We evaluate the neutron electric dipole moment $|{\overrightarrow{d}}_N|$ using lattice QCD techniques. The gauge configurations analyzed are produced by the European Twisted Mass Collaboration using $N_f=2+1+1$ twisted mass fermions at one value of the lattice spacing of $a\simeq 0.082\mathrm{fm}$ and a light quark mass corresponding to $m_{\pi }\simeq 373\mathrm{MeV}$. Our approach to extract the neutron electric dipole moment is based on the calculation of the $CP$-odd electromagnetic form factor $F_3(Q^2)$ for small values of the vacuum angle $\theta$ in the limit of zero Euclidean momentum transfer $Q^2$. The limit $Q^2\to 0$ is realized either by adopting a parametrization of the momentum dependence of $F_3(Q^2)$ and performing a fit or by employing new position space methods, which involve the elimination of the kinematical momentum factor in front of $F_3(Q^2)$. The computation in the presence of a $CP$-violating term requires the evaluation of the topological charge $\mathcal{Q}$. This is computed by applying the cooling technique and the gradient flow with three different actions, namely the Wilson, the Symanzik tree-level improved and the Iwasaki action. We demonstrate that cooling and gradient flow give equivalent results for the neutron electric dipole moment. Our analysis yields a value of $|{\overrightarrow{d}}_N|=0.045(6)(1)\overline{\theta }e·\mathrm{fm}$ for the ensemble with $m_{\pi }=373\mathrm{MeV}$ considered.

• Received 27 October 2015

DOI:https://doi.org/10.1103/PhysRevD.93.074503