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

Understand

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 \pm 12) x 10^{-11}.