The electric dipole moment of the deuteron from the QCD $\theta$-term

TL;DR

This paper calculates the deuteron electric dipole moment induced by the QCD $ heta$-term using effective field theory, providing a precise estimate and identifying dominant uncertainties.

Contribution

It offers the first next-to-next-to-leading order calculation of the deuteron EDM from the QCD $ heta$-term, including detailed uncertainty analysis.

Findings

Deuteron EDM difference: (-5.4 ± 3.9) × 10^{-4} * $ar{ heta}$ e fm.

Main uncertainty from CP- and isospin-violating $ ext{πNN}$ coupling.

Results inform constraints on QCD $ heta$-term from EDM measurements.

Abstract

The two-nucleon contributions to the electric dipole moment (EDM) of the deuteron, induced by the QCD $\theta$-term, are calculated in the framework of effective field theory up-to-and-including next-to-next-to-leading order. In particular we find for the difference of the deuteron EDM and the sum of proton and neutron EDM induced by the QCD $\theta$-term a value of $(-5.4\pm 3.9)\,\bar\theta\times 10^{-4}\, e$ fm. The by far dominant uncertainty comes from the CP- and isospin-violating $\pi NN$ coupling constant.