Two-loop renormalization of general bosonic effective field theories

Abstract: The renormalization of higher-dimensional operators in quantum field theory is essential for phenomenological analyses in particle physics, and plays a significant role in the study of critical phenomena. We present a framework for renormalizing general bosonic effective field theories beyond one loop, with arbitrary gauge symmetry and scalar field content. In particular, we calculate the renormalization group equations in such theories up to two loops and dimension six. When specialized to the bosonic sector of the Standard Model effective field theory (SMEFT) using simple replacement rules, our general expressions reproduce recent results from the literature. Due to the broad applicability of effective field theory, our general results can readily be applied to obtain the anomalous dimensions in extensions of the bosonic SMEFT and in a plethora of other theories. We also envision our results to provide useful data on the scaling dimensions of composite operators in conformal field theories without fermions.