  In this paper, we systematically study the algebraic structure of the ring of
the flavor invariants and the sources of CP violation in the seesaw effective
field theory (SEFT), which is obtained by integrating out heavy Majorana
neutrinos in the type-I seesaw model at the tree level and thus includes the
dimension-five Weinberg operator and one dimension-six operator. For the first
time, we calculate the Hilbert series and explicitly construct all the primary
flavor invariants in the SEFT. We show that all the physical parameters can be
extracted using the primary invariants and any CP-violating observable can be
expressed as the linear combination of CP-odd flavor invariants. The
calculation of the Hilbert series shows that there is an equal number of
primary flavor invariants in the SEFT and in the full seesaw model, which
reveals the intimate connection between the flavor space of the SEFT and that
of its ultraviolet theory. A proper matching procedure of the flavor invariants
is accomplished between the SEFT and the full seesaw model, through which one
can establish a direct link between the CP asymmetries in leptogenesis and
those in low-energy neutrino oscillations.
