Recently it was pointed out that for the evaluation of the numerically dominant pion-exchange contribution to the hadronic light-by-light scattering correction in the muon g−2, a fully off-shell pion-photon-photon form factor should be used. Following this proposal, we first derive a new short-distance constraint on the off-shell form factor which enters at the external vertex for the muon g−2 and show that it is related 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. With a value for the magnetic susceptibility as estimated in the same large-NC framework, we obtain the result aμLbyL;π0=(72±12)×10−11. Updating our earlier results for the contributions from the exchanges of the η and η′ using simple vector-meson dominance form factors, we obtain aμLbyL;PS=(99±16)×10−11 for the sum of all light pseudoscalars. Combined with available evaluations for the other contributions to hadronic light-by-light scattering this leads to the new estimate aμLbyL;had=(116±40)×10−11.

• Received 29 January 2009

DOI:https://doi.org/10.1103/PhysRevD.79.073012