Neutron electric dipole moment using \(N_f{=}2{+}1{+}1\) twisted mass fermions

• Published in: arXiv.org 2016-03
• Main Authors: Alexandrou, C, Athenodorou, A, Constantinou, M, Hadjiyiannakou, K, Jansen, K, Koutsou, G, Ottnad, K, Petschlies, M
• Format: Article
• Language: English
• Subjects: Cooling; Dependence; Dipole moments; Electric dipoles; Fermions; Form factors; Gradient flow; Momentum transfer; Parameterization; Quantum chromodynamics
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1510.05823

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.