Hadronic Light-by-Light Contribution to Muon g-2 in Chiral Perturbation Theory

We compute the hadronic light-by-light scattering contributions to the muon anomalous magnetic moment, $\text{amulbl}$, in chiral perturbation theory that are enhanced by large logarithms and a factor of $N_C$. They depend on a low-energy constant entering pseudoscalar meson decay into a charged lepton pair. The uncertainty introduced by this constant is $\pm 60\times {10}^{-11}$, which is comparable in magnitude to the present uncertainty entering the leading-order vacuum polarization contributions to the anomalous moment. It may be reduced to some extent through an improved measurement of the ${\pi }^0\to e^{+}{e}^{-}$ branching ratio. However, the dependence of $\text{amulbl}$ on non-logarithmically enhanced effects cannot be constrained except through the measurement of the anomalous moment itself. The extraction of information on new physics would require a future experimental value for the anomalous moment differing significantly from the 2001 result reported by the E821 collaboration.