Scaling property of domain-wall QCD in perturbation theory

We estimate the lattice artifacts in loop correction perturbatively for domain-wall QCD with infinite number of extra flavors. We find that there appear no $\mathcal{O}(a)$ errors in renormalization factors of quark wave function, mass and quark bilinear operators at one and two loop level with off-shell quark momentum. Our proof is based on even or oddness of the quantum correction in terms of the quark external momentum and mass, and it can be extended to any loop level.