We perform a detailed analysis of all existing data (CELLO, CLEO, BABAR) on the pion-photon transition form factor by means of light-cone sum rules in which we include the next-to-leading order QCD radiative corrections and the twist-four contributions. The next-to-next-to-leading order radiative correction together with the twist-six contribution are also taken into account in terms of theoretical uncertainties. Keeping only the first two Gegenbauer coefficients a 2 and a 4 , we show that the 1 error ellipse of all data up to 9 GeV 2 greatly overlaps with the set of pion distribution amplitudes obtained from nonlocal QCD sum rules-within the range of uncertainties due to twist-four. This remains valid also for the projection of the 1 error ellipsoid on the ða 2 ; a 4 Þ plane when including a 6 . We argue that it is not possible to accommodate the high-Q 2 tail of the BABAR data with the same accuracy, despite opposite claims by other authors, and conclude that the BABAR data still pose a challenge to QCD.

We present a detailed investigation of the spacelike pion's electromagnetic form factor using threepoint QCD sum rules that exclusively involve nonlocal condensates. Our main methodological tools are a spectral density which includes O(α s ) corrections, a suitably improved Gaussian ansatz to model the distribution of the average momentum of quarks in the QCD vacuum, and a perturbative scheme that avoids Landau singularities. Using this framework, we obtain predictions for the pion form factor together with error estimates originating from intrinsic theoretical uncertainties owing to the perturbative expansion and the nonperturbative method applied. We also discuss our results in comparison with other calculations, in particular, with those following from the AdS/QCD correspondence. We find good agreement of our predictions with measurements in the range of momenta covered by the existing experimental data between 1 − 10 GeV 2 .

Using QCD sum rules with nonlocal condensates, we show that the distribution amplitude of the longitudinally polarized ρ-meson may have a shorttailed platykurtic profile in close analogy to our recently proposed platykurtic distribution amplitude for the pion. Such a chimera distribution de facto amalgamates the broad unimodal profile of the distribution amplitude, obtained with a Dyson-Schwinger equations-based computational scheme, with the suppressed tails characterizing the bimodal distribution amplitudes derived from QCD sum rules with nonlocal condensates. We argue that pattern formation, emerging from the collective synchronization of coupled oscillators, can provide a single theoretical scaffolding to study unimodal and bimodal distribution amplitudes of light mesons without recourse to particular computational schemes and the reasons for them.

We perform a comparative theoretical study of the data at spacelike momentum transfer for the γ * γ → π 0 transition form factor, just reported by the Belle Collaboration, vs. those published before by BaBar, also including the older CLEO and CELLO data. Various implications for the structure of the π 0 distribution amplitude vis-à-vis those data are discussed and the existing theoretical predictions are classified into three distinct categories. We argue that the actual bifurcation of the data with antithetic trends is artificial and reason that the Belle data are the better option.