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

TL;DR

This paper calculates the neutron electric dipole moment using lattice QCD with twisted mass fermions, employing novel position space methods and topological charge evaluations to improve accuracy.

Contribution

It introduces new position space techniques and compares cooling and gradient flow methods for evaluating the neutron EDM in lattice QCD.

Findings

Neutron EDM value: 0.045(6)(1) e·fm for m_pi=373 MeV

Cooling and gradient flow yield equivalent results

Methodology applicable at small Q^2 and non-zero theta

Abstract

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 $F_3(Q^2)$. The computation in the presence of a $CP$-violating term requires the evaluation of the topological charge ${\cal Q}$. 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 $\vert \vec{d}_N\vert=0.045(6)(1)\ \bar{\theta} \ e \cdot {\rm fm}$ for the ensemble with $m_\pi=373$ MeV considered.