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

TL;DR

This paper introduces a novel, renormalization-free method using gradient flow to calculate nucleon electric dipole moments induced by the QCD $ heta$-term, enabling more precise and continuum-extrapolated results.

Contribution

The paper presents a new gradient flow-based approach for computing electric dipole moments in a $ heta$ vacuum, avoiding renormalization ambiguities and applicable to various quantities.

Findings

Successful computation of nucleon EDMs in pure Yang-Mills theory.

First continuum extrapolation of nucleon EDMs with this method.

Proof-of-principle demonstration of the gradient flow approach.

Abstract

We propose a new method to calculate electric dipole moments induced by the strong QCD $\theta$-term. The method is based on the gradient flow for gauge fields and is free from renormalization ambiguities. We test our method by computing the nucleon electric dipole moments in pure Yang-Mills theory at several 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 been successful and demonstrates proof-of-principle, thereby providing a novel method to obtain precise results for nucleon and light nuclear electric dipole moments.