  We match the seesaw model for generating neutrino masses onto the Standard
Model Effective Field Theory (SMEFT). We perform this matching at tree level up
to dimension seven in the operator expansion. We explain how some of the
perturbations of the neutrino mass matrix due to operators of mass dimension
greater than five are tied to integrating out the heavy Majorana mass
eigenstates in sequence. We demonstrate that the low energy limit of seesaw
models are well described by the SMEFT, particularly when constructed using a
flavour space expansion. Flavour space expansions of seesaw models are of
interest as the coupling of the heavy states to the Standard Model, that are
integrated out to generate neutrino masses, are through flavour space vectors
$\in \mathbb{C}^3$. We point out that neutrino phenomenology can be
systematically developed as a perturbation around the unknown eigenvectors
diagonalizing the charged lepton mass matrix using the fact that these
eigenvectors also form a basis of $\mathbb{C}^3$. This point holds in seesaw
models and can also be applied to other models of neutrino mass generation to
develop systematic expansions. We develop the algebra for this flavour space
and discuss some phenomenology to illustrate this approach.
