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

Abstract

We compute the one-loop renormalisation group running of the bosonic Standard Model effective operators to order v^4/\Lambda^4v4/Λ4, with v\sim 246v∼246 GeV being the electroweak scale and \LambdaΛ 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 SS and UU 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.

Standard Model EFTs via on-shell methods

“…The first systematic and complete computation of the one-loop anomalous dimension matrix for dimension-six operators in the SMEFT has been carried out in [94][95][96]. So far, the study of the anomalous dimension of SMEFT interactions has been completed only partially in the literature for operators up to dimension 8 [97][98][99][100][101][102][103]. In this paper, we present the general on-shell set-up which will allow us to fully compute the one-loop anomalous dimension matrix for all the operators in the SMEFT up to mass dimension 8.…”

“…In the present work, we compute the anomalous dimension matrix to linear order in the Wilson coefficients, i.e. we ignore the mixing between dimension-6 and dimension-8 operators, which are however partially known in the literature [103].…”

Positivity bounds in the Standard Model effective field theory beyond tree level

“…because there are no Feynman diagrams, as it is the case in several examples shown in Ref. [24]). Then, provided that c…”

“…can have either sign, γ 12 must be necessarily zero, or else c 8 could be negative for appropriate values of those terms. It would be worth exploring this avenue for understanding the surprising non-renormalisation of some dimension-eight bosonic operators [24], resulting from the exact cancellation of physical and redundant counterterms.…”

“…(2) tree [24], and given that λ can be always made zero by just tuning the renormalisable Lagrangian, the bound above is completely general. Moreover, using the exact same reasoning one concludes that this inequality is valid even when including fermionic dimension-six operators, the relevant of which are:…”