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

We revisit Fπ(Q2) and FPγ(Q2), P = π, η, η′, 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 Q2 ≥ 5–6 GeV2, the accuracy of the method increasing with Q2 in this region. For the pion elastic form factor, the well-measured data at small Q2 give a hint that the LD limit may be reached already at relatively low values of momentum transfers, Q2 ≈ 4–8 GeV2; we therefore conclude that large deviations from LD in the region Q2 = 20–50 GeV2 seem very unlikely. The data on the (η, η′) → γγ* form factors meet the expectations from the LD model. However, the BaBar results for the π0 → γγ* form factor imply a violation of LD growing with Q2 even at Q2 ≈ 40 GeV2, at odds with the η, η′ case and with the general properties expected for the LD sum rule.