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

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