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

TL;DR

This paper studies the renormalisation group evolution of bosonic operators in SMEFT influenced by lepton number violating operators, deriving constraints on Wilson coefficients and analyzing implications for seesaw models and electroweak parameters.

Contribution

It provides the first 1-loop renormalisation group analysis of bosonic SMEFT operators up to dimension eight including LNV effects and derives new sign constraints on Wilson coefficients.

Findings

Derived sign constraints on LNV Wilson coefficients using positivity bounds.

Analyzed the impact of T-parameter bounds on LNV operators.

Connected SMEFT LNV effects to seesaw model matching conditions.

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.