The Electric Dipole Form Factor of the Nucleon in Chiral Perturbation Theory to Sub-leading Order

TL;DR

This paper calculates the nucleon's electric dipole form factor using chiral perturbation theory, revealing non-analytic contributions from the pion cloud and implications for the deuteron electric dipole moment.

Contribution

It provides the first calculation of the isoscalar EDFF's non-analytic contribution at sub-leading order in chiral perturbation theory, including effects from the QCD theta term.

Findings

Lower bound on deuteron EDM: |d_d| > 1.4×10^(-4) θ e fm

Momentum dependence linked to pion-nucleon coupling

Form factor radius scale set by pion mass

Abstract

The electric dipole form factor (EDFF) of the nucleon stemming from the QCD theta term and from the quark color-electric dipole moments is calculated in chiral perturbation theory to sub-leading order. This is the lowest order in which the isoscalar EDFF receives a calculable, non-analytic contribution from the pion cloud. In the case of the theta term, the expected lower bound on the deuteron electric dipole moment is |d_d| > 1.4 10^(-4) \theta e fm. The momentum dependence of the isovector EDFF is proportional to a non-derivative time-reversal-violating pion-nucleon coupling, and the scale for momentum variation ---appearing, in particular, in the radius of the form factor--- is the pion mass.