The anomaly cancellation is a basic property of the Standard Model, crucial for its consistence. We consider a lattice chiral gauge theory of massless Wilson fermions interacting with a non-compact massiveU(1) field coupled with left- and right-handed fermions in four dimensions. We prove in the infinite volume limit, for weak coupling and inverse lattice step of the order of boson mass, that the anomaly vanishes up to subleading corrections and under the same condition as in the continuum.
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