Abstract
The CLEO experimental data on the πγ transition are analyzed to next-to-leading order accuracy in QCD perturbation theory using light-cone QCD sum rules. By processing these data along the lines proposed by Schmedding and Yakovlev, and recently revised by us, we obtain new constraints for the Gegenbauer coefficients a2 and a4, as well as for the inverse moment 〈x−1〉π of the pion distribution amplitude (DA). The former determine the pion DA at low momentum scale, the latter is crucial in calculating pion form factors. From the results of our analysis we conclude that the data confirm the end-point suppressed shape of the pion DA we previously obtained with QCD sum rules and nonlocal condensates, while the exclusion of both the asymptotic and the Chernyak–Zhitnitsky DAs is reinforced at the 3σ- and 4σ-level, respectively. The reliability of the main results of our updated CLEO data analysis is demonstrated. Our pion DA is checked against the di-jets data from the E791 experiment, providing credible evidence for our results far more broadly.
Highlights
The recent high-precision CLEO results [1] for the πγ transition form factor gave rise to dedicated theoretical investigations [2, 3, 4, 5, 6, 7, 8, 9]. These experimental data are of particular importance because they can provide crucial quantitative information on nonperturbative parameters of the pion distribution amplitude (DA) and—as we pointed out in [9]—on the QCD vacuum nonlocality parameter λ2q, which specifies the average virtuality of the vacuum quarks
In the absence of a direct solution of the nonperturbative sector of QCD, we are forced to extract related information from the data, relying upon a theoretical analysis as complete and as accurate as currently possible. It was shown by Khodjamirian [5] that the light-cone QCD sum-rule (LCSR) method provides the possibility to avoid the problem of the photon long-distance interaction in the γ∗(Q2)γ(q2) → π0 form factor by performing all calculations for sufficiently large q2 and analytically continuing the results to the limit q2 = 0
The CLEO data were used to extract a direct constraint on the inverse moment x−1 π(μ20) of the pion DA—at the core of form-factor calculations
Summary
The recent high-precision CLEO results [1] for the πγ transition form factor gave rise to dedicated theoretical investigations [2, 3, 4, 5, 6, 7, 8, 9]. In the absence of a direct solution of the nonperturbative sector of QCD, we are forced to extract related information from the data, relying upon a theoretical analysis as complete and as accurate as currently possible It was shown by Khodjamirian [5] that the light-cone QCD sum-rule (LCSR) method provides the possibility to avoid the problem of the photon long-distance interaction (i.e., when a photon goes on mass shell) in the γ∗(Q2)γ(q2) → π0 form factor by performing all calculations for sufficiently large q2 and analytically continuing the results to the limit q2 = 0. Our predictions for the pion DA are found to be in agreement with the Fermilab E791 data [12]
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