Weight Concentration and Category Heterogeneity in Precision Higgs Combinations: A Robustness Bound from H → μ⁺μ⁻

Abstract

Weight Concentration and Category Heterogeneity in Precision Higgs Combinations: A Robustness Bound from H → μ⁺μ⁻ Precision Higgs measurements combine production-sensitive categories under a common signal strength. This paper quantifies how residual category effects change the combined uncertainty and how well category agreement can detect them. Core resultFor independent multiplicative deviations, the variance contribution is μ²σδ²f², where f = 1/√n_eff measures weight concentration. The ratio R = μσδf/σ_comb fixes the uncertainty broadening √(1+R²), while the expected excess of Cochran’s Q is R²(n_eff−1). Shared sources behave differently: a common shift does not average down and is invisible to the category-contrast statistic. ATLAS applicationThe six-group reconstruction gives μ ≈ 1.44 ± 0.555, f ≈ 0.507, n_eff ≈ 3.88, and Q ≈ 4.00. Under the stated residual models, a 2% uncertainty broadening requires independent deviations of about 15–29%, or a fully shared random deviation scale of about 7.5–7.7%. The public summaries leave a 13-dimensional local family of Gaussian covariance completions; they do not uniquely determine the homogeneity statistic. Version 4 — expanded explanation and derivationsThis 19-page version preserves the corrected version-3 conclusions and develops the full error budget, correlated and grouped sources, conditional coverage, the distribution and power of Q, profile-versus-marginal estimator behavior, coupling interpretation, ATLAS arithmetic, simulation protocol, and experimental implementation. It includes six figures and worked examples. The explanation remains in the main text; the earlier corrections remain documented in Appendix B. ReproducibilityThe paper is supplied as a PDF. Runnable Python code is provided separately in the matching minimal software v4 release below. It contains the baseline analysis, 33 expanded-material checks, the analytic correlation figure, and worked-number generation. Baseline Monte Carlo reference results are retained from the corrected analysis; the paper states the Gaussian-summary and proxy-weight limitations explicitly. Persistent linksPaper v4: 10.5281/zenodo.23110914Software v4: 10.5281/zenodo.23110907Paper, all versions: 10.5281/zenodo.20434179Software, all versions: 10.5281/zenodo.20599199 Related studiesCP-even information flow · CP-odd information flow · Graph transfer and ultraviolet suppression AcknowledgmentThis study arose within the ECOF research program; its statistical analysis is self-contained and assumes no observer-coupled modification of the Standard Model. Foundation reference (all versions). Attribution correction, 2 October 2026. The manuscript now explicitly credits Biggerstaff and Jackson (2008) for the exact distribution of Cochran’s Q under the Gaussian random-effects model and its use for power and heterogeneity intervals: doi:10.1002/sim.3428. Equations, numerical results and software are unchanged; this remains version 4.