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We analyze the accuracy of the pion elastic form factor predicted by a localduality (LD) version of dispersive sum rules. To probe the precision of this theoretical approach, we adopt potential models with interactions that involve both Coulomb and confining terms. In this case, the exact form factor may be obtained from the solution of the Schrödinger equation and confronted with the LD sum rule results. We use parameter values appropriate for hadron physics and observe that, independently of the details of the confining interaction, the deviation of the LD form factor from the exact form factor culminates in the region Q2 " 4-6 GeV2. For larger Q2, the accuracy of the LD description increases rather fast with Q2. A similar picture is expected for QCD. For the pion form factor, existing data suggest that the LD limit may be reached already at the relatively low values Q2 = 4-10 GeV2. Thus, large deviations of the pion form factor from the behavior predicted by LDQCDsum rules for higher values of Q2, as found by some recent analyses, appear to us quite improbable. New accurate data on the pion form factor at Q2 = 4-10 GeV2 expected soon from JLab will have important implications for the behavior of the pion form factor in a broad Q2 range up to asymptotically large values of Q2. [ABSTRACT FROM AUTHOR]

We study the P → γ γ * (P = π0, η, η') transition form factors by means of the local-duality (LD) version of QCD sum rules. For the case of η and η' , the conventional LD model provides a good description of the existing data. However, for the pion form factor we find a disagreement with recent BABAR results for high Q2, even though the accuracy of the LD approximation is expected to increase with Q2. It remains mysterious why both η and η' form factors to virtual photons, on the one hand, and the π0 form factor, on the other hand, show a qualitatively different behaviour, corresponding to a violation of LD that rises with Q2 in the pion case. In a quantum-mechanical example, we show that, for a bound-state size of about 1 fm, the LD sum rule provides an accurate prediction for the form factor for Q2 larger than a few GeV2. [ABSTRACT FROM AUTHOR]