We have studied the P → γ⋆ γ⋆ form factor in Resonance Chiral Theory, with P = π0; η, η', to compute the contribution of the pseudoscalar pole to the hadronic light-by-light piece of the anomalous magnetic moment of the muon. In this work we allow the leading U(3) chiral symmetry breaking terms, obtaining the most general expression for the form factor of order O(m2P). The parameters of the Effective Field Theory are obtained by means of short distance constraints on the form factor and matching with the expected behavior from QCD. Those parameters that cannot be fixed in this way are fitted to experimental determinations of the form factor within the spacelike momentum region of the virtual photon. Chiral symmetry relations among the transition form factors for π0, η and η' allow for a simultaneous fit to experimental data for the three mesons. This shows an inconsistency between the BaBar π0 data and the rest of the experimental inputs. Thus, we find a total pseudoscalar pole contribution of aP,HLbLη = (8:47 ± 0:16) · 10-10 for our best fit (neglecting the BaBar π0 data). Also, a preliminary rough estimate of the impact of NLO in 1=NC corrections and higher vector multiplets (asym) enlarges the uncertainty up to aP,HLbLη = (8:47 ± 0:16stat ± 0:09NC +0:5 -0:0asym).
Dispersive and chiral symmetry constraints on the light meson form factors