  We define a regularization-independent momentum-subtraction scheme for the
$CP$-odd three-gluon operator at dimension six. This operator appears in
effective field theories for heavy physics beyond the Standard Model,
describing the indirect effect of new sources of $CP$-violation at low
energies. In a hadronic context, it induces permanent electric dipole moments.
The hadronic matrix elements of the three-gluon operator are non-perturbative
objects that should ideally be evaluated with lattice QCD. We define a
non-perturbative renormalization scheme that can be implemented on the lattice
and we compute the scheme transformation to $\overline{\text{MS}}$ at one loop.
Our calculation can be used as an interface to future lattice-QCD calculations
of the matrix elements of the three-gluon operator, in order to obtain
theoretically robust constraints on physics beyond the Standard Model from
measurements of the neutron electric dipole moment.
