Non-local generalization of the axial anomaly and x-dependence of the anomalous gluon contribution

The generalization of the axial anomaly is considered. It is shown that bilocal axial quark operators on the light cone possess, beside the point-like anomaly, also a light-like anomaly. The consequences for the definition of anomaly-free quark distribution functions and the effect of both gluon coefficient function and splitting kernels in polarized deep inelastic scattering are discussed. CERN-TH/97-4 January 1997 ∗On leave from the Institut für Theoretische Physik, Universität Leipzig, 04109 Leipzig, Germany 1