Since Wilson work in the 70s, the renormalization technique in QFT is physically justified with the concept of scale dependence(scale anomaly) of the parameters. This apparently is akin to a universal version of the characteristic length usually applied to specific physical systems to define their scale. Can anybody explain how is this scale dependence introduced(independently of the specific procedure:perturbative cutoff, dimensional, lattice...)? Where does it come from? Does the Haag's theorem imply that this scale dependence technique is not even related to the QFT lagrangian?