Abstract
We have studied the P → γ⋆γ⋆ transition form-factors (P = π0, 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 mP2 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 (q2 ≤ 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 P -pole contribution to the Hadronic Light-by-Light scattering of the muon anomalous magnetic moment: we obtain {a}_{mu}^{{}^{P, HLbL}}=left(8.47 pm 0.16right) cdotp {10}^{-10} for our best fit. This result was obtained excluding BaBar π0 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}_{mu}^{P, HLbL}=left(8.47pm {0.16}_{mathrm{sta}} pm {0.09}_{1/{mathrm{N}}_{mathrm{C}}}{{}_{-0}^{+0.5}}_{asym}right)cdotp {10}^{-10} .
Highlights
The J-PARC E34 collaborations have announced new experiments that will reduce the current Brookhaven error by, at least, a factor 4 [20, 21]
We have studied the P → γ γ transition form-factors (P = π0, 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 =/2, through pseudoscalar pole contributions
The combination of data, chiral symmetry relations between form-factors and high-energy constraints allows us to determine with improved precision the on-shell P -pole contribution to the Hadronic Light-by-Light scattering of the muon anomalous magnetic moment: we obtain aPμ,Hadronic Light-by-Light Scattering (HLbL) = (8.47 ± 0.16) · 10−10 for our best fit
Summary
In modeling the TFF we make use of RχT, an extension of χPT that includes the lightest resonance multiplets [61, 62]. Appendix A [76, 77, 79] This non-resonant Lagrangian was considered in the chiral and large-NC limit VVP Green’s function analysis [67], an appropriate description of physical P → γ γ processes requires further pseudo-Goldstone bilinear terms not shown above [80, 93, 138, 139], which dress the φa wave-functions and induce the η − η mixing. In the present work, we will always keep the full mixing coefficients Cq(/)s, not expanded; on the other hand, the large-NC limit will be assumed everywhere else in our space-like TFF analysis and resonance widths, meson loops or multi-trace RχT operators will be considered negligible for our study These subleading effects must be properly taken into account in the analysis of time-like observables (vector and pseudoscalar branching ratios, e+e− → P γ production, etc.). It is illustrative to compare the present results with more involved studies including higher resonance poles [69, 73, 94]
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