Hadronic light-by-light scattering and the pion polarizability

We compute the charged pion loop contribution to the light-by-light scattering amplitude for off-shell photons in chiral perturbation theory through next-to-leading order (NLO). We show that for small photon virtualities (k^2≪m^(2)_(π)) the NLO contributions are relatively more important due to an accidental numerical suppression of the LO terms. This behavior is consistent with previous calculations of the hadronic light-by-light contribution to the muon anomalous magnetic moment, a^(HLBL)_(μ), whose leading order value receives O(1) corrections from models incorporating some of the NLO physics. We also show that models employed thus far for the charged pion loop contribution to a^(HLBL)_(μ) are not fully consistent with low-momentum behavior implied by quantum chromodynamics, having omitted potentially significant contributions from the pion polarizability.