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By employing the gradient/Wilson flow, we derive a universal formula thatexpresses a correctly normalized flavor non-singlet axial-vector current ofquarks. The formula is universal in the sense that it holds independently ofregularization and especially holds with lattice regularization. It is alsoconfirmed that, in the lowest non-trivial order of perturbation theory, thetriangle diagram containing the formula and two flavor non-singlet vectorcurrents possesses non-local structure that is compatible with the triangleanomaly.

Universal formula for the flavor non-singlet axial-vector current from the gradient flow