One-loop Matching of the Type-III Seesaw Model onto the Standard Model Effective Field Theory

TL;DR

This paper performs a detailed one-loop matching of the type-III seesaw model onto the Standard Model Effective Field Theory, identifying operators, calculating Wilson coefficients, and exploring phenomenological implications for collider experiments.

Contribution

It completes the series of one-loop matchings for all canonical seesaw models by deriving the dimension-six operators and their coefficients for the type-III seesaw model.

Findings

Identified 33 dimension-six operators in the Warsaw basis for the type-III seesaw EFT.

Calculated Wilson coefficients for these operators.

Discussed phenomenological implications and observables for collider experiments.

Abstract

In previous works arXiv:2107.12133 and arXiv:2201.05082, we have performed the one-loop matching of both type-I and type-II seesaw models for neutrino masses onto the Standard Model Effective Field Theories (SMEFT). In the present paper, by matching the type-III seesaw model onto the SMEFT at the one-loop level, we complete this series of studies on the construction of low-energy effective field theories (EFTs) for the canonical seesaw models. After integrating out the heavy fermionic triplets in the type-III seesaw model via both functional and diagrammatic approaches, we find 33 dimension-six (dim-6) operators in the Warsaw basis and their Wilson coefficients, while the number of dim-6 operators is 31 (or 41) for the EFT of type-I (or type-II) seesaw model. Furthermore, we calculate the branching ratios of radiative decays of charged leptons in the EFT. Then, the relationship between the beta function of the quartic Higgs coupling $\lambda$ in the full theory and that of $\lambda^{}_{\rm EFT}$ in the EFT is clarified. Finally, we briefly discuss the phenomenological implications of three types of seesaw EFTs and propose working observables that are sensitive to the four-fermion operators, which could be used to distinguish among different seesaw models in collider experiments.