Anomaly Realization in Charge-Flux Detector Correlators

Quantum anomalies provide a bridge between ultraviolet properties of a theory and its infrared sector. We study how this connection appears in axial-charge-flow observables. In the simplest example, an axial-charge detector probes the fermionic cut of the anomalous triangle and resolves its infrared content as an angular distribution. The massless limit does not commute with the angular integration: a contribution suppressed at fixed angle collapses onto the two beam-collinear directions while retaining the finite integrated sum rule fixed by the axial anomaly. We then replace the axial-charge detector by higher-spin helicity (zilch) detectors and study a family of axial-anomaly-controlled energy-weighted sum rules for the corresponding fluxes. We further show that the same singular localization mechanism and finite zilch-flux sum rules persist in the mixed axial-gravitational channel. We briefly comment on extensions to more general states and multipoint correlators.