Renormalisation of SMEFT bosonic interactions up to dimension eight by LNV operators

Abstract

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} (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.