Quark-hadron duality and hadron properties from correlators of pseudoscalar and axial currents

Abstract

We study the operator product expansion (OPE) and quark-hadron duality for 2- and 3-point correlators of the axial (A) and pseudoscalar (P) currents of the light quarks. In the chiral limit these correlators are often dominated by nonperturbative power corrections leading to subtleties of quark-hadron duality relations and of the extraction of properties of light pseudoscalars. For the 2-point correlators, we show the sum rule for $ $ to be sensitive to the excited light pseudoscalar. For the 3-point correlators, we derive the Ward identites which provide the normalization of the pion electromagnetic form factor at zero momentum transfer. For large momentum transfer, we demonstrate the way the correct behaviour of the pion form factor in agreement with perturbative QCD emerges from condensate terms in the OPE for the $ $ and $ $ correlators. The local-duality sum rule for $ $ is shown to lead to the pion form factor with the required properties for all values of the momentum transfer.