Hadronic light-by-light scattering contribution to the muon g-2

We review recent developments concerning the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. We first discuss why fully off-shell hadronic form factors should be used for the evaluation of this contribution to the g-2. We then reevaluate the numerically dominant pion-exchange contribution in the framework of large-NC QCD, using an off-shell pion-photon-photon form factor which fulfills all QCD short-distance constraints,in particular, a new short-distance constraint on the off-shell form factor at the external vertex in g-2, which relates the form factor to the quark condensate magnetic susceptibility in QCD. Combined with available evaluations of the other contributions to hadronic light-by-light scattering this leads to the new result αμLbyL;had=(116 ± 40) x 10-11, with a conservative error estimate in view of the many still unsolved problems. Some potential ways for further improvements are briefly discussed as well. For the electron we obtain the new estimate αeLbyL;had=(3.9 ± 1.3) x 10-14. (author)