One-loop Matching of Scotogenic Model onto Standard Model Effective Field Theory up to Dimension 7

The scotogenic neutrino seesaw model is a minimal extension of the standard model with three $\mathbb{Z}_2$-odd right-handed singlet fermions $N$ and one $\mathbb{Z}_2$-odd Higgs doublet $\eta$ that can accommodate the tiny neutrino mass and provide a dark matter candidate in a unified picture. Due to lack of experimental signatures for electroweak scale new physics, it is appealing to assume these new particles are well above the electroweak scale and take the effective field theory approach to study their effects on low energy observables. In this work we apply the recently developed functional matching formalism to the one-loop matching of the model onto the standard model effective field theory up to dimension seven for the case when all new states $N$ and $\eta$ are heavy to be integrated out. This is a realistic example which has no tree-level matching due to the $\mathbb{Z}_2$ symmetry. Using the matching results, we analyze their phenomenological implications for several physical processes, including the lepton number violating effect, the CDF $W$ mass excess, and the lepton flavor violating decays like $\mu\to e\gamma$ and $\mu\to 3e$.