# On Lattice Calculation of Electric Dipole Moments and Form Factors of the Nucleon

## TL;DR

This paper identifies and corrects a flaw in lattice QCD calculations of nucleon electric dipole form factors, leading to more accurate estimates of the nucleon EDM that align better with phenomenological expectations.

## Contribution

The authors derive a corrected expression for nucleon EDFF calculations on the lattice, improving the accuracy of EDM estimates in lattice QCD simulations.

## Key findings

- Corrected the expression for nucleon EDFF on the lattice.
- Revised lattice results show reduced or zero EDM, aligning better with phenomenology.
- Validated the correction using chirally symmetric domain wall fermions.

## Abstract

We analyze commonly used expressions for computing the nucleon electric dipole form factors (EDFF) $F_3$ and moments (EDM) on a lattice and find that they lead to spurious contributions from the Pauli form factor $F_2$ due to inadequate definition of these form factors when parity mixing of lattice nucleon fields is involved. Using chirally symmetric domain wall fermions, we calculate the proton and the neutron EDFF induced by the CP-violating quark chromo-EDM interaction using the corrected expression. In addition, we calculate the electric dipole moment of the neutron using background electric field that respects time translation invariance and boundary conditions, and find that it decidedly agrees with the new formula but not the old formula for $F_3$. Finally, we analyze some selected lattice results for the nucleon EDM and observe that after the correction is applied, they either agree with zero or are substantially reduced in magnitude, thus reconciling their difference from phenomenological estimates of the nucleon EDM.