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A recent proposal suggests that even if a Ginsparg-Wilson lattice Diracoperator does not possess any topological zero modes intopologically-nontrivial gauge backgrounds, it can reproduce correct axialanomaly for sufficiently smooth gauge configurations, provided that it isexponentially-local, doublers-free, and has correct continuum behavior. In thispaper, we calculate the axial anomaly of this lattice Dirac operator in weakcoupling perturbation theory, and show that it recovers the topological chargedensity in the continuum limit.Comment: 25 pages, v2: calculation up to O(g^4) for nonabelian gauge  backgroun

Perturbation calculation of the axial anomaly of a Ginsparg-Wilson lattice Dirac operator