Heavy-mass power-counting theorem and a proof of decoupling in the momentum-subtraction scheme

We establish a heavy-mass power-counting prescription describing the effects of virtual heavy particles at low energy in an arbitrary Feynman diagram using momentum subtraction to remove divergences from its corresponding Feynman integral. Furthermore, we show that in the absence of heavy-mass-dependent vertices, the virtual heavy-mass effects are suppressed in the low-energy regime by an inverse power of the heavy mass given by our power-counting prescription. As a result, we obtain a simple proof of the Appelquist-Carazzone decoupling theorem.