Pseudoscalar pole light-by-light contributions to the muon (g − 2) in resonance chiral theory

Abstract

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].

Contribution of neutral pseudoscalar mesons to aμHLbL within a Schwinger-Dyson equations approach to QCD

“…Our SDE prediction of a π 0 ,HLbL µ is compatible with other reported values [42,52,55,56,95,96]. For example, −0.25 ) · 10 −10 (dispersive evaluation).…”

Axial-vector exchange contribution to the hadronic light-by-light piece of the muon anomalous magnetic moment

“…−q 1 Although both, F ρω and F φ depart from F V by O(m 2 π,K ) corrections [83], when the appropriate short-distance constraints are required, one recovers F ρω = F φ = F V [83]. We note that the ideal mixing for the spin-one nonets that we have used (that is predicted with…”

Single pseudoscalar meson pole and pion box contributions to the anomalous magnetic moment of the muon

“…which was used in [55] (see also [56] for a recent update) to determine the η and η TFFs from F πγγ . In the results section below we will compare the TFFs from (21) and (22) in order to assess the relevance of the different dynamics of the strange quark.…”