Is the axial anomaly really determined in a continuous non-perturbative regularization?

In the framework of a gauge invariant continuous and non-perturbative regularization scheme based on the smearing of point-like interactions by means of cutoff functions, we show that the axial anomaly, though cutoff independent, depends on the shape of the cutoff functions. The standard value for the strength of the axial anomaly is recovered if we assume that the regularized gauge invariant axial current is in addition local. Received: 11 July 2001 / Published online: 25 January 2002