Hadronic light-by-light scattering in the muon g−2: a new short-distance constraint on pion exchange

We summarize our recent new evaluation of the pion-exchange contribution to hadronic lightby-light scattering in the muon g− 2. We first derive a new short-distance constraint on the off-shell pion-photon-photon form factor at the external vertex in aμ which relates the form factor to the quark condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange contribution in the framework of large-NC QCD using an off-shell form factor which fulfills all short-distance constraints and obtain the new estimate a 0 μ = (72± 12)× 10−11. Updating our earlier results for the contributions from the exchanges of the η and η ′ using simple vectormeson dominance form factors, we get a μ = (99± 16)× 10−11 for the sum of all light pseudoscalars. Combined with available evaluations for the other contributions to hadronic lightby-light scattering this leads to the estimate a μ = (116± 40)× 10−11. The corresponding contributions to the anomalous magnetic moment of the electron are also given.