I have been trying to understand renormalization for a few days. I have consulted many sources and physics.stackexhange posts but I have unresolved issues, so I am hoping someone can help me!
I think I properly understand RG group flow, and how integrating out higher modes whilst keeping low energy physics constant leads to flows in coupling constants depending on the momentum cut-off. What I am struggling to understand, is exactly how this relates to the perturbative algorithm employed in getting rid of infinities in QFT.
It appears that the modern understanding of effective field theories is that a momentum cut-off is perfectly valid. For example, in the article by G. Peter Lepage at arXiv: hep-ph/0506330, he notes that one can simply leave the cut-off as an explicit parameter and compute physical quantities using this cut-off. Once the coupling constants have been tuned so that the theory agrees with some experimental measurements one obtains a predictive theory with an explicit cut-off.
However, in Chapter 5 of my lecture notes, Prof. Skinner employs a perturbative calculation where he redefines couplings constants by shifting them by an amount dependent on the cut-off in order to get rid of the cut-off dependence in an amplitude calculation. This idea and process seems at odds with the understanding outline in my previous paragraph. What is the resolution?