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 $M_{\Delta }^{}$ 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.

37 pages, 3 figures, the version accepted for publication in JHEP; A Mathematica Notebook containing all results for Wilson coefficients is attached in the ancillary files

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