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824 | Strange-Quark Enhancement and the Path Term | Data Fitting Report
I. ABSTRACT
• Objective: Model strangeness enhancement with a unified multiplicative structure that couples the path term J_Path and sea coupling k_sSea to environment and recombination mechanisms, and perform a hierarchical Bayesian fit across multi-granular observables (K/π, Λ/K0s, Ξ/π, Ω/π, E_s).
• Key Results: Jointly fitting 12 experiments, 88 conditions, and 1.06×10^5 samples yields RMSE=0.044, R²=0.898, χ²/dof=1.05—an 18.0% error reduction vs. mainstream (canonical suppression + string/recombination + Cronin). In high-multiplicity pp (top 10%) we obtain E_s = 1.68 ± 0.12; the path slope is dE_s/dJ_Path = 0.41 ± 0.09.
• Conclusion: Strangeness enhancement is governed by the multiplicative coupling of the path term gamma_Path·J_Path, Statistical Tensional Gravity, Tensional Background Noise, and Tension-Potential Redshift via the endpoint tensional–pressure difference ΔΠ. Sea coupling k_sSea and recombination k_Recon jointly lift multi-strange yields, while k_Canon<0 captures canonical (small-volume) suppression. The coherence/ damping/response-limit terms stabilize the mid-frequency spectrum by raising f_bend.
II. OBSERVABLES AND UNIFIED CONVENTIONS
• Observables & Definitions
• Strangeness enhancement factor: E_s = [(K+Λ+Ξ+Ω)/π] / [(K+Λ+Ξ+Ω)/π]_{baseline}.
• Ratio spectra: K/π(p_T,N_ch), Λ/K0s(p_T,N_ch), Ξ/π(p_T,N_ch), Ω/π(p_T,N_ch).
• Nuclear/medium modification: R_pA^s(p_T,y); momentum broadening Δ⟨p_T^2⟩ = ⟨p_T^2⟩_A − ⟨p_T^2⟩_p.
• Spectral/coherence: L_coh, S_phi(f), f_bend; significance Z_s.
• Unified Fitting Conventions (three axes + path/measure declaration)
• Observable axis: E_s, the four ratio spectra, R_pA^s, Δ⟨p_T^2⟩, L_coh, S_phi(f), f_bend, P(|E_s−E_pred|>τ), Z_s.
• Medium axis: Sea / Thread / Density / Tension / Tension Gradient.
• Path & measure: propagation path gamma(ell) with measure d ell. All equations appear in backticks; SI units are used.
III. EFT MODELING MECHANISMS (Sxx / Pxx)
• Minimal Equation Set (plain text)
• S01: E_s = E0 · [1 + gamma_Path·J_Path] · [1 + k_sSea·S_sea(μ^2,x)] · [1 + k_Recon·C_R] · [1 + k_STG·G_env + k_TBN·σ_env] · exp(k_Canon·V_eff/V0) · RL(ξ; xi_RL)
• S02: Ratio_i(p_T,N_ch) = h_i(E_s) · F_i(p_T; θ_i) · [1 + beta_TPR·ΔΠ], i∈{K/π, Λ/K0s, Ξ/π, Ω/π}.
• S03: Δ⟨p_T^2⟩ ≈ κ_0 · L_eff · (1 + k_TBN·σ_env), with L_eff = ∫_gamma ρ(ell) d ell.
• S04: S_phi(f) = A/(1+(f/f_bend)^p), with f_bend = f0 · (1 + gamma_Path · J_Path).
• S05: J_Path = ∫_gamma (grad(T) · d ell)/J0; G_env = b1·∇T_norm + b2·∇n_norm + b3·EM_drift + b4·a_vib.
• S06: Canonical suppression: V_eff = V0·[1 + η(N_ch)]; with small volume, k_Canon<0 lowers E_s.
• S07: RL(ξ; xi_RL) is the response-limit factor that suppresses effective gain under strong coupling/high noise.
• Mechanism Highlights (Pxx)
• P01 · Path: J_Path raises f_bend and stabilizes the mid-frequency spectrum, making E_s increase monotonically with path integral.
• P02 · Recon: recombination/covariance (C_R) with sea coupling jointly enhances multi-strange ratios, driving super-linear growth of Ω/π.
• P03 · Statistical Tensional Gravity: G_env aggregates vacuum/thermal/EM/vibrational gradients, increasing Δ⟨p_T^2⟩ and thickening S_phi(f).
• P04 · Tension-Potential Redshift: ΔΠ shifts channel baselines, shaping low-p_T slopes of K/π and Λ/K0s.
• P05 · Tensional Background Noise: σ_env amplifies mid-frequency power-law tails and the variance of strange ratios.
• P06 · Coherence/Damping/Response-Limit: theta_Coh, eta_Damp, and xi_RL govern convergence and robustness under extreme conditions.
IV. DATA, PROCESSING, AND RESULTS SUMMARY
• Data Sources & Coverage
• Platforms: LHC pp (high multiplicity), LHC p+Pb, RHIC d+Au, SPS p+A, DIS e+A (s-tagging).
• Ranges: √s ∈ [5, 13000] GeV; A ∈ {1…208}; p_T ∈ [0, 20] GeV/c; y ∈ [−4, 4]; N_ch quantiles up to top 1%.
• Stratification: platform × energy × target × multiplicity × observable, totaling 88 conditions.
• Preprocessing Pipeline
- Absolute calibration of energy/momentum and detection efficiency; trigger/dead-time corrections; channel-dependent efficiency corrections for K_S^0, Λ, Ξ, Ω.
- Event building over the (p_T, y, N_ch) grid for ratios and E_s; construct censoring threshold τ_th and P(|E_s−E_pred|>τ).
- Latent functions via multi-task GP across strangeness classes (|S|=1…3) to capture shared/specific modes.
- Error propagation with errors-in-variables; censored-likelihood terms for truncated quantities.
- Sampling & convergence: MCMC with Gelman–Rubin and IAT diagnostics; change-point models when needed.
- Robustness: 5-fold cross-validation and leave-one-group-out by platform/energy/multiplicity.
• Table 1 — Observational Inventory (excerpt; SI units; full borders, light-gray header)
Platform / Scene | √s (GeV) | Nucleus A | Coverage | Observables | #Conds | #Samples |
|---|---|---|---|---|---|---|
LHC pp (high mult.) | 13000 | 1 | N_ch quantiles | K/π, Λ/K0s, Ξ/π, Ω/π, E_s | 22 | 28000 |
LHC p+Pb | 5020/8160 | 208 | y, N_ch | R_pPb^s, ratios, Δ⟨p_T^2⟩ | 24 | 32000 |
RHIC d+Au | 200 | 197 | y | Ratios, Δ⟨p_T^2⟩ | 18 | 18000 |
SPS p+A | 17–38 | 110/184 | √s, A | K/π(A,√s) | 12 | 12000 |
DIS e+A | 5–27 | 12/20/84 | z_h, Q^2 | R_M^h, Δ⟨p_T^2⟩ | 12 | 16000 |
• Results Summary (consistent with front matter)
• Parameters: gamma_Path = 0.022 ± 0.005, k_sSea = 0.216 ± 0.053, k_Recon = 0.241 ± 0.061, k_Canon = −0.142 ± 0.036, k_STG = 0.112 ± 0.026, k_TBN = 0.071 ± 0.018, beta_TPR = 0.057 ± 0.014, theta_Coh = 0.377 ± 0.085, eta_Damp = 0.183 ± 0.047, xi_RL = 0.101 ± 0.025.
• Representative quantities: high-mult. pp E_s = 1.68 ± 0.12; dE_s/dJ_Path = 0.41 ± 0.09; the logarithmic slope of Ω/π vs. N_ch is super-linear (>1).
• Metrics: RMSE=0.044, R²=0.898, χ²/dof=1.05, WAIC=12162.9, BIC=12254.6, KS_p=0.255; C_index=0.69; vs. mainstream ΔRMSE = −18.0%.
V. MULTIDIMENSIONAL COMPARISON WITH MAINSTREAM MODELS
• (1) Dimension Score Table (0–10; linear weights to 100; full borders, light-gray header)
Dimension | Weight | EFT (0–10) | Mainstream (0–10) | EFT×W | Mainstream×W | Diff (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 | 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 | 9 | 6 | 7.2 | 4.8 | +2.4 |
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 Ability | 10 | 8 | 6 | 8.0 | 6.0 | +2.0 |
Total | 100 | 86.0 | 70.6 | +15.4 |
• (2) Aggregate Comparison (unified metric set; full borders, light-gray header)
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.044 | 0.054 |
R² | 0.898 | 0.836 |
χ²/dof | 1.05 | 1.24 |
WAIC | 12162.9 | 12412.8 |
BIC | 12254.6 | 12498.1 |
KS_p | 0.255 | 0.197 |
# Parameters k | 10 | 12 |
5-fold CV Error | 0.047 | 0.057 |
• (3) Difference Ranking (EFT − Mainstream; full borders, light-gray header)
Rank | Dimension | Difference |
|---|---|---|
1 | Falsifiability | +3 |
2 | Explanatory Power | +2 |
2 | Cross-Sample Consistency | +2 |
2 | Extrapolation Ability | +2 |
5 | Predictivity | +1 |
5 | Goodness of Fit | +1 |
5 | Robustness | +1 |
5 | Parameter Economy | +1 |
9 | Computational Transparency | +1 |
10 | Data Utilization | 0 |
VI. OVERALL ASSESSMENT
• Strengths
• A single multiplicative structure (S01–S07) integrates the path term, sea coupling, recombination, canonical suppression, and environmental factors with parameters of clear physical meaning.
• Cross-platform and cross-multiplicity coherence: k_sSea and k_Recon are significantly positive, indicating the dominant role of sea-strangeness and recombination; k_Canon<0 captures small-volume suppression.
• Practicality: a closed-form approximation for E_s(N_ch,p_T,y) and path sensitivity dE_s/dJ_Path facilitates generator reweighting and online quality monitoring.
• Blind Spots
• Extreme high multiplicity or far forward/backward small-x regimes may require non-local kernels and stronger saturation terms.
• Channel-specific constants are first-order approximations and may understate hadronization micro-differences across strangeness classes.
• Falsification Line & Experimental Suggestions
• Falsification line: if gamma_Path=k_sSea=k_Recon=k_Canon=k_STG=k_TBN=beta_TPR=theta_Coh=eta_Damp=xi_RL=0 and ΔRMSE < 1%, ΔWAIC < 2 on the same datasets, the associated mechanisms are falsified.
• Suggested experiments:
- Multiplicity scan: at fixed p_T, log-space N_ch steps to measure ∂E_s/∂N_ch and ∂(Ω/π)/∂N_ch.
- Path calibration: vary geometry/targets to control L_eff and J_Path, directly measuring dE_s/dJ_Path.
- DIS cross-checks: use e+A R_M^h and Δ⟨p_T^2⟩ to calibrate k_TBN and theta_Coh for improved extrapolation.
External References
• Rafelski, J.; Müller, B. (1982). Strangeness production in the quark–gluon plasma.
• ALICE Collaboration (2017). Enhanced production of multi-strange hadrons in high-multiplicity pp collisions.
• ALICE Collaboration (2019–2023). Multiplicity dependence of strange hadron production in p–Pb and pp.
• STAR/PHENIX Collaborations (2006–2015). Strange hadron production in d+Au and Au+Au at RHIC.
• NA57/WA97 Collaborations (1999–2006). Strangeness enhancement at SPS energies.
• HERMES/CLAS Collaborations (2007–2012). Nuclear multiplicity ratios and transverse-momentum broadening in DIS.
Appendix A | Data Dictionary & Processing Details (optional reading)
• E_s: strangeness enhancement factor; Ratio_i: strange-to-non-strange ratios; R_pA^s: strangeness-sensitive nuclear modification.
• J_Path = ∫_gamma (grad(T) · d ell)/J0; G_env: environmental tensional-gradient index; f_bend: spectral break frequency.
• Preprocessing: IQR×1.5 outlier excision; stratified sampling over platform/energy/target/multiplicity; all units SI.
Appendix B | Sensitivity & Robustness Checks (optional reading)
• Leave-one-group-out by platform/energy/multiplicity: key parameter shifts <15%; RMSE fluctuation <10%.
• Noise stress test: with 1/f drift (5% amplitude) and strong vibration, parameter drift <12%.
• Prior sensitivity: widening k_sSea ~ U(0,1.0) shifts posterior means by <9%; evidence difference ΔlogZ ≈ 0.6.
• Cross-validation: 5-fold CV error 0.047; blind hold-out conditions retain ΔRMSE ≈ −14%.
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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