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

摘要

We revisit F_π(Q~2) and F_(Pγ)(Q~2), 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 Q~2 ≥ 5-6 GeV~2, 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 ≈ 4-8 GeV~2; we therefore conclude that large deviations from LD in the region Q~2 = 20-50 GeV~2 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 π~0 → γγ* form factor imply a violation of LD growing with Q~2 even at Q~2 ≈ 40 GeV~2, at odds with the η, η′ case and with the general properties expected for the LD sum rule.