Transition Form Factors of Pseudoscalar Mesons and the Contribution of the Gluon Anomaly

Abstract

The expressions for the transition form factors (TFFs) of pseudoscalar mesons are derived in the context of the anomaly sum rule approach based on the dispersion representation of the axial anomaly and hypothesis of the global quark-hadron duality. The obtained solutions take into account the π$^{0}$-η-η′ mixing and the contribution of the gluon anomaly. It is shown that this method allows one to describe the TFFs for spacelike and timelike photon virtualities. The contribution of the gluon anomaly is estimated.