Pion elastic and (π0, η, η′) → γγ* transition form factors in a broad range of momentum transfers

We analyze F-pi(Q(2)) and F-P gamma(Q(2)), P = pi , eta, eta', within the local-duality (LD) version of QCD sum rules, which allows one to obtain predictions for hadron form factors in a broad range of momentum transfers. To probe the accuracy of this approximate method, we consider, in parallel to QCD, a potential model: in this case, the exact form factors may be calculated from the solutions of the Schrodinger equation and confronted with the results from the quantum-mechanical LD sum rule. On the basis of our quantum-mechanical analysis we conclude that the LD sum rule is expected to give reliable predictions for F-pi(Q(2)) and F-pi gamma(Q(2)) in the region Q(2) >= 5-6 GeV2. Moreover, the accuracy of the method improves rather fast with growing Q(2) in this region. For the pion elastic form factor, the data at small Q(2) indicate that the LD limit may be reached already at relatively low values of momentum transfers, Q(2) approximate to 4-8 GeV2; we therefore conclude that large deviations from LD in the region Q(2) = 20-50 GeV2 reported in some recent theoretical analyses seem unlikely. The data on the (eta, eta') -> gamma gamma* form factors meet very well the expectations from the LD model. Surprisingly, the BABAR results for the pi(0) -> gamma gamma* form factor imply a violation of LD growing with Q(2) even at Q(2) approximate to 40 GeV2, at odds with the eta, eta' case and the experience from quantum mechanics.