{
  "id": "oai:papers.qnfo.org:resolving-the-scale-penalty",
  "slug": "resolving-the-scale-penalty",
  "title": "RESOLVING THE SCALE PENALTY",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The theoretical frameworks of the Renormalization Group and Chiral Perturbation Theory mandate that continuum extrapolations in lattice QCD should contain logarithmic corrections, a phenomenon termed the “Scale Penalty.” However, the computational cost of simulations often leads to data-sparse regimes where resolving these terms is statistically challenging, creating a potential source of under-controlled systematic uncertainty. This paper investigates this tension through a computational simulation. We generated synthetic lattice data for a kaon B-parameter-like observable using a known log-penalty model, then performed an iterative analysis by progressively increasing the number of data points from n=3 to n=10. At each step, the Bayesian Information Criterion (BIC) was used to compare a simple power-law model against the true, more complex log-penalty model. The results show that with n≤6 data points, the statistical evidence was ambiguous (e.g., ΔBIC ≈ 1.0 at n=6). A clear, positive statistical preference for the true model only emerged at n=7 (ΔBIC ≈ 3.5), suggesting a minimum viable dataset for model resolution. [...]",
  "abstract_markdown": "The theoretical frameworks of the Renormalization Group and Chiral Perturbation Theory mandate that continuum extrapolations in lattice QCD should contain logarithmic corrections, a phenomenon termed the “Scale Penalty.” However, the computational cost of simulations often leads to data-sparse regimes where resolving these terms is statistically challenging, creating a potential source of under-controlled systematic uncertainty. This paper investigates this tension through a computational simulation. We generated synthetic lattice data for a kaon B-parameter-like observable using a known log-penalty model, then performed an iterative analysis by progressively increasing the number of data points from n=3 to n=10. At each step, the Bayesian Information Criterion (BIC) was used to compare a simple power-law model against the true, more complex log-penalty model. The results show that with n≤6 data points, the statistical evidence was ambiguous (e.g., ΔBIC ≈ 1.0 at n=6). A clear, positive statistical preference for the true model only emerged at n=7 (ΔBIC ≈ 3.5), suggesting a minimum viable dataset for model resolution. [...]",
  "date": "2025-12-01",
  "first_published": "2025-12-01",
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    "titles": [
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        "title": "RESOLVING THE SCALE PENALTY"
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        "description": "The theoretical frameworks of the Renormalization Group and Chiral Perturbation Theory mandate that continuum extrapolations in lattice QCD should contain logarithmic corrections, a phenomenon termed the “Scale Penalty.” However, the computational cost of simulations often leads to data-sparse regimes where resolving these terms is statistically challenging, creating a potential source of under-controlled systematic uncertainty. This paper investigates this tension through a computational simulation. We generated synthetic lattice data for a kaon B-parameter-like observable using a known log-penalty model, then performed an iterative analysis by progressively increasing the number of data points from n=3 to n=10. At each step, the Bayesian Information Criterion (BIC) was used to compare a simple power-law model against the true, more complex log-penalty model. The results show that with n≤6 data points, the statistical evidence was ambiguous (e.g., ΔBIC ≈ 1.0 at n=6). A clear, positive statistical preference for the true model only emerged at n=7 (ΔBIC ≈ 3.5), suggesting a minimum viable dataset for model resolution. [...]",
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