Lower Bound on the Pion Polarizability from QCD Sum Rules

Making use of QCD sum rules a lower bound is found which relates the electromagnetic polarizability $\alpha_{_E}$ and mean-square radius $\langle r_\pi^2\rangle$ of charged pions through the intrinsic polarizability $\tilde\alpha_{_E}= \alpha_{_E}-\alpha\langle r_\pi^2\rangle/(3M_\pi)$. We find that if present constraints on the QCD continuum (duality) threshold are accepted, this lower bound on the intrinsic polarizability $\tilde\alpha_{_E}$ is incompatible with some previous determinations of $\alpha_{_E}$ and $\langle r_\pi^2\rangle$.