Lattice calculation of electric dipole moments and form factors of the nucleon

Abstract

We analyze commonly used expressions for computing the nucleon electric dipole form factors (EDFF) F3 and moments (EDM) on a lattice and find that they lead to spurious contributions from the Pauli form factor F2 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 F3. 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.

Neutron Electric Dipole Moment on the Lattice

“…Most previous calculations did not correctly account for this subtlety [31]. The problem can be corrected retroactively, and in Figure 3 we show the resulting reduction in the value reported in recent calculations [26,27]).…”

“…The authors of Ref. [31] show that correcting for this omission reduces the value of an already hard to measure F 3 by about a factor of ten. Thus, all previous estimates of the contribution of the Θ-term and the cEDM based on evaluating F 3 need to be revised.…”

“…Unfortunately, as pointed out in Ref. [31], all calculations based on the F 3 extraction prior to their work, starting with the 2005 work in Ref. [23], used the second approach but did not carry out the rotation defined in Eq.…”

“…Further discussion of the mixing between F 2 and F 3 when parity is violated can be found in Ref. [31]. [31,33].…”

“…As noted in Ref. [31], some assumptions are made to calculate the corrected F 3 numbers as some of the original papers do not contain full information needed for the parity induced rotation Eq. (14), so the F 3 results presented in this plot may not be precise.…”