Revisiting renormalization schemes in a differential equation approach

We reconsider the choice of renormalization schemes in a differential-equation approach to aid the discussion of the renormalization of the unstable particles and the CKM matrix in the Standard Model. Certain mass dependent schemes do not satisfy these natural differential equations modulo trace anomaly. By the way, the Callan-Symanzik equations were employed to show that both mass dependent and independent schemes realize fermion decoupling in the same way.