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 aLbyL;hadμ=(116±40)×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 aLbyL;hade=(3.9±1.3)×10-14.