Lower Bound on the Pion Polarizability from QCD Sum Rules

Abstract

Making use of QCD sum rules a lower bound is found which relates the electromagnetic polarizability ${\alpha }_{{}_E}$ and mean-square radius $⟨r_{\pi }^2⟩$ of charged pions through the intrinsic polarizability ${\tilde{\alpha }}_{{}_E}={\alpha }_{{}_E}-\alpha ⟨r_{\pi }^2⟩/(3M_{\pi })$. 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 $⟨r_{\pi }^2⟩$.

Comments: 9 pages, RevTeX, 3 figures added as uu-encoded g-zipped tarred eps files, to appear in Phys. Lett B