Exact sum rules for the decay constant of the neutral pion

Two new sum rules are obtained from fairly general assumptions. They relate the ${\pi }^0$ decay constant to appropriate energy integrals of the differences between the total hadronic production cross sections of two real photons (i) of equal and opposite helicities and (ii) of parallel and perpendicular linear polarizations. The sum rules are derived by both dispersion-theoretic and light-plane methods. The experimental verification of these sum rules will be possible in the near future by studying the reaction $\mathrm{ee}\to \left(ee\gamma \gamma \right)\to \mathrm{ee} +$ "anything hadronic" with polarized colliding beams in storage rings. Theoretical and experimental aspects of these questions are discussed.