On the renormalization group in EFTs: on-shell bases, flavor ambiguities, and divergences

Recent results for two-loop renormalization group (RG) functions in effective field theories exhibit unphysical divergences when calculated in an on-shell operator basis. We demonstrate that this can be understood to be a result of omitting non-minimal source terms in the renormalized vacuum functional, which are essential to maintaining renormalizability of and describing the RG flow of Green’s functions in an on-shell framework. With the inclusion of the missing source terms, any remaining divergences are ambiguous, generating only unphysical RG flow directed along flavor rotations, and the RG functions are RG-finite. We carefully examine the role of flavor rotations in generating ambiguities in both on- and off-shell RG functions and explore the geometry of a physical coupling space.