Nonperturbative Renormalization of the Quark Chromoelectric Dipole Moment with the Gradient Flow:Power Divergences

The CP-violating quark chromoelectric dipole moment (qCEDM) operator, contributing to the electric dipole moment (EDM), mixes under renormalization and particularly on the lattice with the pseudoscalar density. The mixing coefficient is power-divergent with the inverse lattice spacing squared, $1/a^2$, regardless of the lattice action used. We use the gradient flow to define a multiplicatively renormalized qCEDM operator and study its behavior at small flow time. We determine nonperturbatively the linearly divergent coefficient with the flow time, $1/t$, up to subleading logarithmic corrections, and compare it with the 1-loop perturbative expansion in the bare and renormalized strong coupling. We also discuss the O($a$) improvement of the qCEDM defined at positive flow time.