Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I

Abstract

We compute the one-loop renormalisation group running of the bosonic Standard Model effective operators to order $v^4/{\Lambda }^4$, with $v\sim 246$ GeV being the electroweak scale and $\Lambda$ the unknown new physics threshold. We concentrate on the effects triggered by pairs of the leading dimension-six interactions, namely those that can arise at tree level in weakly-coupled ultraviolet completions of the Standard Model. We highlight some interesting consequences, including the interplay between positivity bounds and the form of the anomalous dimensions; the non renormalisation of the $S$ and $U$ parameters; or the importance of radiative corrections to the Higgs potential for the electroweak phase transition. As a byproduct of this work, we provide a complete Green basis of operators involving only the Higgs and derivatives at dimension-eight, comprising 13 redundant interactions.

Comments: 30 pages, 1 figure, 5 tables. v3: Minor corrections. All RGEs obtained in the paper can be found in this repository: https://github.com/SMEFT-Dimension8-RGEs/. Only the notebook will be updated if further typos are found