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  • $\begingroup$ Thank you. I have two followup questions. Could we use these RG classifications to determine whether a term needs to be renormalized or not? For example, with $\phi^4$ in three dimensions we need counter-terms for $\phi^0$ and $\phi^2$, but not for $\phi^4$. Would we be able to predict this without doing any perturbative calculations and just from the RG analysis? Second, does the argument you give also imply that no relevant or marginal terms can appear in the RG flow if none are present in the original (effective) Lagrangian (i.e. only irrelevant terms can appear)? $\endgroup$ Commented 2 hours ago
  • $\begingroup$ The circle with a line going through it has two 3d momenta to integrate and three quadratic propagators. So that is 6 powers is the numerator and another 6 in the denominator leading to 0 in total which is a logarithmic divergence. Do you consider this power counting to be a perturbative calculation? My way of predicting would go along those lines since I'm not sure if there's an easy rule. $\endgroup$ Commented 2 hours ago
  • $\begingroup$ Whether marginal and relevant operators appear along the flow is a question of scheme. Often, there will be papers starting off with a massless scalar in the UV and then saying mass is never generated. But that is just because they are using the MS-bar scheme. With chiral fermions however, the massless limit is protected by symmetry. $\endgroup$ Commented 2 hours ago