One-loop Renormalization Group Equations in Generic Effective Field Theories. Part I: Bosonic Operators

We consider a generic class of effective quantum field theories with arbitrary gauge groups and scalar matter fields. In such theories, we derive the one-loop Renormalization Group Equations (RGEs) for the physical dimension-six operators. The present paper is the first one in a series that is going to cover theories with spin-$\frac{1}{2}$ matter fields, too, including the phenomenologically most relevant SMEFT and LEFT cases. Our present approach provides tools for deriving the yet unknown two-loop RGEs in the SMEFT.