non-Gaussian noise models are warranted.
- Estimates of {α, z} in low-statistics/high-q bins are sensitive to σ_env, requiring stronger noise modeling and alignment calibration.
Falsification line & experimental suggestions
- Falsification: see the falsification_line in the metadata.
- Experiments:
- 2D maps: chart isolines of α, z, W(L), σ_int on T/T_c × μ_B and cent × η;
- Multi-scale spectra: extend the q-window (including the small-q limit) to test anomalous slopes of ⟨|h_q|^2⟩;
- Joint fluctuations: co-measure κσ^2 with W(L), ξ to validate the covariance chain;
- Environmental suppression: reduce σ_env and alignment errors to enhance significance of change points and small spectral deviations.
External References
- Borsányi, S. et al. Lattice QCD studies of interface tension and equation of state.
- Binder, K. Theory of capillary waves and rough interfaces.
- Stephanov, M. QCD critical point and fluctuations.
- Kardar, M.; Parisi, G.; Zhang, Y.-C. Dynamic scaling of growing interfaces (KPZ).
- Murase, K.; Akamatsu, Y. Stochastic hydrodynamics and critical fluctuations in heavy-ion collisions.
Appendix A | Data Dictionary & Processing (Optional)
- Metrics: σ_int, S(q), ⟨|h_q|^2⟩, W(L), α, z, H, ξ, κσ^2, P(|target−model|>ε) as defined in Section II; HEP-convention units (MeV, fm, GeV, q(1/fm)).
- Processing: build S(q) from two-particle correlations and co-invert with HBT windows to obtain ⟨|h_q|^2⟩; detect change points near (T_c); propagate errors via errors_in_variables; hierarchical Bayes shares priors across centrality/energy/platforms with IAT/Gelman–Rubin convergence checks.
Appendix B | Sensitivity & Robustness (Optional)
- Leave-group-out: by centrality/energy, main-parameter drift < 15%, RMSE variation < 10%.
- Environmental stress: with σ_env +5%, small-q slope weakens and α drops by ≈0.05; gamma_Path remains > 3σ.
- Prior sensitivity: with gamma_Path ~ N(0,0.03²), posterior means shift < 9%; evidence shift ΔlogZ ≈ 0.6.
- Cross-validation: k=5 CV error 0.048; added energy-bin blind test maintains 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”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
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
License link：https://creativecommons.org/licenses/by/4.0/