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

TL;DR

This paper calculates the one-loop renormalisation group evolution of bosonic operators in the Standard Model effective field theory up to dimension eight, revealing key effects on electroweak parameters and phase transition dynamics.

Contribution

It provides the first detailed computation of dimension-eight bosonic operator running, including a complete operator basis and insights into electroweak and Higgs sector implications.

Findings

Non-renormalisation of S and U parameters

Interplay between positivity bounds and anomalous dimensions

Radiative corrections impact electroweak phase transition

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.