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

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-N-C 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-N-C framework, we obtain the result a(mu)(LbyL;pi 0)=(72 +/- 12)x10(-11). Updating our earlier results for the contributions from the exchanges of the eta and eta(') using simple vector-meson dominance form factors, we obtain a(mu)(LbyL;PS)=(99 +/- 16)x10(-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 a(mu)(LbyL;had)=(116 +/- 40)x10(-11).