We have studied the P → γ ⋆ γ ⋆ transition form-factors (P = π 0 , η, η ′ ) within a chiral invariant framework that allows us to relate the three form-factors and evaluate the corresponding contributions to the muon anomalous magnetic moment aµ = (gµ − 2)/2, through pseudoscalar pole contributions. We use a chiral invariant Lagrangian to describe the interactions between the pseudo-Goldstones from the spontaneous chiral symmetry breaking and the massive meson resonances. We will consider just the lightest vector and pseudoscalar resonance multiplets. Photon interactions and U (3) flavor breaking effects are accounted for in this covariant framework. This article studies the most general corrections of order m 2 P within this setting. Requiring short-distance constraints fixes most of the parameters entering the form-factors, consistent with previous determinations. The remaining ones are obtained from a fit of these form-factors to experimental measurements in the space-like (q 2 ≤ 0) region of photon momenta. No time-like observable is included in our fits. The combination of data, chiral symmetry relations between form-factors and high-energy constraints allows us to determine with improved precision the on-shell Ppole contribution to the Hadronic Light-by-Light scattering of the muon anomalous magnetic moment: we obtain a P,HLbL µ = (8.47 ± 0.16) · 10 −10 for our best fit. This result was obtained excluding BaBar π 0 data, which our analysis finds in conflict with the remaining experimental inputs. This study also allows us to determine the parameters describing the η − η ′ system in the two-mixing angle scheme and their correlations. Finally, a preliminary rough estimate of the impact of loop corrections (1/NC ) and higher vector multiplets (asym) enlarges the uncertainty up to a P,HLbL µ = ( 8.47 ± 0.16sta ± 0.09 1/N C +0.5 −0 asym ) · 10 −10 .
Conclusions 36A Wess-Zumino-Witten Lagrangian 38 B The P form-factor in the evaluation of a HLbL µ 38 C Additional information on the fit correlations 401 The same deviation is quoted in the updated analysis of the leading hadronic vacuum polarization contribution in ref.[17], while it is 3.7σ according to the most recent study in [18]. See ref.[19] for a discussion on the Monte Carlo needs for these accurate predictions.2 Also lattice QCD simulations have recently managed to give accurate determinations. See, e.g., refs. [25].3 This dominance is not fully understood from a first-principles derivation [32,33].