Nucleon tensor charges and electric dipole moments

Abstract

A symmetry-preserving Dyson-Schwinger equation treatment of a vector-vector contact interaction is used to compute dressed-quark-core contributions to the nucleon $\sigma$-term and tensor charges. The latter enable one to directly determine the effect of dressed-quark electric dipole moments (EDMs) on neutron and proton EDMs. The presence of strong scalar and axial-vector diquark correlations within ground-state baryons is a prediction of this approach. These correlations are active participants in all scattering events and thereby modify the contribution of the singly-represented valence-quark relative to that of the doubly-represented quark. Regarding the proton $\sigma$-term and that part of the proton mass which owes to explicit chiral symmetry breaking, with a realistic $d$-$u$ mass splitting the singly-represented $d$-quark contributes 37% more than the doubly-represented $u$-quark; and in connection with the proton's tensor charges, $\delta_T u$, $\delta_T d$, the ratio $\delta_T d/\delta_T u$ is 18% larger than anticipated from simple quark models. Of particular note, the size of $\delta_T u$ is a sensitive measure of the strength of dynamical chiral symmetry breaking; and $\delta_T d$ measures the amount of axial-vector diquark correlation within the proton, vanishing if such correlations are absent.