The Muon Anomalous Magnetic Moment and the Pion Polarizability

We compute the charged pion loop contribution to the muon anomalous magnetic moment $a_\mu$, taking into account the effect of the charged pion polarizability, $(\alpha_1-\beta_1)_{\pi^+}$. We evaluate this contribution using two different models that are consistent with the requirements of chiral symmetry in the low-momentum regime and perturbative quantum chromodynamics in the asymptotic region. The result increases the disagreement between the present experimental value for $a_\mu$ and the theoretical, Standard Model prediction by as much as $\sim 60\times 10^{-11}$, depending on the value of $(\alpha_1-\beta_1)_{\pi^+}$ and the choice of the model. The planned determination of $(\alpha_1-\beta_1)_{\pi^+}$ at Jefferson Laboratory will eliminate the dominant parametric error, leaving a theoretical model uncertainty commensurate with the error expected from planned Fermilab measurement of $a_\mu$.