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(pi)(2)) 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(mu)(HLBL), 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(mu)(HLBL) are not fully consistent with low-momentum behavior implied by quantum chromodynamics, having omitted potentially significant contributions from the pion polarizability.