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We propose a new method to calculate electric dipole moments induced by thestrong QCD $\theta$-term. The method is based on the gradient flow for gaugefields and is free from renormalization ambiguities. We test our method bycomputing the nucleon electric dipole moments in pure Yang-Mills theory atseveral lattice spacings, enabling a first-of-its-kind continuum extrapolation.The method is rather general and can be applied for any quantity computed in a$\theta$ vacuum. This first application of the gradient flow has beensuccessful and demonstrates proof-of-principle, thereby providing a novelmethod to obtain precise results for nucleon and light nuclear electric dipolemoments.

The nucleon electric dipole moment with the gradient flow: the $\theta$-term contribution