Neutron electric dipole moment using $N_f{=}2{+}1{+}1$ twisted mass fermions

Understand

We evaluate the neutron electric dipole moment $\vert \vec{d}_N\vert$ 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 $a \simeq 0.082 \ {\rm fm}$ and a light quark mass corresponding to $m_{\pi} \simeq 373 \ {\rm MeV}$.
• 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 parameterization 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 $F_3(Q^2)$.