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

• Main Author: Mikael Chala, Guilherme Guedes, Maria Ramos, Jose Santiago
• Format: Article
• Language: English
• Published: SciPost 2021-09-01
• Series: SciPost Physics
• Online Access: https://scipost.org/SciPostPhys.11.3.065

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.