Consider some correlation function computed at some renormalization scale $\mu_0$ in an asymptotically free theory $$ \langle M(z; \mu_o) \rangle. $$ From what I understand of renormalization-group evolution, we can only study how $\langle M(z; \mu_o) \rangle$ changes from $\mu_o \rightarrow \mu_f; \mu_f < \mu_o$. This is because, from a Wilsonion RG point of view, when we change from one renormalization scale to another, we are inherently removing degrees of freedom (it does not make sense to make predictions about high-resolution behavior from a low-resolution image).
However, if we restrict ourselves to only considering an asymptotically free theory, the UV limit of the the theory is trivially known.
Therefore, does is it all right to flow from the IR to the UV?
