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The Scale Magnetic Effect (SME) is the generation of electric current due toconformal anomaly in external magnetic field in curved spacetime. The effectappears in a vacuum with electrically charged massless particles. Similarly tothe Hall effect, the direction of the induced anomalous current isperpendicular to the direction of the external magnetic field $\bf B$ and tothe gradient of the conformal factor $\tau$, while the strength of the currentis proportional to the beta function of the theory. In massive electrodynamicsthe SME remains valid, but the value of the induced current differs from thecurrent generated in the system of massless fermions. In the present paper weuse the Wigner--Weyl formalism to demonstrate that in accordance with thedecoupling property of heavy fermions the corresponding anomalous conductivityvanishes in the large-mass limit with $m^2 \gg |e {\bf B}|$ and $m \gg |\nabla\tau|$.

Scale Magnetic Effect in Quantum Electrodynamics and the Wigner-Weyl Formalism