Chiral properties of the nucleon interpolating current and $\theta$-dependent observables

TL;DR

This paper analyzes the chiral transformation properties of nucleon interpolating currents, highlighting the importance of specific linear combinations for physical consistency in $ heta$-dependent observables like electric dipole moments.

Contribution

It identifies the covariant combinations of nucleon currents under $U(1)_A$ symmetry and demonstrates their impact on $ heta$-dependent calculations, correcting potential unphysical results in previous approaches.

Findings

Only specific linear combinations of currents transform covariantly.

Incorrect current choices can lead to unphysical $ heta$-dependent results.

Calculated ratios of neutron and proton EDMs to magnetic moments are consistent and physically meaningful.

Abstract

We revisit the chiral properties of nucleon interpolating currents, and show that of the two leading order currents $j_1$ and $j_2$, only two linear combinations $j_1\pm j_2$ transform covariantly under the anomalous $U(1)_A$ symmetry. As a result, calculations of quantities which vanish by symmetry in the chiral limit may produce unphysical results if carried out with different linear combinations of the currents. This includes observables such as electric dipole moments, induced by the QCD parameter $\theta$, and the $\theta$-dependence of the nucleon mass. For completeness, we also exhibit the leading order results for nucleon electric dipole moments ($d_{n,p}$) induced by $\theta$, and the nucleon magnetic moments ($\mu_{n,p}$), when calculated using QCD sum rules for both the covariant choices of the nucleon interpolating current. The results in each channel, conveniently expressed as the ratios, $d_{n,p}/\mu_{n,p}$, are numerically consistent, and reflect the required physical dependence on $\theta$.