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 by the Lepton Number Violating operators (LNVs) at 1-loop order up to $\mathcal{O}(v^4/\Lambda^4)$, with $v \sim 246$ GeV as the electroweak scale and $\Lambda$ as the SMEFT cut-off. Using these relations with the positivity bounds on Wilson coefficients of $\phi^4 D^4$ class, we derive sign-constraints on the Wilson coefficients of LNV operators for models where $\phi^4 D^4$ 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.