Relating inclusive e+e− annihilation to electroproduction sum rules in quantum chromodynamics

The Broadhurst-Kataev conjecture, that the “discrepancy” in the connection with the π0 → γγ anomaly equals the beta function β(α) times a power series in the effective coupling α, is proven to all orders of perturbative quantum chromodynamics. The use of nested short-distance expansions is justified via Weinbergʹs power-counting theorem.