The Axial Vector Current Anomaly and the Meson Decay Constants for the Improved Lattice Fermion Action

We discuss the anomaly in the axial vector current for the improved fermion action on the lattice. A detailed discussion of the fermion regularization dependence of the anomaly is given and it is shown that for finite lattice spacing the improved fermion action gives a more reasonable value for the anomaly contribution at finite quark mass than the Wilson action. We also present some results on the perturbative corrections to the decay constants of mesons for the improved fermion action.