On the Renormalization Group in EFTs: On-Shell Bases, Ambiguities, and Divergences

TL;DR

This paper clarifies the origin of unphysical divergences in two-loop RG calculations within EFTs, showing that including non-minimal source terms resolves these issues and clarifies the physical RG flow.

Contribution

It demonstrates the necessity of including non-minimal source terms for consistent on-shell RG calculations and analyzes the geometric structure of coupling space.

Findings

Inclusion of missing source terms removes unphysical divergences.

Remaining ambiguities are related to flavor rotations and are unphysical.

RG functions become finite after proper source term inclusion.

Abstract

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.