Two-loop renormalization of general bosonic effective field theories

TL;DR

This paper develops a comprehensive two-loop renormalization framework for general bosonic effective field theories, enabling precise calculations of renormalization group equations applicable to various models including SMEFT.

Contribution

It introduces a general method for two-loop renormalization of bosonic EFTs with arbitrary gauge symmetry and scalar content, extending previous one-loop results.

Findings

Derived two-loop RG equations up to dimension six.

Reproduced known SMEFT results as special cases.

Provided a versatile framework applicable to multiple 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.