One-loop matching of the type-II seesaw model onto the Standard Model effective field theory

Abstract

In this paper, we continue to construct the low-energy effective field theories (EFTs) of the canonical seesaw models, which are natural extensions of the Standard Model (SM) to accommodate tiny but nonzero neutrino masses. Different from three right-handed neutrino singlets in the type-I seesaw model, the Higgs triplet in the type-II seesaw model participates directly in the electroweak gauge interactions, rendering the EFT construction more challenging. By integrating out the heavy Higgs triplet in the functional-integral formalism, we carry out a complete one-loop matching of the type-II seesaw model onto the so-called Standard Model Effective Field Theory (SMEFT). It turns out that 41 dimension-six operators (barring flavor structures and Hermitian conjugates) in the Warsaw basis of the SMEFT can be obtained, covering all those 31 dimension-six operators in the case of type-I seesaw model. The Wilson coefficients for 41 dimension-six operators are computed up to mathcal{O}left({M}_{Delta }^{-2}right) with M∆ being the mass scale of the Higgs triplet. Moreover, the branching ratios of rare radiative decays of charged leptons {l}_{alpha}^{-}to {l}_{beta}^{-}+gamma are calculated in the EFT and compared with that in the full theory in order to demonstrate the practical application and the correctness of our EFT construction.