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

Abstract

We calculate the renormalisation group running of the bosonic Standard Model (SM) effective operators at one loop and to order $v^4/{\Lambda }^4$, with $v\sim 246$ GeV being the electroweak scale and $\Lambda$ the unknown new physics threshold. We focus on contributions driven by one dimension-eight term and SM couplings, thus extending (and completing) the effort initiated in arXiv:2106.05291, in which quantum corrections from pairs of dimension-six interactions were considered. We highlight some interesting consequences, including the renormalisation of loop-induced interactions by tree-level generated terms and, more importantly, the validity of positivity bounds on different operators inducing anomalous gauge quartic couplings.

Comments: 21 pages, 5 tables, 2 figures, minor typos edited in Table 2, Github file updated. Further corrections will be only updated in Github