Operator-Relative Noncentrality in Localized Correlated-Spectrum Scans: A BABAR–BESIII Benchmark

This technical note investigates whether operator-relative noncentrality can predict the relative empirical power of complementary localized scan statistics in correlated spectra. The motivating real-data benchmark compares BABAR and BESIII measurements of the e⁺e⁻ → π⁺π⁻ cross section in the ρ-resonance region on a common 5 MeV grid from 0.600 to 0.880 GeV. The real-data comparison remains negative, with no statistically supported localized shape tension identified. The methodological study compares a coherent-yield scan with a covariance-profiled shape scan and defines the frozen coordinate Θ = log(ES/EY), where ES and EY represent maximum local operator-accessible signal strengths. An archival confirmatory replication used 50,000 null calibration draws per covariance environment, 15,000 independent null-validation draws per environment, 1,440 signal/covariance conditions, and 576,000 injected pseudoexperiments. Θ predicted which scan had greater empirical power with pooled AUC 0.9820 and mean leave-one-covariance-environment-out AUC 0.9740; its correlation with the empirical power difference was 0.9185. Independent Type-I error estimates ranged from 0.0466 to 0.0540. The results support operator-relative noncentrality as a useful empirical coordinate for complementary globally calibrated scans within the tested benchmark. The underlying ingredients, including Gaussian noncentrality, covariance-weighted subspace detection, quadratic scanning, and Monte Carlo calibration, are established; the contribution is a reproducible computational synthesis and controlled characterization rather than a claim of a new general statistical law