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 $α_{_E}$ and mean-square radius $\langle r_π^2\rangle$ of charged pions through the intrinsic polarizability $\tildeα_{_E}= α_{_E}-α\langle r_π^2\rangle/(3M_π)$. We find that if present constraints on the QCD continuum (duality) threshold are accepted, this lower bound on the intrinsic polarizability $\tildeα_{_E}$ is incompatible with some previous determinations of $α_{_E}$ and $\langle r_π^2\rangle$.