In this proceedings, we lay the foundation for computing the contribution of quark chromo-electric dipole moment (qCEDM) operator to the nucleon electric dipole moment.
By applying the gradient flow technique, we can parameterize the renormalization and operator mixing issues associated with the qCEDM operator on the lattice.
As the nucleon mixing angle $\alpha_N$ is a key component for determining the neutron and proton electric dipole moments induced by the qCEDM operator, we present the formalism and preliminary results for $\alpha_N$ with respect to the gradient flow time $t_f$.
The results are computed on $N_f=2+1$ Wilson-clover lattices provided by PACS-CS~\cite{Ishikawa:2007nn}.
The 3 ensembles have lattice spacing values of $a=\lbrace 0.1095,\,0.0936,\,0.0684\rbrace$~fm, whilst keeping a similar $m_{\pi}\approx701$~MeV, and a fixed box size of $L\approx1.9$~fm.