Nucleon tensor charges and electric dipole moments

A symmetry-preserving Dyson-Schwinger equation treatment of a vector-vector contact interaction is used to compute dressed-quark-core contributions to the nucleon $σ$-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 $σ$-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, $δ_T u$, $δ_T d$, the ratio $δ_T d/δ_T u$ is 18% larger than anticipated from simple quark models. Of particular note, the size of $δ_T u$ is a sensitive measure of the strength of dynamical chiral symmetry breaking; and $δ_T d$ measures the amount of axial-vector diquark correlation within the proton, vanishing if such correlations are absent.

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