We present a basis of dimension-eight Green’s functions involving Standard Model (SM) bosonic fields, consisting of 86 new operators. Rather than using algebraic identities and integration by parts, we prove the independence of these interactions in momentum space, including discussion on evanescent bosonic operators. Our results pave the way for renormalising the SM effective field theory (SMEFT), as well as for performing matching of ultraviolet models onto the SMEFT, to higher order. To demonstrate the potential of our construction, we have implemented our basis in matchmakereft and used it to integrate out a heavy singlet scalar and a heavy quadruplet scalar up to one loop. We provide the corresponding dimension-eight Wilson coefficients. Likewise, we show how our results can be easily used to simplify cumbersome redundant Lagrangians arising, for example, from integrating out heavy fields using the path-integral approach to matching.
We calculate the renormalisation group running of the bosonic Standard Model (SM) effective operators at one loop and to order $$v^4/\Lambda ^4$$ v 4 / Λ 4 , with $$v\sim 246$$ v ∼ 246 GeV being the electroweak scale and $$\Lambda$$ Λ 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 Chala et al. (SciPost Phys 11:065, 2021). 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.
We calculate the renormalisation group running of the bosonic Standard Model (SM) effective operators at one loop and to order v 4 /Λ 4 , with v ∼ 246 GeV being the electroweak scale and Λ 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 Ref. [1], 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 treelevel generated terms and, more importantly, the validity of positivity bounds on different operators inducing anomalous gauge quartic couplings.
We present the renormalisation group running of the bosonic operators of the Standard Model effective field theory (SMEFT) by the Lepton Number Violating operators (LNVs) at 1-loop order up to $$ \mathcal{O} $$ O (v4/Λ4), with v ∼ 246 GeV as the electroweak scale and Λ as the SMEFT cut-off. Using these relations with the positivity bounds on Wilson coefficients of ϕ4D4 class, we derive sign constraints on the Wilson coefficients of LNV operators, for models where ϕ4D4 operators do not appear at tree-level. We inspect these constraints for the LNV Wilson coefficients generated from matching the Type-I and III seesaw models to SMEFT up to dimension seven at tree-level. We also exhibit the unique bounds induced by the T-parameter on LNVs.
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