  In this paper, we accomplish the complete one-loop matching of the type-I
seesaw model onto the Standard Model Effective Field Theory (SMEFT), by
integrating out three heavy Majorana neutrinos with the functional approach. It
turns out that only 31 dimension-six operators (barring flavor structures and
Hermitian conjugates) in the Warsaw basis of the SMEFT can be obtained, and
most of them appear at the one-loop level. The Wilson coefficients of these 31
dimension-six operators are computed up to $\mathcal{O}\left( M^{-2}\right)$
with $M$ being the mass scale of heavy Majorana neutrinos. As the effects of
heavy Majorana neutrinos are encoded in the Wilson coefficients of these
higher-dimensional operators, a complete one-loop matching is useful to explore
the low-energy phenomenological consequences of the type-I seesaw model. In
addition, the threshold corrections to the couplings in the Standard Model and
to the coefficient of the dimension-five operator are also discussed.
