Category-Level Deviations in H → μ⁺μ⁻ and Their Impact on Global Higgs Coupling Fits: A Monte Carlo Sensitivity Study

We present a Monte Carlo sensitivity study of how category-level systematic deviations propagate into combined Higgs signal strength and coupling modifier measurements in the H → μ⁺μ⁻ channel. Using a structured toy Monte Carlo framework, we quantify the impact of small fractional shifts (0.5–5%) in individual production-mode categories (ggF, VBF, VH, ttH) on the combined signal strength extracted via standard inverse-variance weighted combinations. We introduce the weight concentration factor f = √[(Σwᵢ²)/(Σwᵢ)²] as a diagnostic metric for assessing category-level vulnerability, and derive a critical threshold σ_δ,crit = σ_stat/f beyond which explicit category modeling becomes important. For H → μμ at HL-LHC precision (σ_stat ~ 2%, f ~ 0.6), this threshold is approximately 3%, indicating that category-level systematic differences at the few-percent scale require explicit treatment. We define and validate two estimators: Model A (standard weighted combination) and Model B (category-aware fit with Gaussian-constrained nuisance parameters). Model B is shown to recover 5–10% precision relative to Model A at HL-LHC systematic scales, directly improving extracted coupling modifier precision. We establish quantitative thresholds for when category-aware modeling transitions from optional to important, providing practical guidance for Run 3 analyses and HL-LHC planning. The framework is applicable to H → ττ, H → Zγ, and Simplified Template Cross-Section (STXS) combinations.