Neutron electric dipole moment on the lattice

TL;DR

This study explores two lattice QCD methods to calculate the neutron electric dipole moment induced by the $ heta$ term, demonstrating their feasibility and effectiveness with different fermion actions.

Contribution

It introduces and tests two novel lattice QCD approaches for computing the neutron EDM related to the $ heta$ term, including a direct energy difference method.

Findings

Both methods yield good signals for the neutron EDM.

The second method performs well with different fermion formulations.

Feasibility of lattice calculations for neutron EDM is demonstrated.

Abstract

We carry out a feasibility study toward a lattice QCD calculation of the neutron electric dipole moment (NEDM) in the presence of the $\theta$ term using two different approaches. In the first method, we calculate the CP-odd electromagnetic form factor $F_3$, which becomes the NEDM in the zero momentum transfer limit. At the first order in $\theta$, we derive a formula connecting the lattice three-point function to the CP-odd electromagnetic form factor. In the second method we directly extract the NEDM from the energy difference between spin-up and spin-down neutron states in the presence of a constant electric field, without expanding a small but non-zero $\theta$. We test both approaches numerically, employing the domain-wall quark action with the RG improved gauge action in quenched QCD at $a^{-1}\simeq 2$ GeV on a $16^3\times 32\times 16$ lattice, and further applying the second method to the clover quark action at a similar lattice spacing and nucleon mass. We obtain good signals from both approaches. In particular the second method works well with both fermion formulations.