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

TL;DR

This paper computes the one-loop renormalisation group evolution of bosonic operators in the Standard Model effective field theory up to dimension eight, revealing insights into quantum corrections and the validity of positivity bounds.

Contribution

It extends previous work by including contributions from dimension-eight operators and analyzes their impact on renormalisation and positivity bounds.

Findings

Renormalisation of loop-induced interactions by tree-level terms

Validation of positivity bounds on operators inducing anomalous gauge couplings

Completion of the one-loop RG running analysis up to dimension eight

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.