Question

How does the renormalization scale $\mu$ cancel in all finite observables?

Answer 1

⏰⏰ This is done to ensure that the action will have the correct dimensions. Apparently, μ will not affect any observables. ⏰⏰

Answer 2

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I am aware that we do not want to "true" theories to depends on the cut-off Λ→∞Λ→∞ or ϵ=4−d→0ϵ=4−d→0, but this doesn't tell me what will happen with μμ.

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