Elastic and transition form factors of light pseudoscalar mesons from QCD sum rules

We revisit F (pi)(Q (2)) and F (P gamma)(Q (2)), P = pi, eta, eta', making use of the local-duality (LD) version of QCD sum rules. We give arguments that the LD sum rule provides reliable predictions for these form factors at Q (2) a parts per thousand yen 5-6 GeV2, the accuracy of the method increasing with Q (2) in this region. For the pion elastic form factor, the well-measured data at small Q (2) give a hint that the LD limit may be reached already at relatively low values of momentum transfers, Q (2) a parts per thousand 4-8 GeV2; we therefore conclude that large deviations from LD in the region Q (2) = 20-50 GeV2 seem very unlikely. The data on the (eta, eta') -> gamma gamma* form factors meet the expectations from the LD model. However, the BaBar results for the pi (0) -> gamma gamma* form factor imply a violation of LD growing with Q (2) even at Q (2) a parts per thousand 40 GeV2, at odds with the eta, eta' case and with the general properties expected for the LD sum rule.